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Question1)The water diet requires one to drink two cups of water every half hour from when one gets up until one goes to bed, but otherwise allows one to eat whatever one likes

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Question1)The water diet requires one to drink two cups of water every half hour from when one gets up until one goes to bed, but otherwise allows one to eat whatever one likes. Four adult volunteers agree to test the diet. They are weighed prior to beginning the diet and after six weeks on the diet. The weights (in pounds) are

Person 1 2 3 4

Weight before the diet 180 125 240 150

Weight after six weeks 170 130 215 152

For the population of all adults, assume that the weight loss after six weeks on the diet (weight before beginning the diet-weight after six weeks on the diet) is normally distributed with mean μ. Based on these data, what is the p value of the hypothesis test to determine if the diet leads to weight loss? (use 3 decimals)

2. The CEO of a mail order business is reviewing the order filling operations at their two warehouses. The goal is to have 100% of orders shipped within 24 hours. In previous years, neither warehouse has achieved the goal, but the East Coast Warehouse has consistently out-performed the West Coast Warehouse. To compare the current performance of the warehouses, they decide to conduct a hypothesis test at the 5% significance level. They randomly select 200 orders from the West Coast Warehouse (population 1) and 400 orders from the East Coast Warehouse (population 2). They found that 190 of the West Coast Orders were shipped within 24 hours, and the East Coast Warehouse shipped 365 orders within 24 hours.

What is the p-value for testing the hypothesis that the West Coast Warehouse is now outperforming the East Coast Warehouse?
What is the p-value for testing the hypothesis that the East Coast Warehouse is still outperforming the West Coast Warehouse?
What is the p-value for testing the hypothesis of whether there is a difference in the performance of the two the warehouses?

3. A researcher wishes to test the hypothesis of whether Miami Heat fans watch an average of more than 50 of their games this season. They collect a random sample of 100 fans and find that they have watched an average of 52 games with a sample standard deviation of 4 games. What is the value of the test statistic?

4. The vice president of marketing brought to the attention of sales managers that most of the company's manufacturer representatives contacted clients and maintained client relationships in a disorganized, haphazard way. The sales managers brought the reps in for a three-day seminar and training session on how to use an organizer to schedule visits and recall pertinent information about each client more effectively. Sales reps were taught how to schedule visits most efficiently to maximize their efforts. Sales managers were given data on the number of site visits by sales reps on a randomly selected day both before and after the seminar as shown on the following data. What is the margin of error of the 95% confidence interval for the difference between visits before and after the training?

Rep Before After

1. 2 4
2. 4 5
3. 1
4. 3 3
5. 4 3
6. 2 5
7. 2 6
8. 3 4
9. 1 5

5. Compute a 95% Confidence Interval for the population proportion given a sample size n=1000 and a sample proportion = 35%

Question 6

A study will be conducted to estimate the population proportion. A level of confidence of 99% will be used and an error of no more than .03 is desired. There is no knowledge as to what the population proportion will be. The size of sample should be at least

Question 7 A company produces packets of soap powder labeled “Giant Size 32 Ounces.” The actual weight of soap powder in a box has a normal distribution, with a mean of 33.5 oz. and a standard deviation of 0.85 oz. What is the probability that a package would weight 35 oz. or more?

Question 8

The temperature at any random location in a kiln used in the manufacture of bricks is normally distributed with a mean of 1000° F. and a standard deviation of 50° F. If bricks are fired at a temperature above 1125° F, they will crack and must be disposed of. If the bricks are placed randomly throughout the kiln, what is the proportion of bricks that crack during the firing process (Hint : this will be the probability that the breach reaches a temperature above 1125°)

Question 9

A basketball player makes 160 out of 200 free throws. We would estimate the probability that the player makes his next free throw to be

0.16

0.80 (160 / 200 = 0.8)

1.2

50-50. Either he makes it or he doesn’t.

Question 10

High levels of glucose in the blood are indications of diabetes, which is becoming more prevalent in the United States. Diabetes can lead to many complications such as blindness and heart disease. A random sample of 360 individuals had their blood sugar level measured. The five-number summary was:

48 67 89 126 240

Based on these values, what is the Inter-quartile Range (IQR)?
Mark the 5 numbers above on the box plot

Max=

Q3=

Median=

Q1=

Min=

Based on these values, how many individuals had glucose levels above 126 ?
How many individuals had glucose levels above 89?
How many individuals had glucose levels below 126?
How many individuals had glucose levels above 67?

