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 hypothesis that would be used to test the effectiveness of the marketing campaign.
Select; μ, σ, p
Select;
greater than>
equals=
less than<
not equals≠
H0: __ __ __ (Type integers or decimals. Do not round.)
H1: __ __ __ (Type integers or decimals. Do not round.)
(b) A sample of 874 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)
a) There is not sufficient evidence to conclude that the mean consumption of popcorn has stayed the same
b) There is not sufficient evidence to conclude that the mean consumption of popcorn has risen.
c) There is sufficient evidence to conclude that hte mean consumption of popcorn has stayed the same.
d) 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 56 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)
a) 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 _?_.
b)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 _?_.
c)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 _?_.
(d) The marketing department 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 __?__.