The mean consumption of fruit three years ago was 98.7 pounds. A dietician belie

Question

The mean consumption of fruit three years ago was 98.7 pounds. A dietician believes that fruit consumption has fallen since then. (a) Determine the null and alternative hypotheses. Which of the following is correct? A. H_0: mu = 98.7; H_1 mu 98.7 A. H_0: mu = 98.7; H_1 mu notequalto 98.7 (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 sufficient evidence to conclude that the mean consumption of fruit has fallen. B. There is not sufficient evidence to conclude that the mean consumption of fruit has stayed the same. C. There is sufficient evidence to conclude that the mean consumption of fruit has stayed the same. D. There is not sufficient evidence to conclude that the mean consumption of fruit has fallen. (c) Suppose, in fact, the mean consumption of fruits is 98.7 pounds. Did the researcher commit a type I or type II error? A. The researcher committed a type I error because he rejected the null hypothesis when it was true. B. The researcher committed a type II error because he accepted the alternative hypothesis when the null hypothesis was true. C. The researcher committed a type I error because he accepted the alternative hypothesis when the null hypothesis was true. D. The researcher committed a type II error because he rejected the null hypothesis when it was true. If we tested this hypothesis at the alpha = 0.1 level of significance, what is the probability of committing this error?

Explanation / Answer

SOlution:-

a) (A)

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: = 98.7
Alternative hypothesis: < 98.7

Note that these hypotheses constitute a one-tailed test.

b) There is sufficient evidence to conclude that mean consumption of fruit has fallen.

c) A) The researcher commited a type I error because he rejected the null hypothesis when it was true.

In statistical hypothesis testing, a type I error is the incorrect rejection of a true null hypothesis.

The probability of commiting this error is 0.1.

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