# Two-Sample Tests and Evidence

A teacher claims that a grammar seminar will help students reduce the number of grammatical errors they make when writing a 1000-word essay. The table shows the number of grammatical errors made by seven students before participating in the seminar and after participating in the seminar.

Student 1 2 3 4 5 6 7

Errors (before) 15 10 12 8 5 4 9

Errors (after) 11 9 6 5 1 0 9

(2) Which two-sample test should you use for this situation?

(18) Is there enough evidence to conclude that the seminar reduced the number of errors? Use a significance level of ±=0.05. You must state the hypotheses, determine the test statistic, and either the P-value(s) or critical value(s). Finally, you must clearly state your conclusion. Round all answers to two decimal places.

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#### Solution Preview

Please refer to the attachments.

We shall use paired sample t-test to test the given hypothesis.

Null and Alternate Hypothesis:

Null hypothesis, H0: u1 (less than or equal to) u2

Alternate hypothesis: H1: u1 > u2

Critical Value and Decision Rule:

Since the alternative hypothesis is the given test is an upper-tail ...

#### Solution Summary

This solution helps determine the correct two-sample test to use and discusses whether there is enough evidence to conclude that the seminar reduced the number of errors.