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business
business statistics in practice
Business Statistics Plus Pearson Mylab Statistics With Pearson Etext 3rd Edition Norean R Sharpe ,Richard D De Veaux ,Paul Velleman - Solutions
=+b) 95% of the sampled employees paid between $780 and$920 for lunch.c) We’re 95% sure that employees in this sample averaged between $780 and $920 for lunch.M11_SHAR8696_03_SE_C11.indd 388 14/07/14 7:30 AM Exercises 389
=+a) 95% of all employees pay between $780 and $920 for lunch.
=+28. Meal costs. A company is interested in estimating the costs of lunch in their cafeteria. After surveying employees, the staff calculated that a 95% confidence interval for the mean amount of money spent for lunch over a period of six months is ($780, $920). Now the organization is trying to
=+) If this supplement is tested on another sample of cows, there is a 95% chance that their average weight gain will be between 45 and 67 pounds.
=+d) The average weight gain of cows fed this supplement is between 45 and 67 pounds 95% of the time.
=+c) We’re 95% sure that the average weight gain among the cows in this study was between 45 and 67 pounds.
=+a) 95% of the cows studied gained between 45 and 67 pounds.b) We’re 95% sure that a cow fed this supplement will gain between 45 and 67 pounds.
=+27. Marketing livestock feed. A feed supply company has developed a special feed supplement to see if it will promote weight gain in livestock. Their researchers report that the 77 cows studied gained an average of 56 pounds and that a 95% confidence interval for the mean weight gain this
=+c) If we had the same statistics from a sample of 60 stations, what would the 95% confidence interval be now?
=+b) Find the 90% confidence interval for the mean.
=+a) Find a 95% confidence interval for the mean price of regular gasoline in that region.
=+26. Confidence intervals and sample size, part 2. A confidence interval for the price of gasoline from a random sample of 30 gas stations in a region gives the following statistics:y = +4.49 SE1y2 = +0.06
=+) If we had the same statistics from a sample of 60 customers, what would the 95% confidence interval be now?
=+b) Find a 90% confidence interval for the mean price of dinner.
=+a) Find a 95% confidence interval for the mean price of dinner.
=+25. Confidence intervals and sample size. A confidence interval for the amount of money spent on dinner from a random sample of 30 customers at a local restaurant gives the following statistics:y = +4.39 s = +0.39
=+24. Confidence intervals, part 2. Describe how the width of a 95% confidence interval for a mean changes as the sample size (n) increases, assuming the standard deviation remains the same.
=+23. Confidence intervals. Describe how the width of a 95%confidence interval for a mean changes as the standard deviation (s) of a sample increases, assuming sample size remains the same.
=+b) the critical value of t for a 99% confidence interval with df = 102.
=+22. t-models, part 2. Using the t tables, software, or a calculator, estimate:a) the critical value of t for a 95% confidence interval with df = 7.
=+b) the critical value of t for a 98% confidence interval with df = 88.
=+a) the critical value of t for a 90% confidence interval with df = 17.
=+21. t-models. Using the t-tables, software, or a calculator, estimate:
=+b) How large would the sample size have to be to reduce the margin of error to $0.80?Chapter Exercises
=+a) To reduce the margin of error to about $4, how large would the sample size have to be?
=+20. For the confidence interval in Exercise 14 part a:
=+) About how large would the sample size have to be to cut the margin of error by a factor of 10?
=+a) How large would the sample size have to be to cut the margin of error in half?
=+19. For the confidence interval in Exercise 13:
=+18. The analyst in Exercise 8 wants to know if the mean purchase amount of all transactions is at least $40.
=+e) What do you conclude at alpha = 0.05?
=+d) What is the P-value of the test statistic?
=+) What is the value of the test statistic?
=+b) Is the alternative one- or two-sided?
=+a) What is the null hypothesis?
=+17. The charity group from Exercise 7 wants to know if the mean age of all attendees is 25 years old.
=+16. For the confidence intervals of Exercise 14, a histogram of the data looks like this:Amount ($)0 40 80 26 48 Number of Purchases Check the assumptions and conditions for your inference.M11_SHAR8696_03_SE_C11.indd 387 14/07/14 7:30 AM 388 CHAPTER 11 Confidence Intervals and Hypothesis Tests
=+15. For the confidence intervals of Exercise 13, a histogram of the data looks like this:Age 26 10 48 Number of Customers 7.5 22.5 37.5 52.5 Check the assumptions and conditions for your inference.
=+c) How would the confidence interval change if you had assumed that the standard deviation was known to be $20?Section 11.6
=+a) Construct a 90% confidence interval for the mean purchases of all customers, assuming that the assumptions and conditions for the confidence interval have been met.
=+14. For the purchase amounts in Exercise 8:
=+c) How would the confidence interval change if you had assumed that the standard deviation was known to be 10.0 years?
=+b) How large is the margin of error?
=+13. For the ages in Exercise 7:a) Construct a 95% confidence interval for the mean age of all customers, assuming that the assumptions and conditions for the confidence interval have been met.
=+a) a 95% confidence interval based on 24 df.b) a 95% confidence interval based on 99 df.12. Find the critical value t* for:a) a 90% confidence interval based on 19 df.b) a 90% confidence interval based on 4 df.
=+11. Find the critical value t* for:
=+b) How many degrees of freedom would the t-statistic have if the sample size had been 5?Section 11.5
=+10. For the data in Exercise 8:
=+b) How many degrees of freedom would the t-statistic have if the sample size had been 100?
=+a) How many degrees of freedom does the t-statistic have?
=+9. For the data in Exercise 7:
=+b) How would the standard error change if the sample size had been reduced to 10? (Assume that the sample standard deviation did not change.)
