Arandom sample of 64 second-graders in a certain school district are given a standardized mathematics skills test. the sample mean score is 51.48 . assume the standard deviation for the population of test scores is 15. the nationwide average score on this test is 50. the school superintendent wants to know whether the second-graders in her school district have greater math skills than the nationwide average. perform the hypothesis test and compute the p-value?

Given : The sample mean score is 51.48 .

            The standard deviation for the population of test scores is 15.

             The nationwide average score on this test is 50.

To Find :  Perform the hypothesis test and compute the P-value?

Solution:

Sample size = n = 64

Since n > 30

So, we will use z test over here

We are supposed to find The school superintendent wants to know whether the second-graders in her school district have greater math skills than the nationwide average.

Hypothesis :

Formula of z test :

Substitute the values

Find the value of P(z) from z table

p(z)=0.7823

Since we are given that we are supposed to find The school superintendent wants to know whether the second-graders in her school district have greater math skills than the nationwide average.

So, p value = 1-P(z)  = 1-0.7823=0.2177

In general , Level of significance is 0.05

So, p value is greater than alpha.

So, we accept the null hypothesis.