Question

3. Life Satisfaction scores for several individuals are shown below. Test whether these scores come from a population with a mean of 50. You may assume that these scores come from a normally distributed population. 67 58 59 75 74 74 67

Answer 1

Null hypothesis: H:u= 50 That is, these scores come from a population with a mean of 50. Alternative hypothesis: H: 4 50 That is, these scores come from a population with a mean different from 50. Rejection rule: If p-values a(=0.05). then reject the null hypothesis H.. Excel add-in (Mega Stat) procedure:

Step 1: In EXCEL, Select Add-Ins > Mega Stat > Hypothesis Tests. Step 2: Choose Mean Vs Hypothesized Value Step 3: Choose Data Input. Step 4: Enter A1:A3 Under Input Range. Step 5: Enter 50 Under Hypothesized mean. Step 6: Check t-test, enter Confidence level as 95.0. Step 7: Choose not equal in alternative. Step 8: Click OK Excel add-in (Mega Stat) output:

Hypothesis Test: Mean vs. Hypothesized Value 50.000 hypothesized value 67.714 mean Sample 7.111 std. dev. 2.688 std. error 7n 6 df 6.59 t .0006 p-value (two-tailed) Test Statistic: t=6.59. P-value = 0.0006. Conclusion: Use a significance level, a = 0.05 Here, p-value is 0.0006, which is less than the value of a -0.05. That is, p-value (=0.0006) sa(=0.05). Therefore, by the rejection rule, reject the null hypothesis H. Interpretation: There is insufficient evidence at level of significance a = 0.05. That is, these scores come from a population with a mean different from 50.