One study examined the personal values of 116 students studying mortuary science with the intention of becoming funeral directors (Shaw \& Duys, 2005). The students completed a well-established survey measuring different work-related values, one of which was the extent to which the student valued social interaction. The researchers tested the difference between the mean social interaction score of these students \(\mathrm{X}^{-}=\) 12.91 with an estimated population mean \((\mu)\) of 14.50 and a standard deviation \((\sigma)\) of 2.87 .

a. State the null and alternative hypotheses \(\left(\mathrm{H}_{0}\right.\) and \(\left.\mathrm{H}_{1}\right)\).

b. Make a decision about the null hypothesis. 

1. Set alpha (a), identify the critical values, and state a decision rule. 

2. Calculate a statistic: \(z\)-test for one mean. 

3. Make a decision whether to reject the null hypothesis. 

4. Determine the level of significance.

c. Draw a conclusion from the analysis.

d. What might you say about the extent to which mortuary science students value social interaction as part of their jobs?