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 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 Ho Type integers or decimals. Do not round.) (b) A sample of 819 Americans provides enough evidence to conclude that marketing campaign was effective. Provide a statement that should be put out by the marketing department. O A. O B. O C. There is sufficient evidence to conclude that the mean consumption of popcorn has stayed the same There is not sufficient evidence to conclude that the mean consumption of popcorn has stayed the same. 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 risen (c) Suppose, in fact, the mean annual consumption of popcorn after the marketing campaign is 57 quarts. Has a Type I or Type ll error been made by the marketing department? If we tested this hypothesis at the = 0.1 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 l error because the marketing department rejected the null hypothesis when it was true. The probability of making a Type I error is OB. The marketing department committed a Type ll error because the marketing department did not reject the alternative hypothesis when the null hypothesis was true. The probability of making a Type Il error ( C. The marketing department committed a Type l error because the marketing department rejected the null hypothesis when it was true. The probability of making a Type II error is D. The marketing department committed a Type error because the marketing department did not re ect the alternative hypothesis when the null hypothesis was true. The probability of making a Type error is is

Explanation / Answer

(a) Let "c" denote the mean consumption of popcorn by Americans annually. We want to test if the given ad campaign is effective in making Americans to consume even more popcorn. For this,the null and alternate hypotheses considered are: H0: c=57 versus H1: c>57.

(b) If a sample of 819 Americans provides enough evidence to conclude that the marketing campaign was effective, then the suitable statement to be put out by the marketing department is: (D) There is sufficient evidence to conclude that the mean consumption of popcorn has risen.

This is because the marketing campaign maybe considered to be effective only when the null hypothesis is rejected, that is when there is a statistically significant increase in the consumption of popcorn.

(c) After the marketing campaign, suppose the mean consumption still is 57 quarts, which is the same as the mean consumption before the campaign, although from the sample the marketing department concluded that the campaign was effective (that is, the marketing department concluded that there has been significant increase in consumption). This is equivalent to rejecting the null hypothesis, H0, (as mentioned above) when in fact, H0 is true. From the definition of Type-1 error, this scenario is nothing but committing a Type-1 error. Being tested at 0.1 level of significance, the probability Type-1 error becomes 0.1. Thus the correct statement along with the relevant probability is : (A) The marketing department committed a Type-1 error because the marketing department rejected the null hypothesis when it was true. The probability of making a Type-1 error is: 0.1 (level of significance)

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