Not sure how to answer this statistics question or if I understand what is being asked.

Question

The first question is what I am unsure about. I don't know if it is asking what is actually unusual (like the grade value having 100 as the mean) about the test or if it is asking something else like what is rare (unusual because of how small the number is) about the p-value.

A new standardized test is required to have a µ = 100 and σ = 10. A class of 30 students completed the test with a mean grade of 95. Conduct a hypothesis test at α = .05 to determine whether the claim that µ = 100 can be supported using the p-value approach and complete the following.

What is unusual about this hypothesis test? (All other questions aside from this one seem to be straightforward, am I overthinking this?)

State the null and alternative hypotheses in words and in statistical symbols.

What statistical test should be used and why?

What is the value of the test statistic and the p-value of that outcome?

Interpret the outcome in terms of the original claim.

Answer 1

The null hypothesis is that the population distribution is $\mathsf{Norm}(100, 10).$ So it seems you're to test $H_0: \mu = 100$ against $H_a: \mu \ne 100$ with the (unusual?) additional information that $\sigma = 10.$

Then if $\bar X = 95$ and $n = 30,$ the test statistic is $Z = -2.738613.$ Because $|Z| = 2.74 > 1.96$ it seems you'll reject $H_0$ at the 5% level of significance.

I'll let you show the formula for computing $Z$ and use normal tables to get the P-value (remembering to use both tails in the computation because it's a two-sided test).

The wording of the problem seems a bit strange, but this is the only approach that seems sensible.

If I understand the question correctly, the following Minitab output is relevant:

One-Sample Z 

Test of μ = 100 vs ≠ 100
The assumed standard deviation = 10

 N   Mean  SE Mean      95% CI          Z      P
30  95.00     1.83  (91.42, 98.58)  -2.74  0.006

Note: Minitab often rounds P-values to three decimal places.