An insurance company sets up a statistical test with a null hypothesis that the average time for processing a claim is 7 days, and an alternative hypothesis that the average time for processing a claim is greater than 7 days. After completing the statistical test, it is concluded that the average time exceeds 7 days. However, it is eventually learned that the mean process time is really 7 days. What type of error occurred in the statistical test?A. Type II error B. Both Type I and Type II error C. Type I error D. No error occurred in the statistical sense.

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22-11-2019
Mathematics

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An insurance company sets up a statistical test with a null hypothesis that the average time for processing a claim is 7 days, and an alternative hypothesis that the average time for processing a claim is greater than 7 days. After completing the statistical test, it is concluded that the average time exceeds 7 days. However, it is eventually learned that the mean process time is really 7 days. What type of error occurred in the statistical test?A. Type II error B. Both Type I and Type II error C. Type I error D. No error occurred in the statistical sense.

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cchilabert cchilabert · Answer 1 · 2019-11-23T01:26:39+01:00

Answer:

C. Type I error

Step-by-step explanation:

Hello!

The hypothesis tested was:

H₀: μ = 7

H₁: μ > 7

The decision was taken: Reject the null hypothesis.

Reminder:

There are four decisions you can take when you make a hypothesis test.

1. Reject the null hypothesis when the hypothesis is false (This is a correct decision)

2. Reject the null hypothesis when the hypothesis is true (This decision is also known as Type I error)

3. Fail to reject the null hypothesis when the hypothesis is true (This is a correct decision)

4. Fail to reject the null hypothesis when the hypothesis is false (This decision is also known as Type II error)

Since they concluded, that the average process time vas greater than 7 days, when it was 7 days, they rejected the null hypothesis when it was true. This is a Type I error and its associated probability is α.

I hope it helps!