1. The results of a state mathematics test for random samples of students taught by two different teachers at the same school are shown at the left. Can you conclude that there is a difference in the mean mathematics test scores for the students of the two teachers? Use a = 0.10. Assume the populations are normally distributed and the population variances are not equal.
2. The annual earnings of 19 people with a high school diploma and 16 people with an associate’s degree are shown at the left. Can you conclude that there is a difference in the mean annual earnings based on level of education? Use a = 0.01. Assume the populations are normally distributed and the population variances are not equal. (Adapted from U.S. Census Bureau)
a. Identify the claim and state H0 and Ha.
b. Identify the level of significance a and the degrees of freedom.
c. Find the critical values and identify the rejection regions.
d. Find the standardized test statistic t. Sketch a graph.
e. Decide whether to reject the null hypothesis.
f. Interpret the decision in the context of the original claim.
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