The mean consumption of fruit three years ago was 98.1 pounds. A dietician belie

Question

The mean consumption of fruit three years ago was 98.1 pounds. A dietician believes that fruit consumption has risen since then. (a) Determine the null and alternative hypotheses. Which of the following is correct?

A. Upper H0: muequals=98.1; Upper H1: mugreater than>98.1

B. Upper H0: muequals=98.1; Upper H1: muless than<98.1

C. Upper H0: muequals=98.1; Upper H1: munot equals98.1

(b) Suppose sample data indicate that the null hypothesis should be rejected. State the conclusion of the researcher. Which of the following is the conclusion that could be reached?

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

B. There is sufficient evidence to conclude that the mean consumption of fruit has stayed the same.

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

D. There is sufficient evidence to conclude that the mean consumption of fruit has risen.

(c) Suppose, in fact, the mean consumption of fruits isis 98.1 pounds. Did the researcher commit a type I or type II error?

A. The researcher committed a type IIII error because he accepted the alternative hypothesis when the null hypothesis was true.

B. The researcher committed a type IIII error because he rejected the null hypothesis when it was true.

C. The researcher committed a type Upper II error because he accepted the alternative hypothesis when the null hypothesis was true.

D. The researcher committed a type Upper II error because he rejected the null hypothesis when it was true. If we tested this hypothesis at the alphaequals=0.01 level of significance, what is the probability of committing this error? ___

Explanation / Answer

a) A. Upper H0: muequals=98.1; Upper H1: mugreater than>98.1

b) D. There is sufficient evidence to conclude that the mean consumption of fruit has risen.

c) The researcher committed type 1 error, as he rejected the null hypothesis when it was true

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