=+) Find the standard error of the mean.
=+. A random sample of 24 phone conversation was recorded by a local university switch board and the time spent in conversation (in minutes) was noted below:38.12 2.7 32.82 47.51 36.52 34.2 64 52 26.6 31 5 12.4 32 4 1 17 18 33 12 6 8 42 15 16 The average was 24.45 minutes and the standard
=+b) How would the standard error change if the sample size had been tripled? (Assume that the sample standard deviation did not change.)
=+a) What is the standard error of the mean?
=+7. A group of 26 individuals, randomly selected from those attending a dinner for a local charity group, were surveyed and their ages were noted as below:20 32 34 29 30 30 30 14 29 11 38 22 44 48 26 25 22 32 35 44 35 42 44 44 44 48 The mean was 32.77 years and the standard deviation was 10.195
=+b) As the sample size increases, what’s the expected shape of the sampling model for the mean amount purchased of the sample?Section 11.4
=+a) As their sample size increases, what’s the expected shape of the distribution of amounts purchased in the sample?
=+6. In 2008 and 2009, Systemax bought two failing electronics stores, Circuit City and CompUSA. They have Exercises M11_SHAR8696_03_SE_C11.indd 386 14/07/14 7:30 AM Exercises 387 kept both the names active and customers can purchase products from either website. If they take a random sample of a
=+e) Would you be surprised if the mean weight of the 60 fish caught in the competition was more than 4.5 pounds? Use the 68–95–99.7 Rule.
=+d) The 12 contestants competing each caught the limit of 5 fish. What’s the standard deviation of the mean weight of the 60 fish caught?
=+c) Each contestant catches 5 fish each day. Can you determine the probability that someone’s catch averages over 3 pounds? Explain.
=+b) Explain why you cannot use a Normal model to determine the probability that a largemouth bass randomly selected (“caught”) from the lake weighs over 3 pounds.
=+a) Explain why a skewed model makes sense here.
=+5. Organizers of a fishing tournament believe that the lake holds a sizable population of largemouth bass. They assume that the weights of these fish have a model that is skewed to the right with a mean of 3.5 pounds and a standard deviation of 2.32 pounds.
=+4. As in Exercise 3, BMI levels for New Zealand adults aged 15 and over average about 26 kg/m2, with a standard deviation of about 3.5 kg/m2 and are roughly Normally distributed. If BMI measures of a sample of 42 New Zealand adults are collected, what is the probability that the mean BMI level
=+d) If the sample size were increased to 100, how would your answers to parts a–c change?
=+c) What would its standard deviation be?
=+b) What would the mean of the sampling distribution be?
=+a) What shape should the sampling distribution of the mean have?
=+3. The World Health Organization has described being overweight as a global epidemic that is rapidly becoming a major public health problem. Body Mass Index (BMI) values, often used to measure obesity, show strong variability amongst countries, with New Zealand scoring at the high end. A recent
=+ A real-estate agent has been assigned 10 houses at random to sell this month. She wants to know whether the mean price of those houses is typical. What, if anything, does she need to assume about the distribution of prices to be able to use the Central Limit Theorem? Are those assumptions
=+2. For a sample of 36 houses, what would you expect the distribution of the sale prices to be?
=+c) Each club member computes the average price of his or her games. What shape would you expect the distribution of these averages to have?
=+b) Members of the iPad gamers club each own about 50 games. Pat is one such member. What would you expect the shape of the distribution of game prices on her iPad to be?
=+a) Explain why this is what you would expect.
=+1. Games for the iPad have a distribution of prices that is skewed to the high end.
=+• Propose an ethical solution that considers the welfare of all stakeholders.
=+• What are the undesirable consequences?
=+• Has Mohammed interpreted the confidence interval correctly?
=+• Identify the ethical dilemma in this scenario.
=+How large a sample would be needed to produce a 95% confidence interval with a margin of error of 0.004?
=+11 Suppose the standard deviation of the time it takes this software is only 2 minutes instead of 5. Will this widen or narrow your confidence interval for the mean time it takes to download a movie? Why?
=+10 For which situation would you need a larger sample size to see if the software works: the software really reduces the time by 2 minutes or by 10 minutes on average? Why?
=+Test the hypothesis that the mean is $24.85 (as it was before the redesign) against the alternative that it has increased.
=+The alumni organization finds a confidence interval for the mean starting salary of their recent graduates to be ($55,000, $62,000). They release a statement to prospective students saying that 95% of them will earn between $55,000 and $62,000 their first year on the job. Why is this wrong?
=+8 If they manage to get 60 salaries instead of 20, how will this affect their confidence interval?
=+7 Why do they need to base these confidence intervals on t-models?
=+6 If they are successful at obtaining the salaries of only 20 recent graduates, what should they be concerned about when reporting a confidence interval for mean salaries of all recent grads?
=+Are the assumptions and conditions for making a confidence interval for the mean mirex concentration satisfied?
=+ What does the 95% confidence interval say about that value?
=+he Environmental Protection Agency (EPA) recommends to recreational fishers as a “screening value” that mirex concentrations be no larger than 0.08 ppm.
=+5 If the sample size is doubled, what is the impact on the standard error?
=+4 As the sample size increases, what happens to the standard error, assuming the standard deviation remains constant?
=+3 The entrance exam for business schools, the GMAT, given to 100 students had a mean of 520 and a standard deviation of 120. What was the standard error for the mean of this sample of students?
=+Q uestion What’s the probability that a palette will exceed that limit?
=+how would you expect his histogram of the means to differ from the one in (1)?
=+2 If, instead of averaging all customers on each day, he selects the first 10 for each day and just averages those,
=+1 What shape would you expect for this histogram?
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