Question

1. A random sample of 64 second graders in a certain school district are given a standardized mathematics skills test. The sample mean score is 51.93. 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. Based on your P value, what is the conclusion if we test at 0.05 level of significance?

2. Suppose that the mean price of a home in Denver, Colorado in 2008 was 225.3 thousand dollars. A random sample of 49 homes sold in 2010 had a mean price of 200.8 thousand dollars. A real estate firm wants to test to see if the mean price of 2010 differs from the mean price in 2008. Assume that the population standard deviation is 140. Perform the hypothesis test and compute the P value. Based on your P value, what is the conclusion if we test at the 0.05 level of significance? Expert Answer

Answer 1

Given n=64

The population mean

We wants to test the claim that whether the second graders in her school district have greater math skills than the nationwide average

The Hypothesis testing Problem is

The test statistics is

Pvalue is P(Z>=1.0293) =0.1516694

### By using R command

> 1-pnorm(1.0293,0,1)
[1] 0.1516694

Here P value is 0.1517 which is greater han 0.05, Hence we are unable to reject the null hypothesis at 5% level of significance.

Therefore we can not justify the claim that the second graders in her school district have greater math skills than the nationwide average