Question: Would you use a t tool or a nonparametric procedure given Normal q-q p

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Question: Would you use a t tool or a nonparametric procedure given Normal q-q plots?

My Attempts:

a) Use a nonparametric procedure due to the three outliers and the fact that the sample is not large enough to be resilient against outliers.
b) Use a nonparametric procedure, because the sample is less than 15 and is not even approximately normal.
c) We can use a t-tool because the sample is large enough for the sample distribution to be approximately normally distributed, according to the central limit theorem.

4. The following graphs are Normal probability plots for three different sets of data. Suppose we would like to construct a confidence interval for the mean in each case. For each setting, comment on whether a t tool or a non-parametric procedure should be used and explain why you made your decision (a) In this setting, n = 20 Normal Q-Q Plot -2 Theoretical Quantiles (b) In this setting, n 10 Normal Q-Q Plot -1.5 1.0-0.5 0.0 0.5 1.0 1.5 Theoretical Quantiles

Explanation / Answer

a) Use a nonparametric procedure because the sample does not follow a normal distribution. From the plot, we can see that there are three outliers and the fact that the sample is not large enough to be resilient against outliers. Also, the sample may not be follow a normal distribution without these three outliers.
b) Use a nonparametric procedure, because the sample is less than 15 and is not even approximately normal.
c) We can use a t-test because the sample follows a normal distribution with thin-tail. (Note: The distribution of a normal distribution may not happen even in this sample size (100). There is not fixed sample size to say that a sample follows a normal distribution according to the central limit theorem.)

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