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: μ_boys - μ_girls = 0 versus H_a: μ_boys - μ_girls ≠ 0, where μ_boys and μ_girls are the true mean reading speed of all senior boys and girls at her high school.

(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?
This is a  --- right-tailed left-tailed two-tailed  --- test of two proportions two-sample t-test goodness of fit test paired t-test test of independence .

Answer 1

Concept

• Type one error is the error when we reject the null hypothesis even though it is true and should not be rejected.

Solution

a)

Here the hypothesis are

Ho: There is no difference in average reading speed of senior boys and senior girls

Ha: There is a significant difference between average reading speed of senior boys and senior girls

Type one Error: We have rejected the null but we should not have rejected. Meaning, actually, there is no difference in average reading speeds but we have rejected this and proven that there is a difference in the reading speeds of boys and girls.

So, we can say that the type one 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.

So, option D is the answer

b)

Since the null hypothesis and alternate hypothesis have equality and unequality sign, it is an example of two tailed test and two sample t-test.

This is a two-tailed test of two-sample t-test