Homework answers / question archive / Business Statistics Free Response Questions #4: for Chapter 7 Directions: You can either type out answers to these questions then submit a word document or pdf (please no GoogleDoc sharing links or Apple pages files) or you can write out your answer by hand and take a photo (try to avoid HEIC image format, please) or scan the sheet of paper

Business Statistics Free Response Questions #4: for Chapter 7 Directions: You can either type out answers to these questions then submit a word document or pdf (please no GoogleDoc sharing links or Apple pages files) or you can write out your answer by hand and take a photo (try to avoid HEIC image format, please) or scan the sheet of paper

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Business Statistics

Free Response Questions #4: for Chapter 7

Directions: You can either type out answers to these questions then submit a word document or pdf (please no GoogleDoc sharing links or Apple pages files) or you can write out your answer by hand and take a photo (try to avoid HEIC image format, please) or scan the sheet of paper. PLEASE make sure you hand in something that is aligned correctly (not sideways) and clear enough for me to read.

1. a) Your company's Human Resources department administers a test of “Executive Aptitude.” They report test grades as zscores, and you got a score of 2.20. What does this mean?

b) Your company will admit to the executive training program only people who score in the top 3% on the executive aptitude test. With your z-score of 2.20, did you make the cut?

Note: You will need to use technology (preferred) or a table to answer this part.

c) What do you need to assume about test scores to find your answer in part b?

2. Some IQ tests are standardized to a Normal model with a mean of 100 and a standard deviation of 16.

a) Draw the model for these IQ scores. Clearly label it, showing what the 68–95–99.7 Rule predicts about the scores.

b) In what interval would you expect the central 68% of IQ scores to be found? Show work or explain this answer.

c) About what percent of people should have IQ scores above 132? Show work or explain this answer.

d) About what percent of people should have IQ scores between 84 and 100? Show work or explain this answer.

3. Has the Consumer Price Index (CPI) fluctuated around its mean according to a Normal model? Here are some displays. Is

a Normal model appropriate for these data? Explain.

4. Shortly after the introduction of the Belgian euro coin, newspapers around the world published articles claiming the coin is biased. The stories were based on reports that someone had spun the coin 250 times and gotten 150 heads.

Note: A fair coin means 50% heads and 50% tails. Use 0.50 for your p. You will be comparing what you expect against what you observed.

a) Use the Normal model to approximate the Binomial to determine the probability of spinning a fair coin 250 times and getting at least 150 heads. You can use Statcrunch on this, but you will want to find the mean and standard deviation first.

Show those calculations.

b) Do you think this is evidence that spinning a Belgian euro is unfair? Would you be willing to use it at the beginning of a sports event? Explain.

5. In the first quarter of 2017, a group of domestic equity mutual funds had a mean return of 6.8% with a standard deviation of 1.5%. Based on the model N(0.068, 0.015) for quarterly returns, what are the cutoff values for the

a) highest 10% of these funds?

b) lowest 20%?

c) middle 40%?

Note: although you will likely use StatCrunch for these, it is a good idea to explain or show what you think you need to enter / find to answer these questions.

For wrong answers, it helps me identify if the result you get is due to a small error or a major misconception.

