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 51.58. Assume the standard deviation for the population of test scores is 15. The nationwide average score on this test us 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 200.1 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?

Answer 1

1) Given: = 50, = 15, = 51.58, n = 64, = 0.05

The Hypothesis:

H0: = 50

Ha: > 50

This is a right tailed Test.

The Test Statistic: The test statistic is given by the equation:

The p Value:    The p value (Right Tail) for Z = 0.84 is; p value = 0.2

The Decision Rule: If P value is < , Then Reject H0.

The Decision: Since P value (0.2) is > (0.05) , We Fail to Reject H0.

The Conclusion: There is insufficient evidence at the 95% significance level to conclude that the second graders in the superintendents school district have greater math skills than the nationwide average.

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2) Given: = 225.3, = 140, = 200.1, n = 49, = 0.05

The Hypothesis:

H0: = 225.3

Ha: 225.3

This is a 2 tailed Test.

The Test Statistic: The test statistic is given by the equation:

The p Value:    The p value (Two Tail) for Z = 0.84 is; p value = 0.2077

The Decision Rule: If P value is < , Then Reject H0.

The Decision: Since P value (0.2077) is > (0.05) , We Fail to Reject H0.

The Conclusion: There is insufficient evidence at the 95% significance level to conclude that the mean price of a home in Denver, Colorado in 2008 is different from the mean price in 2010.