Homework answers / question archive / Name ______________________ Business Statistics Free Response Questions #6: for Chapter 10 Worth 10 points

Name ______________________ Business Statistics Free Response Questions #6: for Chapter 10 Worth 10 points

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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.