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Business Decision Making Tutorial Questions Note: Feb’19 Selected questions are taken and/or modified from textbooks indicated in Session Plan

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Business Decision Making Tutorial Questions Note: Feb’19 Selected questions are taken and/or modified from textbooks indicated in Session Plan. Topic 1.1 Q1. In each of these statements, tell whether descriptive or inferential statistics have been used. a. By 2040 at least 3.5 billion people will run short of water (Source: World Future Society). b. In a sample of 100 on-the-job fatalities, 90% of the victims were men. c. Expenditures for the cable industry were $5.66 billion in 1996 (Source: USA TODAY). d. The average stay in a hospital for 2000 patients who had circulatory system problems was 4.7 days. e. Allergy therapy makes bees go away (Source: Prevention). f. Drinking decaffeinated coffee can raise cholesterol levels by 7% (Source: American Heart Association). g. The national average annual medicine expenditure per person is $1052 (Source: The Greensburg Tribune Review). h. Experts say that mortgage rates may soon hit bottom (Source: USA TODAY). Q2. Classify each sample as random, systematic, stratified, or cluster. a. In a large school district, all teachers from two buildings are interviewed to determine whether they believe the students have less homework to do now than in previous years. b. Every seventh customer entering a shopping mall is asked to select her or his favorite store. c. Nursing supervisors are selected using random numbers to determine annual salaries. d. Every 100th hamburger manufactured is checked to determine its fat content. e. Mail carriers of a large city are divided into four groups according to gender (male or female) and according to whether they walk or ride on their routes. Then 10 are selected from each group and interviewed to determine whether they have been bitten by a dog in the last year. 1 Business Decision Making Tutorial Questions Feb’19 Q3. Classify each quantitative variable as discrete or continuous. a. Number of laptops owned by each household. b. Cost of a student’s textbooks in a semester. c. Number of patients registered at a clinic. d. Monthly electricity bill (in dollars) in a factory. e. Lowest temperatures of 30 days. f. Number of books sold in a day. g. Ages of contestants signed up for a marathon. Q4. Classify each variable as qualitative or quantitative (discrete or continuous). a. Nationality of students enrolled in a program. b. Blood pressures of runners in a cross-country run. c. Weights of boxes in a store room. d. Types of automobiles in a shopping center parking lot. e. Distance travelled by employees every day. f. Number of audience attending the football match. g. Actual volume (in ml) of soft drink in each bottle. Q5. Classify each as nominal-level, ordinal-level, interval level, or ratio-level measurement. a. Number of pages in the 25 best-selling mystery novels. b. Rankings of golfers in a tournament (first, second, third place). c. Temperatures of a country. d. Weights of selected cell phones. e. Salaries of the coaches in the National Football League. f. Times required to complete a chess game. g. Ratings of textbooks (poor, fair, good, excellent). h. Number of gallons of petrol used last month. i. Ages of children in a day care center. j. Categories of magazines in a physician’s office (sports, women’s, health, men’s, news). 2 Business Decision Making Tutorial Questions Feb’19 Topic 1.2 Q1. The number of sticks picked up by participants in a game is recorded below. 8 8 6 4 6 5 8 7 7 4 8 6 7 7 8 8 8 7 8 7 9 5 8 8 9 5 9 8 8 9 6 9 7 9 8 6 Develop a frequency distribution and relative frequency distribution for the data. Class 4 5 Frequency Relative Freq Q2. The table below shows the number of points scored by a group of college students playing an online game. 72 71 62 68 69 76 85 76 83 75 59 58 65 74 61 55 73 71 66 76 63 52 64 75 51 81 67 65 76 51 a. Determine the number of classes required to construct a grouped frequency distribution. b. Find a suitable class width. c. Using the initial class indicated in the table, define the remaining class boundaries. d. Construct a grouped frequency distribution and a cumulative frequency distribution with 5 classes for the data as indicated in the table below. e. Construct a histogram and a frequency