17 **Question 17:**A researcher wants to see if factory workers’ productivity levels are affected by watching a documentary on the dangers of capitalism. He measures a sample of \( n = 31 \) workers' productivity levels before and after to determine if there were any differences detected. The researcher observed a test statistic of \( t = -3.69 \). What would be his decision and MOST appropriate conclusion if testing at an alpha of \( \alpha = 0.01 \) level?- Retain Null Hypothesis. There was no significant change in workers’ productivity after viewing the documentary.- Reject Null Hypothesis \( H_0 \). The factory workers' productivity was significantly affected by viewing the documentary.- Reject Null Hypothesis. Factory workers increased their productivity after viewing the documentary.**Question 18:**A political scientist obtained recordings of election-night acceptance speeches of 16 newly elected representatives to the U.S. Congress and counted the number of minutes devoted to fiscal problems in these speeches. Half of the representatives were from rural districts while the other half were from urban districts. If she observed test statistics of \( t = 2.93 \), what would be the correct decision and MOST appropriate conclusion if testing at the alpha \( \alpha = 0.05 \) level?- Reject Null Hypothesis \( H_0 \). The urban politicians spent more time talking about fiscal problems than the rural representatives.- Retain Null Hypothesis \( H_0 \). There was no difference between the urban and rural politicians' time talking about fiscal problems.- Retain Null Hypothesis \( H_0 \). There is no evidence that the politicians spent a different amount of time speaking about fiscal issues.**Question 19:**An independent samples study exhibited the following sample characteristics: Sample 1, \( n = 28 \) with a sum of squared deviations (SS1) = 302. Sample 2, \( n = 31 \) with a sum of squared deviations (SS2) = 257.8. Calculate the estimated standard error of differences between means for these samples. (Be sure to round to the second decimal place.)

It is needed to test, whether the there is any significant change in worker’s productivity after viewing the documentary.It is needed to test, whether the there is any significant change in worker’s productivity after viewing the documentary. Consider the hypotheses are as follows: Null hypothesis: H0: There is no significant change in worker’s productivity after viewing the documentary. Alternative hypothesis: H1: There is a significant change in worker’s productivity after viewing the documentary Here, the observations are taken on same workers on two different times. The sample units are independent to each other and, the population observations are correlated. Thus, it is not a independent sample t-test. Thus, the most appropriate test is paired t test or dependent sample t-test. The sample size is n = 31. The value of sample test statistic is t = -3.69. The degrees of freedom for the test statistic is 31 – 1 = 30. Consider the level of significance is α = 0.05. Hence, the P-value using the EXCEL formula =T.DIST(-3.69,30,TRUE), is 0.0004. Decision rule: If P-value is less than or equal to the level of significance, then reject the null hypothesis. Otherwise fail to reject the null hypothesis. Conclusion: Here, the P -value of 0.0004 is less that the level of significance of 0.05. Hence, reject the null hypothesis. That is, “Reject Null Hypothesis (H0), The factory workers productivity was significantly affected by viewing the documentary”.

Math

Statistics

A researcher wants to see if factory workers' productivity levels are affected by watching a documentary on the dangers of capitalism. He measures a sample ofn-31 workers productivity levels before and after to determine if they were affected. The researcher observed a test statisticoft-3.69. What would be his decision and MOST approprlate conclusion if testing at an alpha level - 0.05? O Retain Null Hypothesis. There was no significant change in workers' productivity after viewing the documentary. Reject Null Hypothesis (HO). The factory workers productivity was significantly affected by viewing the documentary. Reject Null Hypothesis. Factory workers increased their productivity after viewing the documentary.