A local supermarket surveyed the results of game day shopper

A local supermarket surveyed the results of game day shoppers compared to their typical shoppers.  The typical store shopper buys an average of $38.51 in a single trip. In a sample of 13 shoppers chosen at random on game day, the average of the game day shoppers spent $54.87 with a sample standard deviation of $6.27.  The sample data appears to be more or less normally distributed.  Does the sample data support the idea that game day shoppers make purchases that are about the same as the store

Solution

Set Up Hypothesis
Null Hypothesis H0: U=38.51
Alternate Hypothesis H1: U!=38.51
Test Statistic
Population Mean(U)=38.51
Sample X(Mean)=54.87
Standard Deviation(S.D)=6.27
Number (n)=13
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =54.87-38.51/(6.27/Sqrt(12))
to =9.408
| to | =9.408
Critical Value
The Value of |t ?| with n-1 = 12 d.f is 2.179
We got |to| =9.408 & | t ? | =2.179
Make Decision
Hence Value of | to | > | t ?| and Here we Reject Ho
P-Value :Two Tailed ( double the one tail ) -Ha : ( P != 9.4078 ) = 0
Hence Value of P0.05 > 0,Here we Reject Ho

NO, game day shoppers make purchases that are not the same as the store