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business
business statistics in practice

Questions and Answers of Business Statistics In Practice

=+• Write up a short report explaining the main differences between the two sets of intervals.
=+• Repeat this for 100 samples of size 100.
=+• How many of these contain 59.7%?
=+Using appropriate software, draw 100 samples of size 25 from the data and compute 90% confidence intervals for the true proportion.
=+ How closely does it matchy the theoretical distribution?
=+ • Examine the distribution of the sampled proportions. What do you expect it to look like?
=+ • Compare the mean and standard deviation of this (sampling) distribution to what you previously calculated.
=+• Using the software of your choice, draw 100 samples of size 50 from this population of homes, find the proportion of homes with fireplaces in each of these samples, and make a histogram of
=+• Calculate the proportion of homes that have fireplaces for all 1063 homes. Using this value, calculate what the standard error of the sample proportion would be for a sample of size 50.
=+17. Suppose you want to estimate the proportion of students in your class having part-time jobs. You have no preconceived idea of what that proportion might be.
=+c) How would the confidence interval change if the confidence level had been 99% instead of 95%?Section 9.4
=+b) How would the confidence interval change if the confidence level had been 90% instead of 95%?
=+a) How would the confidence interval change if the sample size had been 800 instead of 200?
=+16. As in Exercise 13, 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).
=+d) How large would the sample size have to be to make the margin of error half as big in the 95% confidence interval?
=+c) How would the confidence interval change if the confidence level had been 99% instead of 95%?
=+a) What sample size is needed if you wish to be 95% confident that your estimate is within 0.02 of the true proportion?
=+b) What sample size is needed if you wish to be 99%confident that your estimate is within 0.02 of the true proportion?
=+c) What sample size is needed if you wish to be 95% confident that your estimate is within 0.05 of the true proportion?
=+18. As in Exercise 17, you want to estimate the proportion of students in your class having part-time jobs. However, from some research in other classes, you believe the proportion will be near
=+a) What sample size is needed if you wish to be 95%confident that your estimate is within 0.02 of the true proportion?
=+b) What sample size is needed if you wish to be 99%confident that your estimate is within 0.02 of the true proportion?
=+c) What sample size is needed if you wish to be 95% confident that your estimate is within 0.05 of the true proportion?
=+19. It’s believed that as many as 25% of adults over age 50 never graduated from high school. We wish to see if this percentage is the same among the 25 to 30 age group.
=+a) How many of this younger age group must we survey in order to estimate the proportion of nongrads to within 6%with 90% confidence?
=+b) How would the confidence interval change if the sample size had been 300 instead of 200? (Assume the same sample proportion.)
=+a) How would the confidence interval change if the confidence level had been 90% instead of 95%?
=+c) Construct an approximate 95% confidence interval for the true proportion p by taking {2 SEs from the sample proportion.
=+13. 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). Which of the following are true?
=+a) 95% of the coworkers fall in the interval (0.409, 0.551).
=+b) We are 95% confident that the proportion of coworkers
=+who have received this year’s flu vaccine is between 40.9%and 55.1%.
=+c) There is a 95% chance that a random selected coworker has received the vaccine.
=+d) There is a 48% chance that a random selected coworker has received the vaccine.
=+e) We are 95% confident that between 40.9% and 55.1%of the samples will have a proportion near 48%.
=+14. From the survey in Exercise 11, which of the following are true? If they are not true, explain briefly why not.
=+a) 95% of the 200 students are in the interval (0.283, 0.417).
=+b) The true proportion of students who use laptops to take notes is captured in the interval (0.283, 0.417) with probability 0.95.
=+c) There is a 35% chance that a student uses a laptop to take notes.
=+d) There is a 95% chance that the student uses a laptop to take notes 35% of the time.
=+e) We are 95% confident that the true proportion of students who use laptops to take notes is captured in the interval (0.283, 0.417).Section 9.3
=+15. From the survey in Exercise 11,
=+b) What is the standard error of the sample proportion?
=+b) Suppose we want to cut the margin of error to 4%.What’s the necessary sample size?
=+25. Stock picking. In a large Business Statistics class, the professor has each person select stocks by throwing 16 darts at pages of the Wall Street Journal. They then check to see whether their
=+a) What shape would you expect this histogram to be?Why?
=+b) Where do you expect the histogram to be centered?
=+c) How much variability would you expect among these proportions?
=+d) Explain why a Normal model should not be used here.
=+26. Quality management. Manufacturing companies strive to maintain production consistency, but it is often difficult for outsiders to tell whether they have succeeded. Sometimes, however, we can
=+a) If we plot a histogram showing the proportions of green candies in the various bags, what shape would you expect it to have?
