Question

A reading specialist suspects that there is a difference in the average reading speed between senior boys and senior girls at her high school. To test her claim, random samples of 25 senior boys and 25 senior girls were selected. The reading speed of each student was measured. The reading specialist uses the data obtained to test the hypotheses H0: μboys - μgirls = 0 versus Ha: μboys - μgirls ≠ 0, where μboys and μgirls are the true mean reading speed of all senior boys and girls at her high school.

Answer 1

a) The example that best describe a Type I error is: "The reading specialist finds evidence there is a difference in the average reading speed between senior boys and senior girls at the high school when, in fact, there is no difference in the average reading speed between senior boys and senior girls.

b) This is a two-tailed two-samples t-test for difference between means.

Explanation:

The question is incomplete:

(a) Which of the following best describes a Type I error?

• The reading specialist finds evidence there is a difference in the average reading speed between senior boys and senior girls at the high school when, in fact, there is a difference in the average reading speed between senior boys and senior girls.
• The reading specialist fails to find evidence there is a difference in the average reading speed between senior boys and senior girls at the high school when, in fact, there is no difference in the average reading speed between senior boys and senior girls.
• The reading specialist finds evidence there is a difference in the average reading speed between senior boys and senior girls at the high school.
• The reading specialist finds evidence there is a difference in the average reading speed between senior boys and senior girls at the high school when, in fact, there is no difference in the average reading speed between senior boys and senior girls.
• The reading specialist fails to find evidence there is a difference in the average reading speed between senior boys and senior girls at the high school when, in fact, there is a difference in the average reading speed between senior boys and senior girls.

(b) What type of test is this?

a) A Type I error happens when a true null hypothesis is rejected.

If the null hypothesis is true, the reading speed is not significantly different for boys and girls. If the reading specialist makes a Type I error, he will reject this hypothesis and claim that they are significantly different.

b) This is a two-tailed two-samples t-test for difference between means.

It is two-tailed because the alternative hypothesis is defined with an unequal sign, so the both tails are included in the rejection region (significantly higher or lower value for the difference between means).

For evaluating difference between means, a t-test is used instead of a z-test.