Question

A random sample of 61 produced the summary statistics x = 0373 and s2 = 0.054. Complete parts a and b.

a. Test the null hypothesis that u = 0.42 against the alternative hypothesis that < 0.42, using a= 0.10, What is the value of the test statistic?
b. Test the null hypothesis that = 0.42 against the alternative hypothesis that u=!0.42, using a=0.10 What is the value of the test statistic?

Answer 1

To test the null hypothesis and alternative hypothesis, we can use a one-sample t-test and a two-sample t-test respectively.

Step-by-step explanation:

To test the null hypothesis that μ = 0.42 against the alternative hypothesis that μ < 0.42, we can use a one-sample t-test. The test statistic is calculated by subtracting the null hypothesis value from the sample mean and dividing by the standard error of the mean. In this case, the test statistic is calculated as (0.373 - 0.42) / sqrt(0.054/61) = -1.149.

To test the null hypothesis that μ = 0.42 against the alternative hypothesis that μ ≠ 0.42, we can use a two-sample t-test. The test statistic is calculated by subtracting the null hypothesis value from the sample mean difference and dividing by the standard error of the mean difference. In this case, the test statistic is calculated as (0.373 - 0.42) / sqrt(0.054/61) = -1.149.