polygon using frequency distribution. f. Construct an ogive using cumulative frequency distribution. Class Midpoint Frequency Relative Freq Cumulative Frequency Cumulative Relative Frequency 51 – 57 3 Business Decision Making Tutorial Questions Feb’19 Q3. Listed are the weights of the NBA’s top 50 players (in kilograms). Find a suitable class width to construct a grouped frequency distribution and a cumulative frequency distribution with 6 classes. Complete the table below. Analyze the results in terms of peaks, extreme values, etc. 109 100 114 105 151 75 93 114 100 105 114 105 109 102 80 98 111 98 89 109 118 86 105 95 84 95 118 89 123 102 134 105 95 95 92 120 95 111 135 98 107 114 95 109 102 95 118 86 105 118 a. Determine the number of classes required to construct a grouped frequency distribution. b. Find a suitable class width. c. Using the initial class indicated in the table, define the remaining class boundaries. d. Construct a grouped frequency distribution and a cumulative frequency distribution with 6 classes for the data as indicated in the table below. e. Construct a histogram and frequency polygon using frequency distribution. f. Construct an ogive using cumulative frequency distribution. Class Midpoint Frequency Relative Freq Cumulative Frequency Cumulative Relative Frequency 75 and under 90 Q4. Repeat part e and part f of Question 2 and 3 using relative frequency and cumulative relative frequency. NOTE: Grids for graphs are provided at the end of this tutorial. 4 Business Decision Making Tutorial Questions Feb’19 Topic 2 Q1. Six Physics final exam grades are shown below. 65 86 64 76 50 89 a. Find three measures of center discussed (mean, median and mode). b. Find the measures of variation discussed (range, variance and standard deviation). c. Find the interquartile range. [a. 71.67, 70.5, none; b. 39, 219.47, 14.81; c. 64(Q1), 86(Q3), 22] Q2. The sales (in thousands of dollars) for the past 8 months are listed below. 72 82 89 122 107 95 82 100 a. Find three measures of center discussed (mean, median and mode). b. Find the measures of variation discussed (range, variance and standard deviation). c. Find the interquartile range. [a. 93.63, 92, 82; b. 50, 255.13, 15.97; c. 82(Q1), 103.5(Q3), 21.5] Q3. The number of hours undergraduate students spent on revision a day before the statistics exam is as follow. 7 8 8 10 9 4 12 9 11 5 10 3 a. Find three measures of center discussed (mean, median and mode). b. Find the measures of variation discussed (range, variance and standard deviation). c. Find the interquartile range. [a. 8, 8.5, (8, 9, 10); b. 9, 7.82, 2.80; c. 6(Q1), 10(Q3), 4] Q4. Fill in the blank: Based on the empirical rule we can expect about _________ of the values in bellshaped distributions to be within ± one standard deviation of the mean. 5 Business Decision Making Tutorial Questions Feb’19 Topic 3.1 Q1. Classify each statement as an example of classical probability, relative frequency, or subjective probability assessment. a. The probability that a person will watch the 6 o’clock evening news is 0.15. b. The probability of getting at least a Head when 2 coins are tossed is c. The probability that a bus will be in an accident on a specific road is about 6%. d. The probability of getting a diamond when a card is selected at random is e. The probability that a student will get a C or better in a statistics course is about 70%. f. The probability that a new fast-food restaurant will be a success in Chicago is 35%. g. The probability that Team A will win the basketball match next month is 0.70. 3 . 4 13 . 52 Q2. If two dice are rolled once, find the probability of getting these results. a. A sum of 5 b. A sum of 3 or 12 c. Doubles d. A sum less than 4 e. A sum greater than or equal to 10 Q3. A shopping mall has set up a promotion as follows. With any mall purchase of $50 or more, the customer gets to spin the wheel shown here. If a number 1 comes up, the customer wins $10. If the number 2 comes up, the customer wins $5; and if the number 3 or 4 comes up, the customer wins a discount coupon. Find the following probabilities. a. The customer wins $10. b. The customer wins money. c. The customer wins a coupon. 