A random sample of 60 second graders in a certain school district are given a standardized mathematics skills test. The sample mean score is = 52. Assume the standard deviation of test scores is σ = 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.
a) State the appropriate null and alternate hypotheses. b) Compute the P-Value.

a) Null hypothesis:  

Alternative hypothesis:  

b)    

Step-by-step explanation:

Information suministred

represent the sample mean score for the econd graders

represent the population standard deviation

sample size  

represent the value that we want to test

z would represent the statistic

represent the p value for the test (variable of interest)  

Part a: System of hypothesis

We want to check if the second graders in her school district have greater math skills than the  nationwide average, the system of hypothesis would be:  

Null hypothesis:  

Alternative hypothesis:  

Part b

The statistic is given by:

 (1)  

Replacing into the formula we got:

We have a right tailed test then the p value would be:  

answer: city needs 2.4 inches of rainfall more to match the record of 40 inches.

step-by-step explanation:

since we have given that

total annual rainfall a city record = 40 inches

this year, total rainfall recorded = 37.6 inches

number of inches of rainfall   is needed to match the record of 40 inches is given by

hence, city needs 2.4 inches of rainfall more to match the record of 40 inches.