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##### New Member

Suppose the standard deviation of a normal population is known to be 10 and the mean is hypothesized

to be 8. Suppose a sample size of 100 is considered. What is the range of sample means that allows the

hypothesis to be accepted at a level of significance of 0.05?

a. Between -11.60 and 27.60

b. Between 6.04 and 9.96

c. Between 6.355 and 9.645

d. Between -8.45 and 24.45

Answer: b

a. Incorrect. This answer is the range of values that contain 95% of observations drawn from a normal

distribution of mean 8 and standard deviation 10. However, to accept the hypothesis that the mean is

8 at a 0.05 significance level, the test statistic Z = (X - 8) / (10 / ÷ (n)) must fall between -1.96 and

1.96, where X is the sample mean.

b. Correct. To accept the hypothesis at a 0.05 significance level, the test statistic Z must fall between

-1.96 and 1.96 -1.96 ? Z = (X - 8) / (10 / ÷ (100)) ? 1.96, which implies that the sample mean X

must be between 6.04 and 9.96.

c. Incorrect. This answer is the range of values the sample mean must fall within to accept the

hypothesis at a 0.10 significance level.

d. Incorrect. This answer is the range of values that contain 90% of observations drawn from a normal

distribution of mean 8 and standard deviation 10. However, to accept the hypothesis that the mean

is 8 at a 0.05 significance level, the test statistic Z = (X - 8) /(10/ ÷(n)) must fall between -1.96 and

1.96, where X is the sample mean.

Answer b is clear once you divide standard deviation by sqrt(n). In terms of wording, is the simple fact that since the number of samples is provided then you should use the sample std deviation (10/sqrt(100)) as opposed to using the standard deviation (10)?

Furthermore, what in the world are they trying to say in answer A and B? So far, I have seen many typos and rather mediocre explanations in these practice exams so I'm reluctant to think the answers always correct. Anyway, if A and B have any useful information please confirm. Otherwise, this is just a simple 'trick' question to get you to use sample std. dev. How useful...