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:
| 97 | 62 | 73 | 58 | 84 |
| 74 | 66 | 93 | 73 | 85 |
Professor B:
| 85 | 64 | 74 | 55 | 76 |
| 67 | 72 | 84 | 71 | 98 |
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:
- Is this a test of two means or two proportions?
- Are the population standard deviations known or unknown?
- Which distribution do you use to perform the test?
- What is the random variable?
- What are the null and alternative hypotheses? Write the null and alternative hypotheses in words and in symbols.
- Is this test right-, left-, or two-tailed?
- What is the p-value?
- Do you reject or not reject the null hypothesis?
- At the ___ level of significance, from the sample data, there ___ (is/is not) sufficient evidence to conclude that ___.