The mean consumption of fruit three years ago was 976 pounds

The mean consumption of fruit three years ago was 97.6 pounds. A dietician believes that fruit consumption has risen since then.

A. H0: u=97.6; H1: u not= 97.6

B. H0: u=97.6; H1: u < 97.6

C. H0: u=97.6; H1: u > 97.6

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

A. There is not sufficient eidence to conclude that the mean consumption of fruit has risen.

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

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

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

Suppose, in fact, the mean consumption of fruits is 97.6 pounds. Did the researcher commit a type I or type II error?

A. The researcher committed a type I error beause he accepted the alternative hyplothesis when the null hypothesis was true.

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

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

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

If we tested this hypothesis at the a=0.02 level of significance, what is the probability of committing this error?

Solution

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

B. There is sufficient evidence to conclude that the mean consumption of fruit has risen. [ANSWER]

[As the null hypothesis is rejected, then the claim of the dietician is true.]

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Suppose, in fact, the mean consumption of fruits is 97.6 pounds. Did the researcher commit a type I or type II error?

C. The researcher committed a type I error because he rejected the null hypothesis when it was true. [ANSWER, by definition]

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If we tested this hypothesis at the a=0.02 level of significance, what is the probability of committing this error?

It is 0.02 as well. [ANSWER, 0.02.]