6 Business Decision Making Tutorial Questions Feb’19 Topic 3.2 Q1. There are 6 packets of peanuts, 8 packets of raisins, and 2 packets of chocolate chips. If a packet is selected at random, find the probability that it is a packet of a. raisins b. raisins or chocolate chips c. peanuts or raisins d. not peanuts [0.5; 0.625; 0.875; 0.625] Q2. Andy bought a packet of chocolate candies with 5 flavors. Mint 35% Lime 25% Orange 20% Cherry 10% Strawberry 10% If he randomly picks a candy from the packet, find the probability that he will get a candy a. with mint flavor b. with cherry or lime flavor c. which is neither orange nor strawberry flavor d. with mint and lime flavor [0.35; 0.35; 0.7; 0] Q3. The table below represents the qualifications awarded (in thousands) by a university in a recent academic year by gender. Men Women Bachelor’s Degree 624 818 Master’s Degree 211 301 Doctorate Degree 24 22 Choose an award at random. Find the probability that it is a. a bachelor’s degree b. a doctorate degree and it is awarded to a woman c. a doctorate degree or it is awarded to a woman d. not a master’s degree e. a degree awarded to a man, given that it is a bachelor degree [0.721; 0.011; 0.583; 0.744; 0.433] 7 Business Decision Making Tutorial Questions Q4. Feb’19 In addition to being grouped into four types, human blood is grouped by its Rhesus (Rh) factor. Consider the figures below which show the distributions of these groups for Americans. O Rh+ A B 37% 34% 10% Rh - 6% 6% 2% AB 4% 1% Choose 1 American at random. Find the probability that the person a. is a universal donor, i.e., the person has O negative blood b. has Rh– and type AB c. has type A or Rh+ d. has A+ blood or AB– blood e. has type O blood, given that the person is Rh+ f. has Rh–, given that the person has type B blood [0.06; 0.01; 0.91; 0.35; 0.435; 0.167] Q5. The medal distribution from the 2008 Summer Olympic Games for the top 23 countries is shown below. Gold Silver Bronze United States 36 38 36 Russia 23 21 28 China 51 21 28 Great Britain 19 13 15 173 209 246 Others Choose 1 medal winner at random. Find the probability that the winner a. won the Silver medal. b. was from the Russia. c. was from China and won the Gold medal. d. won a bronze medal or was from Great Britain e. won the gold medal, given that the winner was from the United States. f. was from the United States, given that she or he won a gold medal. g. Are the events “medal winner is from United States” and “gold medal won” mutually exclusive? Explain. [0.316; 0.075; 0.053; 0.402; 0.327; 0.119; No] 8 Business Decision Making Tutorial Questions Feb’19 Topic 4 Q1. A company found that 70% of the customers who used the new coffee maker were satisfied with it. Last weekend, 10 customers bought this coffee maker. Find the probability that a. all of them will be satisfied. b. exactly 5 of them will be satisfied. c. more than 8 of them will be satisfied. d. Find the mean and standard deviation of the number of customers who are satisfied. [0.0282; 0.1029; 0.1493; 7, 1.449] Q2. It is found that 80% of the preschool children like to play jigsaw puzzle. A random sample of 8 preschool children is selected. Find the probability that a. all of them like to play jigsaw puzzle. b. exactly 5 of them like to play jigsaw puzzle. c. at least 6 of them like to play jigsaw puzzled. d. Find the mean and standard deviation of the number of children who like to play jigsaw puzzle. [0.1678; 0.1468; 0.7969; 6.4, 1.131] Q3. A mid-term test consists of 20 questions with 5 choices each. Supposed a student guessed all questions, find the probability that he/she will a. score exactly 50% of the mark. b. score 6 out of 20. c. Find the mean and standard deviation of the number of questions guessed correctly. [0.0020; 0.1091; 4, 1.789] Q4. A fair coin is tossed for 16 times. The number of tails is observed. Find the probability of getting a. exactly 5 tails. b. at least 2 tails. c. Find the mean and standard deviation of the number of tails observed. [0.0667; 0.9998; 8, 2] 9 Business Decision Making Tutorial Questions Feb’19 Topic 5.1 Q1. Find the probabilities below using the standard normal distribution. a. P(z > 1.38) b. P(z < -0.73) c. P(0 < z < 2.15) d. P(-1.93 < z < 0) e. P(-3.12 < z < 0.27) f. P(1.06 < z < 3.09) g. P(z < 2.48) [a. 0.0838 b. 0.2327 c. 0.4842 d. 0.4732 e. 0.6063 f. 0.1436 g. 0.9934] Q2. Find the z value that corresponds to the given area. a. b. c. 10 Business Decision Making Tutorial Questions Feb’19 Q3. The assembly times for a type of toy train follow a normal distribution with a mean of 40 minutes and a standard deviation of 5 minutes. Find the probability that a randomly