=+b) Can that histogram be approximated by a Normal model? Explain.
=+c) Where should the center of the histogram be?
=+d) What should the standard deviation of the proportion be?
=+27. Bigger portfolio. The class in Exercise 25 expands its stock-picking experiment.
=+a) The students use computer-generated random numbers to choose 25 stocks each. Use the 68–95–99.7 Rule to describe the sampling distribution model.
=+b) Confirm that you can use a Normal model here.
=+c) They increase the number of stocks picked to 64 each.Draw and label the appropriate sampling distribution model. Check the appropriate conditions to justify your model.
=+d) Explain how the sampling distribution model changes as the number of stocks picked increases.
=+d) What does the Success/Failure Condition say about the choice you made in part c?
=+c) Looking at the histograms in Exercise 22, at what sample size would you be comfortable using the Normal model as an approximation for the sampling distribution?
=+c) What sample size would produce a margin of error of 3%?
=+20. In preparing a report on the economy, we need to estimate the percentage of businesses that plan to hire additional employees in the next 60 days.
=+a) How many randomly selected employers must we contact in order to create an estimate in which we are 98%confident with a margin of error of 5%?
=+b) Suppose we want to reduce the margin of error to 3%.What sample size will suffice?
=+c) Why might it not be worth the effort to try to get an interval with a margin of error of 1%?Chapter Exercises
=+21. Send money. When they send out their fundraising letter, a philanthropic organization typically gets a return from about 5% of the people on their mailing list. To see what the response rate
=+22. Character recognition. An automatic character recognition device can successfully read about 85% of handwritten credit card applications. To estimate what might happen when this device reads a
=+23. Send money, again. The philanthropic organization in Exercise 21 expects about a 5% success rate when they send fundraising letters to the people on their mailing list. In Exercise 21 you
=+a) According to the Normal model, what should the theoretical mean and standard deviations be for these sample sizes?
=+b) How close are those theoretical values to what was observed in these simulations?
=+c) Looking at the histograms in Exercise 21, at what sample size would you be comfortable using the Normal model as an approximation for the sampling distribution?
=+d) What does the Success/Failure Condition say about the choice you made in part c?
=+24. Character recognition, again. The automatic character recognition device discussed in Exercise 22 successfully reads about 85% of handwritten credit card applications.In Exercise 22 you looked
=+a) According to the Normal model, what should the theoretical mean and standard deviations be for these sample sizes?
=+b) How close are those theoretical values to what was observed in these simulations?
=+28. More quality. Would a bigger sample help us to assess manufacturing consistency? Suppose instead of the 50-candy bags of Exercise 26, we work with bags that contain 200 M&M’s each. Again we
=+1. If the proportion needing help is independent from day to day, what shape would you expect his histogram to follow?
=+6 If the organization had polled more people, would the interval’s margin of error have likely been larger or smaller?
=+How large a sample would she need to take to have a 99% interval half as wide? One quarter as wide?
=+What if she wanted a 99% confidence interval that was plus or minus 3 percentage points?
=+ How large a sample would she need?
=+Identify the ethical dilemma in this scenario.
=+• What are the undesirable consequences?
=+• Propose an ethical solution that considers the welfare of all stakeholders
=+1. An investment website can tell what devices are used to access the site. The site managers wonder whether they should enhance the facilities for trading via “smart phones”
=+so they want to estimate the proportion of users who access the site that way (even if they also use their computers sometimes). They draw a random sample of 200 investors from their customers.
=+a) What would you expect the shape of the sampling distribution for the sample proportion to be?
=+b) What would be the mean of this sampling distribution?
=+c) If the sample size were increased to 500, would your answers change? Explain.
=+2. The proportion of adult women in Latvia is approximately 54%. A marketing survey telephones 400 people at random.
=+a) What proportion of women in the sample of 400 would you expect to see?
=+b) How many women, on average, would you expect to find in a sample of that size? (Hint: Multiply the expected proportion by the sample size.)
=+5 Our margin of error was about {3%. If we wanted to reduce it to {2%without increasing the sample size, would our level of confidence be higher or lower?
=+4 If we wanted to be 98% confident, would our confidence interval need to be wider or narrower?
=+2. Is the assumption of independence reasonable?
=+1 You want to poll a random sample of 100 shopping mall customers about whether they like the proposed location for the new coffee shop on the third floor, with a panoramic view of the food court.
=+2 Where would the center of that histogram be?
=+3 If you think that about half the customers are in favor of the plan,
=+what would the standard deviation of the sample proportions be?

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