A researcher working at a particular company wants to know if workers\' health w

Question

A researcher working at a particular company wants to know if workers' health would improve tf they were given extra days A off. In this company, all workers undergo a standard physical exam twice a year and after each exam an overall health rating (higher scores mean better health) is automatically provided to the company. To conduct the study, the researcher selected five workers at random. She then arranged to have these five workers receive an additional 2 days off every month over the period between health exams. She then compared the health scores on the two exams. Do the results shown In the table below support the notion that extra days off improves health? (Use the.05 level.) Use the five steps of hypothesis testing Health Rating, Before and After Period of Extra Days Off

Explanation / Answer

Step 1: Assuptions used in the process:

1. The samples are taken randomly.

2. The variable health rating is a quantitative , measured on a continuous scale.

Step 2; Null hypothesis: There is no difference in health rating before and after period of extra days off

alternative hypothesis: The health rating improved after period of extra days off

Step 3: Here the samples are dependent, repeated measures design, use t- test for paired differences

t = d-bar * sqrt(n)/SD ; where di= health rating after period of extra days off-health rating before

Calculations:

Conclusion: The p-value of the test statistic is 0.04 which is less than 0.05 so reject the null hypothesis

Hence conclude that the health rating improved after period of extra days off

t-Test: Paired Two Sample for Means After Before Mean 74.2 72 Variance 325.7 328.5 Observations 5 5 Pearson Correlation 0.99206 Hypothesized Mean Difference 0 df 4 t Stat 2.157277 P(T<=t) one-tail 0.048593 t Critical one-tail 2.131847 P(T<=t) two-tail 0.097185 t Critical two-tail 2.776445

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