A statistics student has heard that about 19% of the students on his campus attend sporting eventsweekly. He wants to know if statistics students attend events in the same proportions as the generalstudent body. Explain what type II error would be in this caseA) Type II error would be saying that there is no difference in the attendance of statistics students andthe student body as a whole at sporting events, even though statistics students actually go much lessoften.B) Type II error would be saying that statistics students attend sporting events in different proportionsthan the student body as a whole, even though they actually have the same attendance proportion.C) Type II error would be saying that there is no difference in the attendance of statistics students andthe student body as a whole at sporting events, even though there really is.D) Type II error would be saying that statistics students attend sporting events in much higherproportions than the student body as a whole, even though they actually have the same attendanceproportion

To answer the question step by step:

1. Understand the context: The student wants to compare the attendance of statistics students at sporting events to the general student body, where 19% of the general student body attends weekly.

2. Define Type II error: A Type II error occurs when we fail to reject the null hypothesis when it is actually false. In this context, the null hypothesis (H0) would be that the proportion of statistics students attending sporting events is the same as the general student body (19%).

3. Identify the correct scenario: We need to find the option that describes failing to reject the null hypothesis (saying there is no difference) when there actually is a difference.

4. Evaluate the options:

   • Option A: This describes a scenario where we say there is no difference (fail to reject H0) even though statistics students attend much less often. This matches the definition of a Type II error.
   • Option B: This describes a scenario where we say there is a difference (reject H0) even though the attendance proportions are the same. This is a Type I error.
   • Option C: This describes a scenario where we say there is no difference (fail to reject H0) even though there really is a difference. This matches the definition of a Type II error.
   • Option D: This describes a scenario where we say statistics students attend in much higher proportions (reject H0) even though the attendance proportions are the same. This is a Type I error.

5. Conclusion: Both Option A and Option C describe a Type II error, but Option C is more general and directly matches the definition without specifying the direction of the difference.

Therefore, the correct answer is: C) Type II error would be saying that there is no difference in the attendance of statistics students and the student body as a whole at sporting events, even though there really is.