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business
business statistics in practice

Questions and Answers of Business Statistics In Practice

=+a) Test the null hypothesis at a = 0.05 using the pooled t-test. (Show the t-statistic, P-value, and conclusion.)
=+13. For the data in Exercise 1,
=+d) What does it say about the null hypothesis that the mean difference is 0?Section 13.5
=+c) Is 0 within the confidence interval?
=+) Why is the confidence interval narrower than the one you found in Exercise 10?
=+a) Find a 95% confidence interval for the mean difference in page views from the two websites.
=+12. Using the summary statistics in Exercise 4, and assuming that the data come from a distribution that is Normally distributed,
=+d) What does it say about the null hypothesis that the mean difference is 0?
=+b) Why is the confidence interval narrower than the one you found in Exercise 9?c) Is 0 within the confidence interval?
=+a) Find a 95% confidence interval for the mean difference in ages of houses in the two neighborhoods using the df given in Exercise 7.
=+11. Using the summary statistics in Exercise 3, and assuming that the data come from a distribution that is Normally distributed,
=+c) What does it say about the null hypothesis that the mean difference is 0?
=+b) Is 0 within the confidence interval?
=+a) Find a 95% confidence interval for the mean difference in page views from the two websites.
=+10. Using the data in Exercise 2, and assuming that the data come from a distribution that is Normally distributed,
=+c) What does it say about the null hypothesis that the mean difference is 0?
=+) Find a 95% confidence interval for the mean difference in ages of houses in the two neighborhoods.b) Is 0 within the confidence interval?
=+9. Using the data in Exercise 1, and assuming that the data come from a distribution that is Normally distributed,
=+c) What do you conclude at a = 0.05?Section 13.4
=+b) Calculate the P-value of the statistic using the rule that df is at least min1n1 - 1, n2 - 12.
=+a) Calculate the P-value of the statistic knowing that the approximation formula gives 163.6 df.
=+8. Using the data in Exercise 4, test the hypothesis that the mean number of page views from the two websites is the same. You may assume that the number of page views from each website follow a
=+c) What do you conclude at a = 0.05?
=+b) Calculate the P-value of the statistic using the rule that df is at least min1n1 - 1, n2 - 12.
=+a) Calculate the P-value of the statistic knowing that the approximation formula gives 62.2 df (you will need to round or use technology).
=+7. Using the data in Exercise 3, test the hypothesis that the mean age of houses in the two neighborhoods is the same.You may assume that the ages of houses in each neighborhood follow a Normal
=+f) What do you conclude at a = 0.05?
=+e) Find the P-value using the degrees of freedom from part c.
=+b) Calculate the degrees of freedom from the formula in the footnote of page 426.c) Calculate the degrees of freedom using the rule that df = min1n1 - 1, n2 - 12.d) Find the P-value using the
=+a) Using the values you found in Exercise 2, find the value of the t-statistic for the difference in mean ages for the null hypothesis.
=+6. For the data in Exercise 2, we want to test the null hypothesis that the mean number of page visits is the same for the two websites. Assume that the data come from a population that is
=+f) What do you conclude at a = 0.05?Exercises M13_SHAR8696_03_SE_C13.indd 452 14/07/14 7:30 AM Exercises 453
=+e) Find the P-value using the degrees of freedom from part d.
=+d) Find the P-value using the degrees of freedom from partb. (You can either round the number of df and use a table or use technology or a website).
=+c) Calculate the degrees of freedom using the rule that df = min1n1 - 1, n2 - 12.
=+b) Calculate the degrees of freedom from the formula in the footnote of page 426.
=+a) Using the values you found in Exercise 1, find the value of the t-statistic for the difference in mean ages for the null hypothesis.
=+5. For the data in Exercise 1, we want to test the null hypothesis that the mean age of houses in the two neighborhoods is the same. Assume that the data come from a population that is Normally
=+c) Calculate the t-statistic for the observed difference in mean page visits assuming that the true mean difference is 0.Section 13.2
=+b) Find the standard error of the estimated mean difference.
=+a) Find the estimated mean difference in page visits between the two websites.
=+4. Not happy with the previous results, the analyst in Exercise 2 takes a much larger random sample of customers from each website and records their page views. Here are the data:Website A Website
=+c) Calculate the t-statistic for the observed difference in mean ages assuming that the true mean difference is 0.
=+b) Find the standard error of the estimated mean difference.
=+a) Find the estimated mean age difference between the two neighborhoods.
=+3. The developer in Exercise 1 hires an assistant to collect a random sample of houses from each neighborhood and finds that the summary statistics for the two neighborhoods look as
=+e) Find the standard error of the difference of the sample means.
=+d) Find the sample standard deviations for each website.
=+c) Find the sample variances for each website.
=+b) Find the estimated difference of the sample mean page views of the two websites.
=+a) Find the sample mean page views for each website.
=+2. A market analyst wants to know if the new website he designed is showing increased page views per visit. A customer is randomly sent to one of two different websites, offering the same
=+e) Find the standard error of the difference of the two sample means.
=+d) Find the sample standard deviation for each neighborhood.
=+c) Find the sample variances for each neighborhood.
=+) Find the estimated difference of the mean ages of the two neighborhoods.
=+a) Find the sample mean for each community.
