Two Population Means with Unknown Standard Deviations · Try It 3

Two professors, A and B, teach classes on the same subjects. Scores of 10 students from each class are selected randomly. The final exam scores of the students are as follows:

$$\begin{array}{ccccc}\text{97}& \text{62}& \text{73}& \text{58}& \text{84}\\ \text{74}& \text{66}& \text{93}& \text{73}& \text{85}\end{array}$$

$$\begin{array}{ccccc}\text{85}& \text{64}& \text{74}& \text{55}& \text{76}\\ \text{67}& \text{72}& \text{84}& \text{71}& \text{98}\end{array}$$
Professor A says that the mean score of their class is more than the mean of professor B’s class. Is professor A correct? Test at a 5% significance level. Answer the following questions:

(a) Is this a test of two means or two proportions?
(b) Are the population standard deviations known or unknown?
(c) Which distribution do you use to perform the test?
(d) What is the random variable?
(e) What are the null and alternative hypotheses? Write the null and alternative hypotheses in words and in symbols.
(f) Is this test right-, left-, or two-tailed?
(g) What is the p-value?
(h) Do you reject or not reject the null hypothesis?
(i) At the ___ level of significance, from the sample data, there ___ (is/is not) sufficient evidence to conclude that ___.

OpenStax, Introductory Statistics 2e · §10.1 Two Population Means with Unknown Standard Deviations · Try It 3