Question

eBook Video Consider the following hypothesis test. H0: 1 - 2 ≤ 0 Ha: 1 - 2 > 0 The following results are for two independent samples taken from the two populations. Sample 1 Sample 2 n 1 = 40 n 2 = 50 x 1 = 25.5 x 2 = 22.3 σ 1 = 5.6 σ 2 = 6 a. What is the value of the test statistic (round to 2 decimals)? b. What is the p-value (round to 4 decimals)? Use z-table. Use z-value rounded to 2 decimal places. c. With = .05, what is your hypothesis testing conclusion? p-value is H0

Answer 1

a. Given the null and alternative hypothesis:

To find the test statistic, we need to find the standard deviation of the joint sample. It can be done in the following way:

The test statistic is:

b. p-value from the z table for the calculated test statistic is 0.006. This is calculated by finding the area to the left of the calculated test statistic from the z table and subtracting this are from 1.

c. At 5% level of significance, we can reject the null hypothesis because the p-value is less than the level of significance. This means that the calculated test statistic lies to the right of the critical z value and the result is statistically significant. Hence, we conclude that .