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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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Answer:

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.

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