Question 11

The following boxplot illustrates the GPA for a sample of 160 students.

According to the graph, how many students had GPA above 3.6?
According to the graph, how many students had GPA below 3.2?
According to the graph, how many students had GPA above 2.8?

Question 12

A company manufacturing computer chips has historical data showing that 8% chips manufactured are defective. Management is concerned that high employee turnover is partially responsible for the high defect rate. In an effort to decrease the percentage of defective chips, management decides to provide additional training to those employees hired within the last year. After training was implemented, a sample of 300 chips revealed only 10 defects. They use a 5% significance level to do a hypothesis test whether the additional training was effective in lowering the defect rate. Based on the results, the correct conclusion is

Question 13

A random sample of size 49 is to be taken from a population that is normally distributed with mean 120 and standard deviation 21.

What is the mean of the sampling distribution of ? hat is the standard de iation of the sampling distribution of ?

Questions 14-16

The San Francisco Bay Area's commuter rail system is called BART, short for Bay Area Rapid Transit. The

Each of the 39 stations in the BART system can be assigned to one of four geographic areas: San Francisco Downtown, San Francisco South, East Bay Urban, and East Bay Suburban. Based on data collected in 2000, the probability that a rider's destination will be in each of these regions is shown below.

Q14. What is the probability that a rider's destination will be the East Bay Urban region?

Q15. What is the probability that a rider’s destination will be in the San Francisco region (owntown or South)?

Q16. If we assume that the probability a train was on time in 2001 was 0.922, what is the probability that a train was not on time in 2001?

Geographic Area	Probability
San Francisco Downtown	0.343
San Francisco South	0.172
East Bay Urban	?
East Bay Suburban	0.149

Question 17

Assume that among all passengers riding BART within the city of San Francisco, the number of stations between a passenger's starting point and ending point is a random variable with the following distribution. What is the mean of this random variable? What is the probability of a San Francisco passenger having three stations or more between her starting point and her ending point?

Number of stations	1	2	3	4	5	6	7	8
Probability	0.096	0.127	0.193	0.194	0.168	0.098	0.030	0.094

Question 18

Suppose the marketing department at Wrigley's wanted to conduct their own research to see if gum chewing increased memory. Assuming that the mean number of words remembered by gum chewers is 8.6 words and the standard deviation is 0.7 words, how many people should participate in the study so that the margin of error for a 95% confidence interval is 0.25 words?

Question 19

A bank officer conducted a study which found that 48% of customers had defaulted on their mortgages over the last year due to the economic crisis. Suppose a random sample of 150 bank customers is selected. What is the probability that more than 70 customers have defaulted on their mortgages over the last year?

Question 20

A small store keeps track of the number X of customers that make a purchase during the first hour that the store is open each day. Based on the records, X has the following probability distribution.

X 0 1 2 3 4

P(X) 0.1 0.1 0.1 0.1 0.6

The standard deviation of the number of customers that make a purchase during the first hour that the store is open is

The variance of the number of customers that make a purchase during the first hour that the store is open is

The expected number of customers that make a purchase during the first hour that the store is open is

Question 21

The staff of Mr. Wayne Wertz, VP of Operations at Portland Peoples Bank, prepared a frequency histogram of waiting time for walk-in customers.

Approximately how many walk-in customers waited more than 7 minutes?

Approximately how many walk-in customers waited less than 2 minutes?

Approximately how many walk-in customers waited less than 1 minute?

Question 22

An automobile dealer wishes to investigate the relation between the gender of the buyer and type of vehicle purchased. Based on the following joint probability table that was de eloped from the dealer’s records for the previous year,

Type of Buyer Gender

Vehicle Female Male Total

SUV 0.08 0.12 0.20

Not SUV 0.32 0.48 0.80

Total 0.40 0.60 1.00

The probability that a randomly selected vehicle is an SUV is

The probability that a randomly selected vehicle is Not an SUV is

What is the probability that a randomly selected buyer is a female and purchased a SUV?

What is the probability that a randomly selected FEMALE buyer purchased an SUV?

If a buyer who purchased a SUV is randomly selected, what’s the probability that he or she is male?

Question 23

The superintendent of certain school district decided to launch a tutoring program for those elementary school students who had reading scores that placed them at the bottom 10% of all students in the district. Assume that reading scores are normally distributed with mean 86.5 and standard deviation 12.25. What reading score would be required for a student to qualify for the tutoring program?

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