selected assembly worker will finish assembling the toy train in a. less than 34 minutes b. between 43 and 46 minutes c. more than 50 minutes [0.1151; 0.1592; 0.0228] Q4. A speed limit of 50 km per hour was posted near Exit A of a highway due to some construction work. Assume that the speeds of the vehicles passing through this area are normally distributed with a mean of 55 km per hour and a standard deviation of 6 km per hour. Find the probability that a randomly selected vehicle will be driving at a speed of a. less than 50 km per hour b. between 45 and 55 km per hour c. more than 80 km per hour [0.2033; 0.4525; 0.0001] Q5. A manufacturing company has recently come out with a new type of 2-meter cable wire. The lengths of this cable must be within 1.7 to 2.3 meters. Otherwise, it will be rejected. It is assumed that the length of wire follows a normal distribution with a mean of 2 meters and a standard deviation of 0.15 meters. Find the probability that a randomly selected wire manufactured is a. less than 1.7 meters b. between 1.7 and 2.3 meters c. The company manufactured 1,000 such wires last week, how many of these wires will be rejected? [0.0228; 0.9544; ~46] 11 Business Decision Making Tutorial Questions Feb’19 Topic 5.2 Q1. A retail manager is concerned about the waiting time of his customers at the check-out counter. He estimated that the customers currently have to wait for an average of 10 minutes at the counter, with a standard deviation of 3 minutes. The waiting times are assumed to be normally distributed. Find the probability that a random sample of 16 customers will have an average waiting time of a. less than 8 minutes b. between 9 and 11 minutes [0.0038; 0.8164] Q2. Thomas, the manager of a food manufacturing company, wants to monitor the amount of yoghurt dispensed from a new machine. It is estimated that the average amount dispensed is 152 ml, with a standard deviation of 8 ml. Assumed that the amounts dispensed are normally distributed. The quality control operator randomly sample 40 cups of the yoghurt dispensed. Find the probability that the mean amount will be a. more than 150 ml b. between 149 and 151 ml [0.9429; 0.2059] Q3. The amounts of household utility charges for apartments in an area are assumed to be normally distributed with a mean of $205 and a standard deviation of $30. Find the probability that a random sample of 16 household will have an average utility charges of a. less than $200 b. more than $215 c. between $202 and $210 [0.2514; 0.0918; 0.4040] 12 Business Decision Making Tutorial Questions Feb’19 Topic 6.1 Q1. The owner of a restaurant that serves Japanese food wants to introduce some new dishes. She believes that the amount of money spent per diner will be helpful in her decision making. The standard deviation of the amount spent is known to be $6. The average spending of a random sample of 25 diners is $35. a. Find the best point estimate of the population mean. b. Construct the 95% confidence interval of the population mean amount spent. c. Construct the 90% confidence interval of the population mean amount spent. d. Explain why 95% confidence interval is larger, without further calculation. e. Explain, without further calculation, the change to the confidence interval if the sample size taken is 36. [32.65 < µ < 37.35; 33.02 < µ < 36.98; narrower] Q2. The Human Resource Manager of a manufacturing company wishes to study the absenteeism of production operators. It is known that the standard deviation of the absenteeism is 3 days per year. The attendance records of a random sample of 60 production operators are checked and an average of 8.8 days of absence is observed. a. Find the 99% confidence interval of the population mean number of days of absence. b. Interpret the confidence interval obtained. c. How large a sample is needed to estimate the true mean to within half a day with 99% confidence? [7.80 < µ < 9.80; 240] Q3. A researcher found that the average number of self-study hours spent by 30 college students was 20 per week. The standard deviation of the population was 4 hours per week. a. Construct the 95% confidence interval of the population mean number of hours spent. b. Interpret the confidence interval obtained. c. A researcher wishes to be accurate within 1 hour of the population mean, with 95% confidence. Find the minimum sample size required. [18.6 < µ < 21.4; 62] 13 Business Decision Making Tutorial