Name ______________________ Business Statistics Free Response Questions #5: for Chapters 8 and 9 Worth 10 points. Directions: You can either type out answers to these questions then submit a word document or pdf (please no GoogleDoc sharing links or Apple pages files) or you can write out your answer by hand and take a photo (try to avoid HEIC image format, please) or scan the sheet of paper. PLEASE make sure you hand in something that is aligned correctly (not sideways) and clear enough for me to read. 1. A bus company is interested in the opinions of their frequent riding customers about their proposed new bus routes. Specifically, they want to know what proportion of them plan to use one of their new hubs in the next year. They take a random sample of 1,000 from the database of all frequent riders and send them an e-mail message with a request to fill out a survey in exchange for free bus tickets. a) What is the population? b) What is the sampling frame? c) What is the population parameter of interest? d) What sampling method is used? 2. Examine each of the following questions for possible bias. If you think the question is biased, indicate how and propose a better question. Explain your answers. a) Do you think that price or quality is more important in selecting a tablet computer? b) Given humanity's great tradition of exploration, do you favor continued funding for space flights? 3. A market researcher for a provider of iPhone accessories wants to know the proportion of customers who own cars to assess the market for a new iPhone car charger. A sample of 400 customers indicates that 72% own cars. SHOW WORK. a) What is the standard error of the sampling distribution of the proportion? b) How large would the standard error have been if he had surveyed only 100 customers (assuming the proportion is about the same)? 4. From a survey of coworkers you find that 48% of 200 have already received this year's flu vaccine. An approximate 95% confidence interval is (0.409,0.551). For the following, would the confidence interval be wider or narrower and explain why. a) How would the confidence interval change if the sample size had been 800 instead of 200? Why? b) How would the confidence interval change if the confidence level had been 90% instead of 95%? Why? c) How would the confidence interval change if the confidence level had been 99% instead of 95%? Why? 5. Advertisers. Direct mail advertisers send solicitations (“junk mail”) to thousands of potential customers in the hope that some will buy the company's product. The response rate is usually quite low. Suppose a company wants to test the response to a new flyer and sends it to 1000 people randomly selected from their mailing list of over 200,000 people. They get orders from 123 of the recipients. a) Create a 90% confidence interval for the percentage of people the company contacts who may buy something. Give x, n, and p-hat for this as well as the StatCrunch output. **Make sure you provide images or screenshots of your StatCrunch output, you will lose points if you don’t. b) b) Explain what this interval means. c) The company must decide whether to now do a mass mailing. The mailing won't be cost-effective unless it produces at least a 5% return. What does your confidence interval suggest? Explain.
Name ______________________ Business Statistics Free Response Questions #6: for Chapter 10 Worth 10 points. Directions: You can either type out answers to these questions then submit a word document or pdf (please no GoogleDoc sharing links or Apple pages files) or you can write out your answer by hand and take a photo (try to avoid HEIC image format, please) or scan the sheet of paper. PLEASE make sure you hand in something that is aligned correctly (not sideways) and clear enough for me to read. 1. For each of the following situations, write the null and alternative hypotheses in terms of parameter values (in other words, in symbols). Note: H0 always has the “=” for this course despite what you may find out on the internet. Example: We want to know if the proportion of up days in the stock market is 50%. Answer: Let p = the proportion of up days. H0: p = 0.5 vs. HA: p ≠ 0.5. a) A recent University of Iowa study found that seat-belt compliance in Iowa was 87% in 2018. The state wants to know if it has changed. b) Wired magazine discovered that 15% of a certain computer tablet had warranty problems over the first three months. From a random sample, the manufacturer wants to know if a new model has improved that rate. c) Regular card customers have a default rate of 5.2%. A credit card bank wants to know if that rate is different for their platinum card customers. 2. A survey of 100 small business owners finds that 58 think the economy will improve next year. Is there evidence that the rate is higher among all small business owners than the 52% reported by the public at large? a) Find the standard deviation of the sample proportion based on the null hypothesis. Show work. b) Find the z-statistic. Show work. c) Does the z-statistic seem like a particularly large or small value? Explain your answer. 3. For the following situation, state whether a Type I, a Type II, or neither error has been made. Explain your answer. A test of H0: p = 0.8 vs. HA: p < 0.8 rejects the null hypothesis. Later it is discovered that p = 0.9 (i.e. the truth). 4. A car company is counting on selling more electric vehicles to the older market segment in the U.S. -- drivers over the age of 55. The company's market researchers survey to investigate whether or not the proportion of today's diver’s over the age of 55 that own an electric vehicle is higher than it was a decade ago. They find a P-value of 0.019. Is it reasonable to conclude that more drivers over the age of 55 own electric vehicles? Assume α = 0.05. Explain. 5. An insurance company that collects insurance claims for doctors' offices in the area is concerned that the percentage of claims being paid by Medicaid has increased. Historically, that percentage has been 25%. An examination of 2865 recent bills reveals that 28% of these claims are being paid by Medicaid. Is this evidence of an increase in the percent of claims being paid by Medicaid? Assume α = 0.05 a) Write appropriate hypotheses. b) Check the assumptions and conditions. c) Perform the test and find the P-value and test statistic. GIVE THE STATCRUNCH OUTPUT. **Make sure you provide images or screenshots of your StatCrunch output, you will lose points if you don’t. d) Do you reject or not reject the null hypothesis? Why? e) State the conclusion.
