A psychologist was interested in whether different TV shows lead to a more positive outlook on life. People were split into 3 groups and then taken to a room to view a program. The three groups saw: The American Got Talent show, BSC News and DSTV. After the program a blood sample was taken and serotonin levels measured (remember more serotonin means more happy). multicolumn(2)(|c|)( TV shows ) American Got Talent show & BSC News & DSTV 11 & 8 & 10 7 & 6 & 6 6 & 7 & 12 Carry out a one-way ANOVA to test the hypothesis that some TV shows make people happier than others. Test at 5 % level of significance.

# Brief Explanations:A one-way ANOVA (Analysis of Variance) is used to determine if there are statistically significant differences between the means of three or more independent groups. Here, we test if the serotonin levels differ significantly among the three TV show groups at a 5% significance level.# Answer:1. **State the Hypotheses:** - Null Hypothesis ( ): There is no difference in mean serotonin levels among the three TV show groups. - Alternative Hypothesis ( ): At least one group has a different mean serotonin level.2. **Calculate Group Means:** - American Got Talent: - BBC News: - DSTV: 3. **Calculate the Overall Mean:** - Overall Mean: 4. **Calculate the Sum of Squares Between Groups (SSB):** 5. **Calculate the Sum of Squares Within Groups (SSW):** 6. **Calculate the Degrees of Freedom:** - Between Groups: - Within Groups: 7. **Calculate the Mean Squares:** - Mean Square Between (MSB): - Mean Square Within (MSW): 8. **Calculate the F-ratio:** 9. **Determine the Critical Value and Compare:** - For and at , the critical F-value from F-distribution tables is approximately 5.14. - Since is less than 5.14, we fail to reject the null hypothesis.10. **Conclusion:** - There is no statistically significant difference in serotonin levels among the three TV show groups at the 5% significance level.# Answer:- Null Hypothesis ( ): There is no difference in mean serotonin levels among the three TV show groups.- Alternative Hypothesis ( ): At least one group has a different mean serotonin level.- F-ratio: 0.710- Critical F-value: 5.14- Conclusion: Fail to reject the null hypothesis. There is no significant difference in serotonin levels among the groups.