Page 1 of 3 MGMT 650 Fall 2016 Problem Set 3 (Last updated 10/25/2016) 1. Confidence Interval: 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? Problem 1 is worth 25% 10 points for the first correct confidence interval 5 points for the second correct confidence interval 10 points for describing an outlier and how it affects a confidence interval 2. Confidence Interval: A sample from a normal population has size = 109 observations, mean = 7.99, and standard deviation = 3.67. What is the 95 percent confidence interval for the population mean? Use the Excel function, =CONFIDENCE.T() to find the margin of error. The inputs of CONFIDENCE.T are the probability (alpha), the sample standard deviation, and the sample size. Find the confidence limits = sample mean margin of error. Problem 2 is worth 20%. 10 points for using the Excel function 5 points for each correct limit Page 2 of 3 3. Confidence Limit: 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. Again, use CONFIDENCE.T a. Using the .10 level of significance, is there evidence that the population mean is above $300? b. What is your answer if x(bar) = $315.40, s = $75.00, and the level of significance is 0.05? c. What is your answer if x(bar) = $305.11, s = $43.20, and the level of significance is 0.10? d. 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? Problem 3 is worth 25% Parts a, b, and c are worth 5 points each Part d is worth 10 points 4. t-Test: Paired Two Sample for Means In week 7 we will study Hypothesis Testing in detail. For answering the following question, you need a brief idea of what hypothesis testing is. Please read the following introduction: http://www.socialresearchmethods.net/kb/hypothes.php The director for Weight Watchers International wants to determine if the a new program results in better weight loss. She selected 25 Weight Watcher members at random. The weight in the column labeled \"After\" represents their weights six months later and \"Before\" represents their weight at the start of the six-month period. Person 1 weight change was 164 - 176 = -12 lbs, a weight loss. The director used .05 as the significance level. Use Excel Data Analysis, t-Test: Paired Two Sample for means, to test H0: Mean difference (After - Before) 0, weight is gained, vs. HA: Mean difference < 0, weight is lost. For each pair of data, we compute After - Before. So, in Data Analysis, select the After data for Variable 1 Range and the Before data for Variable 2. Note that the critical value output by Data Analysis for this test is always positive. In this problem, the sign of the critical value is negative corresponding to a 1-tailed test with lower reject Page 3 of 3 region and negative lower critical value. In your conclusion, compare the test statistic to the critical value and state your decision about whether to reject or not reject H0, and whether to put the new program into use or not. Person 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 After 164 191 176 176 185 169 196 172 158 193 185 189 175 210 173 180 204 192 152 200 161 166 203 186 170 Before 176 192 185 177 196 178 196 181 158 201 191 193 176 212 177 183 210 198 157 213 161 177 210 192 178 Problem 4 is worth 30% Correctly stating the null and alternative hypotheses is worth 5% Choosing the correct Data Analysis test is worth 5% Correctly computing the test statistic and critical value is worth 10% Correct conclusion is worth 10%