A professor claims that the average score on a recent exam w

A professor claims that the average score on a recent exam was 83. Assume that the test scores are normally distributed. You ask some people in class how they did, and you record the following scores: 82, 77, 85, 76, 81, 91, 70, and 82. Suppose you want to test whether the professors statement was correct against the alternative that his claim is not correct.

1. Perform a 10% level of significance test about the professors claim. State clearly the null and alternative hypotheses in terms of appropriate parameter, formula and value of the test statistic, the rejection region and the conclusion in the context of the current problem.

Solution

Set up Hypothesis
Null, H0: U=83
Alternate, H1: U!=83
Test Statistic
Population Mean(U)=83
Sample X(Mean)=80.5
Standard Deviation(S.D)=6.302
Number (n)=8
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =80.5-83/(6.302/Sqrt(7))
to =-1.122
| to | =1.122
Critical Value
The Value of |t | with n-1 = 7 d.f is 1.895
We got |to| =1.122 & | t | =1.895
Make Decision
Hence Value of |to | < | t | and Here we Do not Reject Ho
P-Value :Two Tailed ( double the one tail ) -Ha : ( P != -1.122 ) = 0.2989
Hence Value of P0.1 < 0.2989,Here We Do not Reject Ho