Question

The average number of pages for a simple random sample of 40 physics textbooks is 435. The average number of pages for a simple random sample of 30 mathematics textbooks is 410. Assume that all page length for each types of textbooks is normally distributed. The standard deviation of page length for all physics textbooks is known to be 55, and the standard deviation of page length for all mathematics textbooks is known to be 55. Part One: Assuming that on average, mathematics textbooks and physics textbooks have the same number of pages, what is the probability of picking samples of these sizes and getting a sample mean so much higher for the physics textbooks (one-sided p-value, to four places)?WebAssign will check your answer for the correct number of significant figures. The above p-value comes from a test-statistic of z=WebAssign will check your answer for the correct number of significant figures. (enter number without sign).

Answer 1

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho:μ1​=μ2​

Ha:μ1​>μ2​

This corresponds to a right-tailed test, for which a z-test for two population means, with known population standard deviations will be used.

Rejection Region

Based on the information provided, the significance level is α=0.05, and the critical value for a right-tailed test is z=1.64.

The rejection region for this right-tailed test is R={z:z>1.64}

Test Statistics

The z-statistic is computed as follows:

Decision about the null hypothesis: Since it is observed that z=1.882>zc​=1.64, it is then concluded that the null hypothesis is rejected.

Using the P-value approach: The p-value is p=0.0299, and since p p=0.0299<0.05, it is concluded that the null hypothesis is rejected.