W8 Q8

M650 Question 1 The director for Weight Watchers International wants to determine if a change in their program results in better weight loss at the 5% significance level. She selected 25 Weight Watcher members at random. The weight of each member was recorded at the start and end of the program 6 months later. The results are in this excel file: Person Before After 1 176 164 2 192 191 3 185 176 4 177 176 5 196 185 6 178 169 7 196 196 8 181 172 9 158 158 10 201 193 11 191 185 12 193 189 13 176 175 14 212 210 15 177 173 16 183 180 17 210 204 18 198 192 19 157 152 20 213 200 21 161 161 22 177 166 23 210 203 24 192 186 25 178 170 The weight in the column labeled "After" represents their weights six months later and "Before" represents their weight at the start of the program. Keep the Excel file open for the next 3 questions. What are the Null and Alternate Hypotheses?  H0: After – Before ≥ 0; HA: After – Before < 0  H0: After – Before = 0; HA: After – Before ≠ 0  H0: After – Before > 0; HA: After – Before ≤ 0  H0: After – Before ≥ 0; HA: After – Before > 0

M650 Question 2 Test H0 of Question 1 using Excel Data Analysis, t-Test: Paired Two Sample for means. In Data Analysis. Select the After data for Variable 1 Range. What is the t-statistic (t-score) in the Data Analysis output?  9.321  None of the answers match my calculation result.  -9.321  -7.087  7.087 Question 3 Continuing with Weight Watchers.xlsx, what is the critical t-value in the Data Analysis output?  -7.861  -3.645  -1.711  -5.614  None of the answers match my result. Question 4 Continuing with Weight Watchers.xlsx, what is your decision?  Do not reject the NULL Hypothesis because the test statistic is less than the critical value.  Do not reject the NULL Hypothesis because the test statistic is greater than the critical value.  None of the answers match my result.  Reject the NULL Hypothesis because the test statistic is less than the critical value.  Reject the NULL Hypothesis because the test statistic is greater than the critical value. Question 5 A new drug is created to help people with depression. When testing the drug, what are the null and alternative hypotheses?  H0: The drug XYZ-10 will not reduce depression. HA: The drug XYZ-10 will reduce depression.  H0: The drug XYZ-10 will reduce depression.

M650 1. Type 1 error 2. Type 2 error 3. Not an error 4. α 5. β 6. 1 - β Question 9 For a test of the population proportion, what is the distribution of the test statistic?  Z  F  T Question 10 H0: μ ≤ 16.96 vs. HA: μ > 16.96 What is the test statistic for sample of size 25, mean 11.50, and standard deviation 1.36? Enter the test statistic with 2 decimal places.  -20.07 Question 11 A sample of size 20 yields a sample mean of 23.5 and a sample standard deviation of 4.3. Test H0: Mean ≥ 25 at α = 0.10.  None of the answers match my calculation result.  Pvalue 0.068. H0 rejected. Conclude mean < 25  Pvalue 0.932. H0 not rejected. Conclude mean ≥ 25 plausible  Pvalue 0.135. H0 not rejected. Conclude mean ≥ 25 plausible Question 12 The results of sampling independent populations:

M650 sample 1 from population 1 o mean 80 o population variance 3 o sample size 25 sample 2 from population 2 o mean 81 o population variance 2 o sample size 50 Test H0: (population1 mean - population2 mean) ≤ 0 at α = 0.05. HA: (population1 mean - population2 mean) > 0.  Pvalue 0.0062. H0 rejected. Conclude difference of means > 0.  None of the answers match my calculation result.  Pvalue 0.0124. H0 rejected. Conclude difference of means > 0.  Pvalue 0.9938. H0 not rejected. Conclude difference of means ≤ 0 is plausible Question 13 The results of sampling independent populations: sample 1 from population 1 o mean 1000 o sample standard deviation 400 o sample size 50 sample 2 from population 2 o mean 1250 o sample standard deviation 500 o sample size 75 Test the H0: population1 mean = population2 mean at α = 0.01. HA: population1 mean ≠ population2 mean. Assume the variances are separate.  Test statistic of 65.28 > Critical value of -2.36. H0 is not rejected. Conclude difference of means = 0.  None of the answers match my calculation result.  None of the answers match my calculation result.  Test statistic of -3.09 < Critical value of -1.29. H0 rejected. Conclude difference of means ≠ 0.