Answer:
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.
Step-by-step 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.
