Question

A shampoo manufacturer guarantees every bottle they sell has at least 32 ounces of shampoo, and...

A shampoo manufacturer guarantees every bottle they sell has at least 32 ounces of shampoo, and a hypothesis test supports this guarantee. After a study of recent shipments, the average was 31 ounces. Which of the following errors were made during this hypothesis test?

Type I error

Type II error

Both Type I and Type II error

Neither Type I nor Type II error
Math   Statistics-And-Probability   
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Answer #1

It is given that the shampoo manufacturer guarantees every bottle they sell has at least 32 ounces of shampoo, and a hypothesis test supports this guarantee

This means that the null hypothesis (claim that mean is at least 32 ounces) is not rejected.

We know that in type I error, we always reject null hypothesis, but in type II error we never reject the null hypothesis

If the mean is less than 32, then we must have failed to reject the false null hypothesis that the mean is at least 32 ounces

therefore, there is possibility of making a type II error only since null hypothesis was not rejected

option B

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