A national survey showed that 75 of all restaurant employees

A national survey showed that 75% of all restaurant employees report that work stress has a negative impact on their personal lives.? The human resources manager of a chain of restaurants wants to know if employees at his restaurants would report negative impacts of work stress less frequently than the nation as a whole.? He randomly chooses 100 employees and 70 answer \"yes\" to the question, \"Does work stress have a negative impact on your personal life?\"

Solution

1)mean = 70 /100 = 0.7
s.d = root( p * (1-p) / n) = 0.0458

2) yes the normal distn is a good model for the sampling distn of p-hat.

n=100 ,p = .7 so,np=70,nq =30 both >10,so here we can assume normal approximations!

3) p(sample prop <= 0.70) =p( z <= 0.70-.75/ root over((.75* .25) /100) [using CLT]
=p(z <= -1.1547) =0.1241066

4)test H0:p=0.75 ag H1:p < 0.75

here p0=0.75

z= phat-p0/ root( p0(1-p0) /n)

= 0.70-0.75/ root( 0.75*0.25 /100) = -1.1547

p(z <= -1.1547) =0.1241066
which is greater than 0.05(the typical cutoff for blowing the whistle on a claim about a population value)
so,we can conclude that the sample data does not provide enough evidence that employees at his restaurents would report negative impacts of work stress less frequently than the nation as a whole.The restaurent data are compatible with the national survey results.