7) You are thinking of employing a t-procedure to test hypotheses about the mean

Question

7) You are thinking of employing a t-procedure to test hypotheses about the mean of a population using a significance level of 0.05. Your histogram of an SRS shows a distribution which has a single peak but is moderately skewed. Which of the following statements is correct? Circle One.

A) Because the population does not have a perfectly normal distribution, you should not use the t-procedure,

B) If your sample size is large, say n = 50, you may use the t-procedures

C) If you use the t-procedure you can claim the significance level is only P = 0.10.

D) You may not use the t-procedure, because t-procedures are robust to non-Normality for confidence intervals but not for tests of hypotheses.

Explanation / Answer

Solution: The answer is D)

You may not use the t-procedure, because t-procedures are robust to non-Normality for confidence intervals but not for tests of hypotheses.

Beacuse of when we testing the t test we assume the given data data is approximately normal in the testing.

Upon the inspection of our data, say using histograms, we were to find that our data looked non-normal. In particular, we would worry that the t-test will not perform as it should - i.e. that if the null hypothesis is true, it will falsely reject the null 5% of the time ( assuming using the usual significance level).

Also, for the same reasons, the 95% confidence interval for the means will have correct coverage, even when X is not normal (again, when the sample size is sufficiently large). Of course, for small samples, or highly skewed distributions, the above asymptotic result may not give a very good approximation.

So the anwer is D

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