Name ______________________ Business Statistics Free Response Questions #6: for Chapter 10 Worth 10 points. Directions: You can either type out answers to these questions then submit a word document or pdf (please no GoogleDoc sharing links or Apple pages files) or you can write out your answer by hand and take a photo (try to avoid HEIC image format, please) or scan the sheet of paper. PLEASE make sure you hand in something that is aligned correctly (not sideways) and clear enough for me to read. 1. For each of the following situations, write the null and alternative hypotheses in terms of parameter values (in other words, in symbols). Note: H0 always has the “=” for this course despite what you may find out on the internet. Example: We want to know if the proportion of up days in the stock market is 50%. Answer: Let p = the proportion of up days. H0: p = 0.5 vs. HA: p ≠ 0.5. a) A recent University of Iowa study found that seat-belt compliance in Iowa was 87% in 2018. The state wants to know if it has changed. b) Wired magazine discovered that 15% of a certain computer tablet had warranty problems over the first three months. From a random sample, the manufacturer wants to know if a new model has improved that rate. c) Regular card customers have a default rate of 5.2%. A credit card bank wants to know if that rate is different for their platinum card customers. 2. A survey of 100 small business owners finds that 58 think the economy will improve next year. Is there evidence that the rate is higher among all small business owners than the 52% reported by the public at large? a) Find the standard deviation of the sample proportion based on the null hypothesis. Show work. b) Find the z-statistic. Show work. c) Does the z-statistic seem like a particularly large or small value? Explain your answer. 3. For the following situation, state whether a Type I, a Type II, or neither error has been made. Explain your answer. A test of H0: p = 0.8 vs. HA: p < 0.8 rejects the null hypothesis. Later it is discovered that p = 0.9 (i.e. the truth). 4. A car company is counting on selling more electric vehicles to the older market segment in the U.S. -- drivers over the age of 55. The company's market researchers survey to investigate whether or not the proportion of today's diver’s over the age of 55 that own an electric vehicle is higher than it was a decade ago. They find a P-value of 0.019. Is it reasonable to conclude that more drivers over the age of 55 own electric vehicles? Assume α = 0.05. Explain. 5. An insurance company that collects insurance claims for doctors' offices in the area is concerned that the percentage of claims being paid by Medicaid has increased. Historically, that percentage has been 25%. An examination of 2865 recent bills reveals that 28% of these claims are being paid by Medicaid. Is this evidence of an increase in the percent of claims being paid by Medicaid? Assume α = 0.05 a) Write appropriate hypotheses. b) Check the assumptions and conditions. c) Perform the test and find the P-value and test statistic. GIVE THE STATCRUNCH OUTPUT. **Make sure you provide images or screenshots of your StatCrunch output, you will lose points if you don’t. d) Do you reject or not reject the null hypothesis? Why? e) State the conclusion.
Name ______________________ Business Statistics Free Response Questions #6: for Chapter 10 Worth 10 points. Directions: You can either type out answers to these questions then submit a word document or pdf (please no GoogleDoc sharing links or Apple pages files) or you can write out your answer by hand and take a photo (try to avoid HEIC image format, please) or scan the sheet of paper. PLEASE make sure you hand in something that is aligned correctly (not sideways) and clear enough for me to read. 1. For each of the following situations, write the null and alternative hypotheses in terms of parameter values (in other words, in symbols). Note: H0 always has the “=” for this course despite what you may find out on the internet. Example: We want to know if the proportion of up days in the stock market is 50%. Answer: Let p = the proportion of up days. H0: p = 0.5 vs. HA: p ≠ 0.5. a) A recent University of Iowa study found that seat-belt compliance in Iowa was 87% in 2018. The state wants to know if it has changed. b) Wired magazine discovered that 15% of a certain computer tablet had warranty problems over the first three months. From a random sample, the manufacturer wants to know if a new model has improved that rate. c) Regular card customers have a default rate of 5.2%. A credit card bank wants to know if that rate is different for their platinum card customers. 2. A survey of 100 small business owners finds that 58 think the economy will improve next year. Is there evidence that the rate is higher among all small business owners than the 52% reported by the public at large? a) Find the standard deviation of the sample proportion based on the null hypothesis. Show work. b) Find the z-statistic. Show work. c) Does the z-statistic seem like a particularly large or small value? Explain your answer. 