You are thinking of employing a t procedure to test hypotheses about the mean of a population using a significance level of 0.05. you suspect the distribution of the population is not normal and may be moderately skewed. which of the following statements is correct?

a. you may not use the t procedure because t procedures are robust to non-normality for confidence intervals, but not for tests of hypotheses.
b. you may use the t procedure, but you should probably claim the significance level is only 0.10.
c. you may use the t procedure, provided your sample size is large enough.
d. you should not use the t procedure because the population does not have a normal distribution.

C. You may use the t procedure, provided your sample size is large enough.

True, from the central limit theorem if we ensure that the sample size is large enough n>30, we can approximate the sample mean with a normal distribution. And on this case we have all the requirements in order to conduct a t test procedure.

Step-by-step explanation:

We want to conduct a t test in order to test an hypothesis about the mean with a significance level and we know that the distribution for the population data is not normal and the distribution is moderately skewed.

Let's remember an important concept.

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

Let's analyze the possible options to select the most appropiate.

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

That's not true since the t test procedure and the confidence interval for the sample mean are robust to non normality when we have a large sample size since the distribution for the sample size when n is large is approximately normal by the central limit theorem.

B. You may use the t procedure, but you should probably claim the significance level is only 0.10.

False, the t test procedure is not affected by the significance level selected, since that's a fixed value used for the researcher in order to test the hypothesis and is associated to the Error of Type I that the researcher want to accept in the test.

C. You may use the t procedure, provided your sample size is large enough.

True, from the central limit theorem if we ensure that the sample size is large enough n>30, we can approximate the sample mean with a normal distribution. And on this case we have all the requirements in order to conduct a t test procedure.

D. You should not use the t procedure because the population does not have a normal distribution.

False, as we can see from the central limit theorem if we satisfy the condition that the sample size is large, then we can assume that the distribution for the sample mean is approximately normal and the t procedure is appropiate.

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d. bc = 12 and ef = 16

step-by-step explanation:

we are given that δabc : δdef such that .

also, it is given that

so, from the options, we need that .

a.

b.

c.  

d.

as, we can see that only option d gives the same ratio as i.e. .

hence, the possible lengths are bc = 12 and ef = 16.