According to a food website, the mean consumption of popcorn anually by American

Question

According to a food website, the mean consumption of popcorn anually by Americans is 62 quarts. The marketing division of the food website unleashes an aggressive campaign designed to get Americans to consume even more popcorn. complete parts (a) through (c) below.

(a) Determine the null and alternative hypothesis that would be used to test the effectiveness of the marketing campaign.

H0: __ __ __ (Type integers or decimals. Do not round.)

H1: __ __ __ (Type integers or decimals. Do not round.)

(b) A sample of 839 Americans provides enough evidence to conclude that marketing campaign was effective. Provide a statement that should be put out by the marketing department. (Multiple choice)

aa) There is not sufficient evidence to conclude that the mean consumption of popcorn has stayed the same

bb) There is nit sufficient evidence to conclude that the mean consumption of popcorn has risen.

cc) There is sufficient evidence to conclude that hte mean consumption of popcorn has stayed the same.

dd) There is sufficient evidence to conclude that the mean consumption of popcorn has risen.

(c) Suppose, in fact, the mean annual consumption of popcorn after the marketing campaign is 62 quarts. Has a Type I of Type II error been made by the marketing department? If we tested thsi hypothesis at the a=0.05 level of significance, what is the probability of commiting this error? Select the correct choice below and fill in the answer box within you choice. (Type an integer or a decimal. Do not round)

aa) the marketing department committed a Type II error becasue the marketing department rejected the null hypothesis when it was true. The probability of making a Type II error is __.

bb)The marketing departmetn committed a Type II error becasue the amrketing department did not reject the alternative hypothesis when the null hypothesis was true. The probability of making a Type II error is __.

cc)The marketing department committed a Type I error because the markeitng department rejected the null hypothesis when it was true. The probabiltiy of making a Type I error is __.

dd) The marketing departmetn committed a Type I error becasue the marketing department did not reject the alternative hypothesis when the null hypothesis was true. The probability of making a Type I error is __.

Explanation / Answer

(a) H0 : = 62 quarts

H0 ; > 62 quarts

Here is the mean consumption of popcorn anually by Americans after he agressive marketing campaign.

(b) As marketing campaign was effective that means we have reject the null hypothesis that means:

There is sufficient evidence to conclude that the mean consumption of popcorn has risen. Option D is correct.

(c) In fact, the mean annual consumption of popcorn after the marketing campaign is 62 quarts. So, in reality the null hypothesis is correct but we have reject it. So, this is a type I error.

so, The marketing department committed a Type I error because the markeitng department rejected the null hypothesis when it was true. The probabiltiy of making a Type I error is 0.05.

Option C is correct.

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