3. For the following situation, state whether a Type I, a Type II, or neither error has been made. Explain your answer. A test of H0: p = 0.8 vs. HA: p < 0.8 rejects the null hypothesis. Later it is discovered that p = 0.9 (i.e. the truth). 4. A car company is counting on selling more electric vehicles to the older market segment in the U.S. -- drivers over the age of 55. The company's market researchers survey to investigate whether or not the proportion of today's diver’s over the age of 55 that own an electric vehicle is higher than it was a decade ago. They find a P-value of 0.019. Is it reasonable to conclude that more drivers over the age of 55 own electric vehicles? Assume α = 0.05. Explain. 5. An insurance company that collects insurance claims for doctors' offices in the area is concerned that the percentage of claims being paid by Medicaid has increased. Historically, that percentage has been 25%. An examination of 2865 recent bills reveals that 28% of these claims are being paid by Medicaid. Is this evidence of an increase in the percent of claims being paid by Medicaid? Assume α = 0.05 a) Write appropriate hypotheses. b) Check the assumptions and conditions. c) Perform the test and find the P-value and test statistic. GIVE THE STATCRUNCH OUTPUT. **Make sure you provide images or screenshots of your StatCrunch output, you will lose points if you don’t. d) Do you reject or not reject the null hypothesis? Why? e) State the conclusion.
Name ______________________ Business Statistics Free Response Questions #6: for Chapter 10 Worth 10 points. Directions: You can either type out answers to these questions then submit a word document or pdf (please no GoogleDoc sharing links or Apple pages files) or you can write out your answer by hand and take a photo (try to avoid HEIC image format, please) or scan the sheet of paper. PLEASE make sure you hand in something that is aligned correctly (not sideways) and clear enough for me to read. 1. For each of the following situations, write the null and alternative hypotheses in terms of parameter values (in other words, in symbols). Note: H0 always has the “=” for this course despite what you may find out on the internet. Example: We want to know if the proportion of up days in the stock market is 50%. Answer: Let p = the proportion of up days. H0: p = 0.5 vs. HA: p ≠ 0.5. a) A recent University of Iowa study found that seat-belt compliance in Iowa was 87% in 2018. The state wants to know if it has changed. b) Wired magazine discovered that 15% of a certain computer tablet had warranty problems over the first three months. From a random sample, the manufacturer wants to know if a new model has improved that rate. c) Regular card customers have a default rate of 5.2%. A credit card bank wants to know if that rate is different for their platinum card customers. 2. A survey of 100 small business owners finds that 58 think the economy will improve next year. Is there evidence that the rate is higher among all small business owners than the 52% reported by the public at large? a) Find the standard deviation of the sample proportion based on the null hypothesis. Show work. b) Find the z-statistic. Show work. c) Does the z-statistic seem like a particularly large or small value? Explain your answer. 3. For the following situation, state whether a Type I, a Type II, or neither error has been made. Explain your answer. A test of H0: p = 0.8 vs. HA: p < 0.8 rejects the null hypothesis. Later it is discovered that p = 0.9 (i.e. the truth). 4. A car company is counting on selling more electric vehicles to the older market segment in the U.S. -- drivers over the age of 55. The company's market researchers survey to investigate whether or not the proportion of today's diver’s over the age of 55 that own an electric vehicle is higher than it was a decade ago. They find a P-value of 0.019. Is it reasonable to conclude that more drivers over the age of 55 own electric vehicles? Assume α = 0.05. Explain. 5. An insurance company that collects insurance claims for doctors' offices in the area is concerned that the percentage of claims being paid by Medicaid has increased. Historically, that percentage has been 25%. An examination of 2865 recent bills reveals that 28% of these claims are being paid by Medicaid. Is this evidence of an increase in the percent of claims being paid by Medicaid? Assume α = 0.05 a) Write appropriate hypotheses. b) Check the assumptions and conditions. c) Perform the test and find the P-value and test statistic. GIVE THE STATCRUNCH OUTPUT. **Make sure you provide images or screenshots of your StatCrunch output, you will lose points if you don’t. d) Do you reject or not reject the null hypothesis? Why? e) State the conclusion.