Questions Feb’19 Topic 6.2 Q4. A process dispenses packets of jelly mix. The weights of the contents of these packets are approximately normally distributed. The quality control officer randomly selected 16 packets and found that the mean weight was 252 grams with a standard deviation of 4.8 grams. a. Develop the 99% confidence interval of the population mean weight for all packets. b. Interpret the confidence interval obtained. c. Is it reasonable to comment that the population mean weight is 260 grams? Justify your answer. [248.5 < µ < 255.5; no] Q5. The time (in minutes) taken by employees in a company to drive to work is assumed to be normally distributed. A random sample of 10 employees surveyed revealed a mean of 35 minutes with a standard deviation of 4 minutes. a. Find the standard error of the mean time taken. b. Construct the 95% confidence interval of the population mean time. c. Explain, without further calculation, the change to the confidence interval if the confidence level is changed to 90%. [1.265; 32.1 < µ < 37.9; narrower] Q6. A recent study of petrol prices was conducted using truck drivers with equivalent years of experience. The fuel consumption of 15 trucks showed a mean of 7.2 kms per litre and a standard deviation of 1.2 kms per litre. Assume that the population is normally distributed. a. Calculate the standard error of the mean fuel consumption. b. Find the 90% confidence interval of the population mean fuel consumption. c. Interpret the confidence interval obtained. d. Explain, without further calculation, the change to the confidence interval if the confidence level is changed to 99%. [0.31; 6.65 < µ < 7.75; wider] 14 Business Decision Making Tutorial Questions Feb’19 Topic 6.3 Q1. Human Resource Manager wants to estimate the proportion of employees who favor the new employee benefit scheme. From a random sample of 350 employees, a total of 256 employees responded that they were in favor of this scheme. a. Develop the 99% confidence interval of the population proportion that favors this new scheme. b. Interpret the confidence interval obtained. c. Find the minimum sample size required if a researcher wishes to be accurate within 5% of the true proportion. [0.67 < p < 0.79; 525] Q2. A random sample of 80 retail companies revealed that 55 of them had obtained a quality certificate within the last one year. a. Calculate the standard error of the sample proportion. b. Develop the 95% confidence interval of the population proportion that has been certified within the last one year. c. Interpret the confidence interval obtained. [0.052; 0.59 < p < 0.79] 15 Business Decision Making Tutorial Questions Feb’19 Topic 7.1 Q1. For each conjecture, state the null and alternative hypotheses. a. The average age of degree students is 24.6 years. b. The average income of retail managers is $62,000. c. The average length of the cable is greater than 25.4 cm. d. The average score of Accounting Test is less than 80. e. The average pulse rate of male marathon runners is less than 70 beats per minute. f. The average cost of a DVD player is $ 79.95. g. The average weight loss for people who exercise 30 minutes per day for 6 weeks is more than 8.2 pounds. Q2. Find the critical value (or values), z, for each of the following cases. a. α = 0.10, two-tailed test b. α = 0.10, left-tailed test c. α = 0.05, right-tailed test d. α = 0.05, two-tailed test e. α = 0.01, left-tailed test f. α = 0.005, right-tailed test [a. ±1.65 b. -1.28 c. 1.65 d. ±1.96 e. -2.33 f. 2.58] Q3. The average production from a product line is 88 units per hour with a population standard deviation of 9 units. Thirty-five observations over a period of 2 weeks revealed a sample mean of 92 units. Can it be concluded at the 0.05 level of significance that the average production has changed? [z = 2.63, CV = ±1.96, reject null] Q4. A company is expecting a shipment of batteries that are known to have a mean lifetime of 60 hours. The incoming quality department will return the whole shipment if it is found that the mean lifetime is significantly lower than 60 hours. A random sample of 64 batteries is tested and the mean is 57.2 hours. The standard deviation of the population is 8 hours. At α = 0.01 should the company return the shipment? [z = -2.80, CV = -2.33, reject null] Q5. A process produces ball bearings with a mean weight of 150 grams and a population standard deviation of 3 grams. Assume