Suppose, in fact, the mean annual consumption of popcorn after the marketing campaign is 58 58 quarts. has a type i or type ii error been made by the marketing department? if we tested this hypothesis at the alpha α equals = 0.01 0.01 level of significance, what is the probability of committing this error? select the correct choice below and fill in the answer box within your choice.

Question

Mathematics

Zackary Johnston

30 October, 07:23

Suppose, in fact, the mean annual consumption of popcorn after the marketing campaign is 58 58 quarts. has a type i or type ii error been made by the marketing department? if we tested this hypothesis at the alpha α equals = 0.01 0.01 level of significance, what is the probability of committing this error? select the correct choice below and fill in the answer box within your choice.

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Angel Crawford · Answer 1

The marketing department committed a Type I error because the marketing department rejected the null hypothesis when it was true. The probability of making a Type I error is 0.01.

Explanation:

Null Hypothesis: H₀ : µ = 58.58

Alternative Hypothesis: H₁ : µ> 58.58

A type I error is made by the marketing department if the null hypothesis is rejected when it is true and a type II error occurs, when the marketing department fails to reject the null hypothesis when it should be rejected.

The probability of making a Type I error is α, which is the level of significance you set for your hypothesis test, in our case 0.01 while the probability of making a Type II error is β, which depends on the power of the test.

Based on this we can therefore conclude that the marketing department committed a Type I error because the marketing department rejected the null hypothesis when it was true. The probability of making a Type I error is 0.01.