MGMT 650 Fall 2016 Problem Set 3 1. Compute a 95% confidence interval for the population mean, based on the sample numbers 21, 22, 33, 34, 25, 26, and 139. Change the last value to 29 and re-compute the confidence interval. What is an outlier and how does it affect the confidence interval? 2. The director of admissions at the University of Maryland, University College is concerned about the high cost of textbooks for the students each semester. A sample of 25 students enrolled in the university indicates that x(bar) = $315.40 and s = $43.20. a. Using a 90% confidence interval, is there evidence that the population mean is above $300? What is the chance you may be wrong? b. What is your answer if x(bar) = $315.40, s = $75.00, and the confidence interval is 95%? c. Based on the information in part a, what decision should the director make about the books used for the courses if the goal is to keep the cost below $300? 3. Explain the difference between the terms \"standard deviation\" and \"standard error\". 4. Explain the difference between sampling error and sampling bias. Give one example of a biased cluster sample. 5. The proportion of adult women in the US is 51%. A marketing survey telephones 400 people at random. a) How many women on average, would you expect to find in a sample of 400? b) What is the sampling distribution of the observed proportion that are women? c) What is the standard deviation of that proportion? 6. According to recent studies, cholesterol levels in healthy US adults average 215 mg/dL, with a standard deviation of 30 mg/dL and are Normally distributed. If the cholesterol levels of a sample of 42 healthy US adults is taken a) What shape should the sampling distribution of the mean have? b) What would the mean of the sampling distribution be? c) What would the standard deviation be? d) If the sample size were increased to 100, would your answers to the above questions change? e) What is the probability that the mean cholesterol level of the sample will be between 205 and 225? 7. From a survey of 250 workers you find that 155 would like the company to provide on-site day care. a) What is the value of the sample proportion, p^ hat? b) What is the standard error of the sample proportion? c) Construct a 95% confidence interval for the true proportion, P. 8. From a survey of coworkers you find that 48% of 200 have already received this year's flu vaccine. A 95% confidence interval is (0.409, 0.551). Which of the following (a - e) are true. a) 95% of the coworkers fall in the interval (.409, .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%. f) How would the confidence interval change if the sample size had been 800 instead of 200? g) Would the confidence interval become smaller or larger if the confidence level had been 90% instead of 95%? h) Would the confidence interval become smaller or larger if the confidence level had been 99% instead of 95%? 9. Suppose you want to estimate the proportion of traditional college students on your campus who own their own car. You have no preconceived idea of what that proportion might be. 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? d) What if you know from some prior research on other college campuses that you believe the proportion will be near 20%. How would a), b), and c) change? 10. What is the Central Limit Theorem? Why is it important in Statistics? 11. Why does confidence intervals and hypothesis testing for means require the \"t\" distribution rather than the \"z\" distribution