that the weights are normally distributed. A new equipment is recently used. The production officer randomly selected 30 ball bearings and found that the mean was 150.5 grams. Using 10% significance level, test that the mean weight of the ball bearings produced from the new equipment is higher. [z = 0.91, CV = 1.28, do not reject null] 16 Business Decision Making Tutorial Questions Feb’19 Topic 7.2 Q1. Find the critical value (or values), t, for each of the following cases. a. α = 0.10, two-tailed test, n = 15 b. α = 0.10, left-tailed test, n = 15 c. α = 0.05, right-tailed test, n = 15 d. α = 0.05, two-tailed test, n = 10 e. α = 0.01, left-tailed test, n = 10 f. α = 0.005, right-tailed test, n = 10 [a. ±1.7613 b. -1.3450 c. 1.7613 d. ±2.2622 e. -2.8214 f. 3.2498] Q2. From past data, the average of the accounts payable for a company was $140. An auditor took a random sample of 16 accounts. The sample mean was $148.30 with a standard deviation of $14.50. At α = 0.05 can it be concluded that the average accounts payable is different from $140? [t = 2.290, CV = ±2.1315, reject null] Q3. A manufacturer of beverage claims that the average contents of the bottles is at least 250 ml. A random sample of 20 bottles yielded a mean of 252 ml with a standard deviation of 10 ml. At the 0.01 level of significance, is there sufficient evidence to support the claim? [t = 0.894, CV = 2.5395, do not reject null] Q4. A manager wants to determine if the average weekly sales of 300-ml canned soft drinks has dropped. The weekly mean number of cans sold has been 360 over the past 3 months. A random sample of 15 retail stores shows a mean of 353 cans, with a standard deviation of 25 cans. At the 0.10 level of significance, can it be concluded that the sales have dropped? [t = -1.084, CV = -1.3450, do not reject null] 17 Business Decision Making Tutorial Questions Feb’19 Topic 8 Q1. A large furniture retailer with stores in three cities had the following results from a special weekend sale. At α = 0.05, is there sufficient evidence that the type of furniture sold was dependent upon the store? Store 22A Store 22B Store 22C Recliner 15 20 10 Sofa 12 10 10 Loveseat 18 12 10 [χ2 = 2.864, CV = 9.488, do not reject null] Q2. Is the choice of exercise equipment dependent upon gender? Recent records from a large gym indicated the following equipment usage. At the 0.05 level of significance, is there a relationship? Male Female Treadmill 120 100 Elliptical 60 95 Bike 75 82 [χ2 = 9.144, CV = 5.991, reject null] Note: The test value in 3 decimal points is calculated based on expected values (E) of 2 decimal points. 18 Business Decision Making Tutorial Questions Feb’19 Topic 9 Q1. The director of an alumni association for a small college wants to determine whether there is any type of relationship between the amount of an alumnus’s contribution (in dollars) and the number of years the alumnus has been out of school. The data follow. Years Contribution 1 5 3 10 8 6 500 250 300 50 75 160 a. Identify the independent and dependent variables. b. Draw the scatter plot for the variables. c. Compute the value of the correlation coefficient and give a brief explanation of the type of relationship. d. Find the coefficients of determination and explain the meaning. e. Find the equation of the regression line. f. Predict the amount of contribution for an alumnus who has been out of school for 4 years. [c. -0.965; d. 0.931; e. ? = 493.131 – 49.206x; f. $296.31] 19 Business Decision Making Tutorial Questions Feb’19 Q2. The average normal daily temperature (in degrees Fahrenheit) and the corresponding average monthly precipitation (in inches) for the month of June are shown here for seven randomly selected cities in the United States. Avg. daily temp Avg. mo. precip. 