MGMT 650 Fall 2016 Problem Set 4 *Note: For problems, complete the 5-step process: Step 1: State the null hypothesis and the alternate hypothesis. Step 2: Select the level of significance. Step 3: Evaluate the test statistic. Step 4: Formulate a decision rule with critical value of test statistic. Step 5: Compare the test statistic to the critical value and make the decision about H0. 1. a. b. c. d. e. The hypothesis is that the mean IQ of the population is 100. A random sample of six IQs in this population resulted in the following values: 118, 105, 112, 119, 105, and 111. Using the .05 significance level, is it possible to conclude that the mean is different from 100? State the hypotheses. State the decision rule. Compute the test statistic What is your conclusion? What is the p-value. What does it mean? 2. The administration of UMUC is concerned that a significant number of their students are not graduating in 4 years. One factor that may contribute to the low graduation rate after 4 years could be the number of students that change their majors after the first year at UMUC. A nationwide study found that about 50% of first year students at any university change their major after the first year. UMUC sampled 100 students and found that 48 had changed their major after their first year. At the .05 level, is the proportion of students at UMUC that change their major higher than 50%? a. b. c. d. e. State the hypotheses. State the decision rule. Compute the test statistic What is your conclusion? What is the p-value. What does it mean? 3. The director for Weight Watchers International wants to determine if the changes in their program results in better weight loss. She selected 25 Weight Watcher members at random and compared their weight 6 months later to weight at the start of the program. Here are the results: (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.) The director used .05 as the significance level. Use Excel to test H0: After - Before 0 vs. HA: After - Before < 0. For each paired difference, compute After - Before. In Data Analysis, t-Test: Paired Two Sample for means, select the After data for Variable 1 Range. 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 region and negative lower critical value. a. b. c. d. e. State the hypotheses. State the decision rule. Compute the test statistic What is your conclusion? What is the p-value. What does it mean? Perso n Befor e After 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 176 192 185 177 196 178 196 181 158 201 191 193 176 212 177 183 210 198 157 213 161 177 210 192 178 164 191 176 176 185 169 196 172 158 193 185 189 175 210 173 180 204 192 152 200 161 166 203 186 170 4. A random sample of 20 purchases showed the following amounts (in $) 39.0 5 37.9 1 56.9 5 21.5 7 75.1 6 2.73 34.3 5 81.5 8 40.8 3 74.3 32.9 2 64.4 8 47.8 0 38.2 4 47.5 4 47.5 1 51.9 6 11.7 2 32.9 8 65.6 2 An analyst wants to know if the mean purchase amount of all transactions is at least $40? Assume a significance level of 5%. a) What is the null hypothesis? b) Is the alternative hypothesis one-sided or two-sided? c) What is the value of the test statistic? d) What is the p-value of the test statistic? e) What do you conclude at sigma = .05? 5. UMUC's Business Management department is concerned that dual degree students may be receiving lower grades than the regular management students. Two independent random samples have been selected. 150 observations from population 1 (dual degree students) and 150 from population 2 (management only degree.) It is known from past studies that the population variance for dual degree students is 4.5 and the population variance for management only students is 5.0. The current study found that the mean score for the dual degree students is 79 and the mean score for the management only students is 82. Is there evidence that the dual degree students are receiving lower grades than regular management students? a. b. c. d. e. State the hypotheses. State the decision rule. Compute the test statistic What is your conclusion? What is the p-value. What does it mean? 6. A webmaster wants to know if a website he designed is showing increased page views per visit. A customer is randomly sent to one of two different websites, offering the same products, but with different designs. The page views are below: web a web b 9 10 4 13 14 2 7 3 2 7 a) Test the null hypothesis that the mean number of page visits is the same for the two websites. What do you conclude at alpha = 0.05? b) Find a 95% confidence interval for the mean difference in page views from the two websites. c) Where is 0 and what does that say about the null hypothesis that the mean difference is 0