Solution:
Given No. of sample = 64
Sample Mean = 51.80
Population mean = 50
Population Standard deviation =15
Here sample size is greater than 30 and data is normal so we will use Z test and standard devaition is also known
Z = (51.8-50)/15/sqrt(64) = 1.8/15/8 = 0.96
Here Null Hypothsis is School Maths mean score <= 50
Alternate Hypothesis is School Maths mean score > 50
So it is right tailed test so P- value = (1- 0.8315) = 0.1685
Alpha = 0.05
so here we can see that p-value is greater than alpha value so we have weak evidence against the null hypothesis so we are failed to reject the null hypothesis.
and its answer is C. i.e. there is not enough evidence to conclude that the second graders in her district have greater math skill.
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