86 3.4 81 1.8 83 3.4 89 3.6 80 2.2 74 1.5 64 0.2 a. Identify the independent and dependent variables. b. Draw the scatter plot for the variables. c. Compute the value of the correlation coefficient and give a brief explanation of the type of relationship. d. Find the coefficients of determination and explain the meaning. e. Find the equation of the regression line. f. Predict the average monthly precipitation when the average normal daily temperature is 70oF. [c. 0.949; d. 0.901; e. ? = -9.034 + 0.142x; f. 0.91] 20 Business Decision Making Tutorial Questions Feb’19 21 Business Decision Making Tutorial Questions Feb’19 22 Business Decision Making Tutorial Questions Feb’19 23 Business Decision Making Tutorial Questions Feb’19 24 Question 1 1 points 1 points Save Answer When small samples are used to estimate a population mean, in cases where the population standard deviation is unknown: the t-distribution must be used to obtain the critical value. the resulting margin of error for a confidence interval estimate will tend to be fairly small. there will be a large amount of sampling error. None of the above A Moving to another question will save this response. Question 1 of 24 Question 2 1 points Save Answer The file Danish Coffee contains a random sample of 144 Danish coffee drinkers and measures the annual coffee consumption in kilograms for each sampled coffee drinker. A marketing research firm wants to use this information to develop an advertising campaign to increase Danish coffee consumption. A 90% confidence interval estimate is developed for the mean annual coffee consumption of Danish coffee drinkers. Interpret the interval: (6.3881, 6.6855). We are 90% confident that the sample mean annual coffee consumption of Danish coffee drinkers between 6.39 and 6.69 kilograms We are 90% confident that the population mean annual coffee consumption of Danish coffee drinkers is between 6.39 and 6.69 kilograms 90% of the Danish coffee drinkers consume between 6.39 and 6.69 kilograms of coffee annually We are certain that 90% of the population mean annual coffee consumption of Danish coffee drinkers is between 6.39 and 6.69 kilograms Question 3 1 points Save Answer What sample size is needed to estimate a population mean within +50 of the true mean value using a confidence level of 95%, if the true population standard deviation is known to be 350? 211 214 189 155 Question 4 1 points Save Answer A drug store owner plans to survey a random sample of his customers with the objective of estimating the mean dollars spent on pharmaceutical products during the past three months. He has assumed that the population standard deviation known to be $15.50. Given this information, what would be the required sample size to estimate the population mean with 95% confidence and a margin of error of +$2.00? O 16 231 15 163 Question 5 1 points Save Answer When o is unknown, the margin of error is computed by using: t-distribution. the mean of the sample. normal distribution. the mean of the population. Question 6 1 points Save Answer A study was recently conducted to estimate the mean number of hours females over the age of 40 years spent exercising in a week. From a random sample of 15 women, the mean was found to be 5.6 hours with a sample standard deviation of 1.4 hours. To find the 90% confidence interval estimate for the mean, the correct critical value to use is: 1.65 1.7613 1.7531 1.96 Question 7 1 points Save Answer The officer of a telecommunication firm wants to determine whether the mean service time with its customers is significantly more than 5 minutes. A random sample of 30 customers was taken. The average length of service time in the sample was 5.2 minutes with a standard deviation of 1 minutes. At a 0.05 level of significance, it can be concluded that the mean of the population is: significantly less than 5. not significantly greater than 5. O significantly greater than 5. O not significantly different from 5.2. Question For the following hypothesis: Ho: μs 245 HA: u> 245 With n= 10, 7 = 255, s = 17.9, and a = 0.01, state the calculated value of the test value t. 1.77 0.99 3.25 2.82 Save Answer Question 9 1 points If an analyst wishes to find out whether there is evidence that average waiting time in the emergency unit is below 25 minutes. The best null hypothesis is: Ομ2 25. O = 25. ONS 25. O > 25. Question 10 1 points Save Answer For the following hypothesis: Ho: μs 245 HA:u > 245 With n = 10, x = 255, s = 17.9, and a = 0.01, state the calculated value of the test value t. O 0.99 2.82 1.77 3.25 Question 22 9 points Save An Company A makes a soft drink dispensing machine that allows customers to get soft drinks from the machine in a cup with ice. When the machine is running properly, the average number of fluid Ounces in the cup should be 14. Periodically the machines need to be tested to make sure that they have not gone out of adjustment. That means, the average number of fluid Ounces in the cup should not be significantly less than or more than 14. To do this, eight cups are filled by the machine and a