Name ______________________ Business Statistics Free Response Questions #6: for Chapter 10 Worth 10 points. Directions: You can either type out answers to these questions then submit a word document or pdf (please no GoogleDoc sharing links or Apple pages files) or you can write out your answer by hand and take a photo (try to avoid HEIC image format, please) or scan the sheet of paper. PLEASE make sure you hand in something that is aligned correctly (not sideways) and clear enough for me to read. 1. For each of the following situations, write the null and alternative hypotheses in terms of parameter values (in other words, in symbols). Note: H0 always has the “=” for this course despite what you may find out on the internet. Example: We want to know if the proportion of up days in the stock market is 50%. Answer: Let p = the proportion of up days. H0: p = 0.5 vs. HA: p ≠ 0.5. a) A recent University of Iowa study found that seat-belt compliance in Iowa was 87% in 2018. The state wants to know if it has changed. b) Wired magazine discovered that 15% of a certain computer tablet had warranty problems over the first three months. From a random sample, the manufacturer wants to know if a new model has improved that rate. c) Regular card customers have a default rate of 5.2%. A credit card bank wants to know if that rate is different for their platinum card customers. 2. A survey of 100 small business owners finds that 58 think the economy will improve next year. Is there evidence that the rate is higher among all small business owners than the 52% reported by the public at large? a) Find the standard deviation of the sample proportion based on the null hypothesis. Show work. b) Find the z-statistic. Show work. c) Does the z-statistic seem like a particularly large or small value? Explain your answer. 3. For the following situation, state whether a Type I, a Type II, or neither error has been made. Explain your answer. A test of H0: p = 0.8 vs. HA: p < 0.8 rejects the null hypothesis. Later it is discovered that p = 0.9 (i.e. the truth). 4. A car company is counting on selling more electric vehicles to the older market segment in the U.S. -- drivers over the age of 55. The company's market researchers survey to investigate whether or not the proportion of today's diver’s over the age of 55 that own an electric vehicle is higher than it was a decade ago. They find a P-value of 0.019. Is it reasonable to conclude that more drivers over the age of 55 own electric vehicles? Assume α = 0.05. Explain. 5. An insurance company that collects insurance claims for doctors' offices in the area is concerned that the percentage of claims being paid by Medicaid has increased. Historically, that percentage has been 25%. An examination of 2865 recent bills reveals that 28% of these claims are being paid by Medicaid. Is this evidence of an increase in the percent of claims being paid by Medicaid? Assume α = 0.05 a) Write appropriate hypotheses. b) Check the assumptions and conditions. c) Perform the test and find the P-value and test statistic. GIVE THE STATCRUNCH OUTPUT. **Make sure you provide images or screenshots of your StatCrunch output, you will lose points if you don’t. d) Do you reject or not reject the null hypothesis? Why? e) State the conclusion.
Name ______________________ Business Statistics Free Response Questions #6: for Chapter 10 Worth 10 points. Directions: You can either type out answers to these questions then submit a word document or pdf (please no GoogleDoc sharing links or Apple pages files) or you can write out your answer by hand and take a photo (try to avoid HEIC image format, please) or scan the sheet of paper. PLEASE make sure you hand in something that is aligned correctly (not sideways) and clear enough for me to read. 1. For each of the following situations, write the null and alternative hypotheses in terms of parameter values (in other words, in symbols). Note: H0 always has the “=” for this course despite what you may find out on the internet. Example: We want to know if the proportion of up days in the stock market is 50%. Answer: Let p = the proportion of up days. H0: p = 0.5 vs. HA: p ≠ 0.5. a) A recent University of Iowa study found that seat-belt compliance in Iowa was 87% in 2018. The state wants to know if it has changed. b) Wired magazine discovered that 15% of a certain computer tablet had warranty problems over the first three months. From a random sample, the manufacturer wants to know if a new model has improved that rate. c) Regular card customers have a default rate of 5.2%. A credit card bank wants to know if that rate is different for their platinum card customers. 2. A survey of 100 small business owners finds that 58 think the economy will improve next year. Is there evidence that the rate is higher among all small business owners than the 52% reported by the public at large? a) Find the standard deviation of the sample proportion based on the null hypothesis. Show work. b) Find the z-statistic. Show work. c) Does the z-statistic seem like a particularly large or small value? Explain your answer. 3. For the following situation, state whether a Type I, a Type II, or neither error has been made. Explain your answer. A test of H0: p = 0.8 vs. HA: p < 0.8 rejects the null hypothesis. Later it is discovered that p = 0.9 (i.e. the truth). 4. A car company is counting on selling more electric vehicles to the older market segment in the U.S. -- drivers over the age of 55. The company's market researchers survey to investigate whether or not the proportion of today's diver’s over the age of 55 that own an electric vehicle is higher than it was a decade ago. They find a P-value of 0.019. Is it reasonable to conclude that more drivers over the age of 55 own electric vehicles? Assume α = 0.05. Explain. 5. An insurance company that collects insurance claims for doctors' offices in the area is concerned that the percentage of claims being paid by Medicaid has increased. Historically, that percentage has been 25%. An examination of 2865 recent bills reveals that 28% of these claims are being paid by Medicaid. Is this evidence of an increase in the percent of claims being paid by Medicaid? Assume α = 0.05 a) Write appropriate hypotheses. b) Check the assumptions and conditions. c) Perform the test and find the P-value and test statistic. GIVE THE STATCRUNCH OUTPUT. **Make sure you provide images or screenshots of your StatCrunch output, you will lose points if you don’t. d) Do you reject or not reject the null hypothesis? Why? e) State the conclusion.