According to a food website, the mean consumption of popcorn annually by America

Question

According to a food website, the mean consumption of popcorn annually by Americans is 61 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 hypotheses that would be used to test the effectiveness of the marketing campaign.

Upper H 0H0:

sigma

pp

mu

not equals

equals=

nothing

Upper H 1H1:

pp

sigma

mu

greater than>

less than<

not equals

nothing

(Type integers or decimals. Do not round.)

(b) A sample of 809 Americans provides enough evidence to conclude that marketing campaign was effective. Provide a statement that should be put out by the marketing department.

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

B. There is not sufficient evidence to conclude that the mean consumption of popcorn has risen.

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

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

(c) Suppose, in fact, the mean annual consumption of popcorn after the marketing campaign is

6161

quarts. Has a Type I or Type II error been made by the marketing department? If we tested this hypothesis at the

alphaequals=0.10.1

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.

(Type an integer or a decimal. Do not round.)

A. The marketing department committed a Type II error because the marketing department rejected the null hypothesis when it was true. The probability of making a Type II error is nothing .

B. The marketing department committed a Type II error because the marketing department did not reject the alternative hypothesis when the null hypothesis was true. The probability of making a Type II error is nothing .

C. The marketing department committed a Type I error because the marketing department did not reject the alternative hypothesis when the null hypothesis was true. The probability of making a Type I error is nothing .

D. 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 nothing .

Upper H 0H0:

sigma

pp

mu

not equals

equals=

nothing

Upper H 1H1:

pp

sigma

mu

greater than>

less than<

not equals

nothing

Explanation / Answer

Solution:-

a)

Null hypothesis: H0, = 61
Alternative hypothesis H1, : > 61

Note that these hypotheses constitute a one-tailed test.

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

c) (D) 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 0.10.

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