technician carefully measures the volume in each cup. The mean is found to be 13.73 ounces, with a sample standard deviation of 0.46. At 5% significance level, the company wishes to test whether the machine is dispensing an average of less than 14 fluid Ounces. State the null hypothesis. A. No State the alternative hypothesis. B. There is not enough evidence to conclude that the machine is dispensing an average of 14 fluid Ounces. Is the test one-tailed test or two-tailed test? C. - 1.6602 State the critical value. D. - 1.8946 Calculate the test value. E. 1.6602 State the decision. F. one-tailed test Justify your choice of decision. G. The test value falls outside of the non-critical region. 4 Summarise the conclusion. H. μ< 14 Does the machine need adjustment? I. > 14 J. μs14 K. The test value falls in the non-critical region. L. two-tailed test Μ. με 14 N. Do not reject the null hypothesis. O. 1.8946 4 Summarise the conclusion. H. μ 14 J. NS 14 K. The test value falls in the non-critical region. L. two-tailed test Μ. μΣ 14 N. Do not reject the null hypothesis. O. 1.8946 P. There is not enough evidence to conclude that the machine is dispensing an average of less than 14 fluid ounces. Q. - 1.65 R. Yes S. Reject the null hypothesis. Question 23 11 points Save Ans A researcher wants to find out the relationship between the age of a person and the use of text messaging. A random sample of 300 customers were asked: “Do you regularly use text messaging?" The following data has been collected. Yes 54 No 66 Age Group Below 21 21 - 39 40 and above 51 40 37 52 Conduct a contingency analysis using a 0.10 level of significance to test whether there is enough evidence to conclude that the age of a persor is not related to the use of text messaging. (a) The null hypothesis will be phrased as: The use of text messaging is associated with the age. (True / Flase) (b) The appropriate critical value is (c) Calculate the expected values in two decimal places, and fill in the respective blanks in the sequence C11, C21, 222, C32: Age Group Below 21 21 - 39 40 and above Yes C11 C21 C31 No C12 C22 C32 (d) The test value is in three decimal places. (e) Decision of the test is to choose an option below) A-reject null hypothesis B - not reject null hypothesis (f) Justification for the decision in previous part is because (choose an option below) A- the test value falls in the non-critical region B - the test value is more than the critical value C- the test value falls in the critical region (9) Conclusion to the test is (choose an option below for each blank): There is evidence to conclude that the use of text messaging is the age. A-enough B - not enough C - not associated with D-associated with E - independent of Question 11 1 points Save Answ A contingency analysis test is performed with a 3 x 5 contingency table and results in a test value of 15.02. With a significance level of 0.10, which of the following is correct? The null hypothesis which indicates that the row and column variable are independent should be rejected The null hypothesis which indicates that the row and column variable are dependent should not be rejected The null hypothesis which indicates that the row and column variable are independent should not be rejected The null hypothesis which indicates that the row and column variable are dependent should be rejected Question 12 1 points Save Answer A contingency analysis test is performed with a 3 x 4 contingency table. With a significance level of 0.10, the critical value from the chi-square distribution is 12.592 10.645 18.549 14.684 Question 13 1 points Save Answer In a contingency analysis the expected values are based on the assumption that the two variables are independent of each other. True False Question 14 1 points Save Answer A regression analysis between the number of cup of hot beverage sold (Y) and temperature of the day in degree Celsius (X) resulted in the following equation: Y = 242 - 18X The figure 18 in the equation implies that, on average, O an increase of one degree Celsius in the temperature results in an increase of 18 cups of hot beverage in sales. an increase of one degree Celsius in the temperature results in a decrease of 18 cups of hot beverage in sales. O a decrease of one degree Celsius in the temperature is correlated with a decrease of 18 cups of hot beverage in sales. 18 cups of hot beverage were sold regardless of the temperature.