=+1. A developer wants to know if the houses in two different neighborhoods were built at roughly the same time. She takes a random sample of eight houses from each neighborhood and finds their ages
=+9 These same 50 companies are surveyed again one year later to see if their perceptions, business practices, and R&D investment have changed
=+8 A total of 50 companies are surveyed about business practices.Some are privately held and others are publicly traded. We wish to investigate differences between these two kinds of companies.
=+7 A random sample of work groups within a company was identified. Within each work group, one male and one female worker were selected at random. Each was asked to rate the secretarial support that
=+Random samples of students were surveyed on their perception of ethical and community service issues both in their first year and fourth year at a university. The university wants to know whether
=+5 Random samples of 50 men and 50 women are surveyed on the amount they invest on average in the stock market on an annual basis. We want to estimate any gender difference in how much they invest.
=+We’ve concluded on page 427 that, on average, women receive a larger discount than men at this car dealership. How big is the difference, on average? Find a 95% confidence interval for the
=+The P-value of the test was less than 0.05. State a brief conclusion.
=+3 What alternative hypothesis would you test?
=+2 Check the assumptions and conditions needed to test whether there really is a difference in behavior due to the difference in pictures.
=+1 What null hypothesis were the researchers testing?
=+We saw (on page 426) that the difference between the average discount obtained by men and women appeared to be large if we assume that there is no true difference. Test the hypothesis, find the
=+If there is no difference between them, does this seem like an unusually large value?
=+What is its standard error?
=+What is the mean difference of the discounts received by men and women?
=+43. TV safety. The manufacturer of a metal stand for home TV sets must be sure that its product will not fail under the weight of the TV. Since some larger sets weigh nearly 300 pounds, the
=+42. Free gift. A philanthropic organization sends out “free gifts” to people on their mailing list in the hope that the receiver will respond by sending back a donation. Typical gifts are
=+41. Collections. Credit card companies lose money on cardholders who fail to pay their minimum payments.They use a variety of methods to encourage their delinquent cardholders to pay their credit
=+b) Does this improvement seem to be practically significant?
=+a) Should the professor spend the money for this software?Support your recommendation with an appropriate test.
=+40. Software, part II. 481 students signed up for the Stats course in Exercise 39. They used the software suggested by the salesman, and scored an average of 112 points on the final with a standard
=+e) What is meant by the power of this test?
=+d) In this context, explain what would happen if the professor makes a Type II error.
=+a) Is this a one-tailed or two-tailed test? Explain.b) Write the null and alternative hypotheses.c) In this context, explain what would happen if the professor makes a Type I error.
=+b) Explain what will happen if the inspectors commit a Type I error.
=+39. Software for learning. A Statistics professor has observed that for several years students score an average of 105 points out of 150 on the semester exam. A salesman suggests that he try a
=+force them to cut back to 20. How would this affect the power of the test? Explain.
=+instead of 5%, how will this affect the power of the test?f) The engineers hoped to base their decision on the reactions of 50 drivers, but time and budget constraints may
=+c) Explain what will happen if the inspectors commit a Type II error.
=+) In this context, what would a Type II error be?d) In this context, what is meant by the power of the test?e) If the hypothesis is tested at the 1% level of significance
=+a) Is this a one-tailed or a two-tailed test? Why?b) In this context, what would a Type I error be?
=+38. Stop signs. Highway safety engineers test new road signs, hoping that increased reflectivity will make them more visible to drivers. Volunteers drive through a test M12_SHAR8696_03_SE_C12.indd
=+44. Catheters. During an angiogram, heart problems can be examined via a small tube (a catheter) threaded into the heart from a vein in the patient’s leg. It’s important that the company that
=+f) The lawsuit is based on a survey 1165 business owners. Is the power of the test higher than, lower than, or the same as it would be if it were based on 2000 business owners?
=+e) If the hypothesis is tested at the 1% level of significance instead of 5%, how will this affect the power of the test?
=+b) In this context, what would a Type I error be?c) In this context, what would a Type II error be?
=+37. Equal opportunity? A bank is sued for gender discrimination because 12% of the businesswomen who asked for loans were turned down when only 9% of all loan applications were turned down. Is
=+) Suppose that, as a day passes, one of the machines on the assembly line produces more and more items that are defective. How will this affect the power of the test?
=+c) Their test currently uses a 5% level of significance.What are the advantages and disadvantages of changing to an alpha level of 1%?
=+b) They are currently testing 5 items each hour. Someone has proposed that they test 10 instead. What are the advantages and disadvantages of such a change?
=+a) In this context, what is meant by the power of the test the inspectors conduct?
=+36. Production. Consider again the task of the quality control inspectors in Exercise 34.
=+a) Is this a one-sided or two-sided test? In the context of the problem, why do you think this is important?

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