Question

According to a food ​website, the mean consumption of popcorn annually by Americans is

57 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.

H0​:	▼ p σ μ	▼ ≠ =	_______?
H1​:	▼ σ p μ	▼ ≠ > <	_______?

​(Type integers or decimals. Do not​ round.)

​(b) A sample of 849 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 stayed the same.

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

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 57 quarts. Has a Type I or Type II error been made by the marketing​department? If we tested this hypothesis at the α=0.10 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 did not reject the alternative hypothesis when the null hypothesis was true. The probability of making a Type II error is _______

B.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 ______

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 __________

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 ____________

Answer 1

(a)
H0​: μ = 57
H1​: μ > 57

(b)
If the results are significant and provides enough evidence, then we reject the null hypothesis and can conclude that alternative hypothesis is true.
A.There is sufficient evidence to conclude that the mean consumption of popcorn has risen.

(c)
If in​ fact, the mean annual consumption of popcorn after the marketing campaign is 57 quarts, we have wrongly rejected null hypothesis when the null hypothesis is true.
So, we have committed Type I error.
Probability of committing this ​error = α=0.10

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