A department store claims that their average customer satisf

A department store claims that their average customer satisfaction rating is 28.5...

A department store claims that their average customer satisfaction rating is 28.5. We believe that this is too high so we randomly sample 40 customers and find a sample average of 25.2. If the standard deviation of customer satisfaction for this store is 13.1, what is the probability of observing a sample at least this far below the claimed mean, assuming the claim is tine?

Solution

Set Up Hypothesis
Null Hypothesis H0: U=28.5
Alternate Hypothesis H1: U<28.5
Test Statistic
Population Mean(U)=28.5
Given That X(Mean)=25.2
Standard Deviation(S.D)=13.1
Number (n)=40
we use Test Statistic (Z) = x-U/(s.d/Sqrt(n))
Zo=25.2-28.5/(13.1/Sqrt(40)
Zo =-1.5932
P-Value : Left Tail - Ha : ( P < -1.5932 ) = 0.0556

[ANSWER] 0.0559