Question

1. You are constructing a 90% confidence interval for the difference of means from simple random samples from two independent populations. The sample sizes are = 6 and = 14. You draw dot plots of the samples to check the normality condition for two-sample t-procedures. Which of the following descriptions of those dot plots would suggest that it is safe to use t-procedures?

I. The dot plot of sample 1 is roughly symmetric, while the dot plot of sample 2 is moderately skewed left. There are no outliers.

II. Both dot plots are roughly symmetric. Sample 2 has an outlier.

III. Both dot plots are strongly skewed to the right. There are no outliers.

A) I only

B) II only

C) I and II

D) I, II, and III

E) t-procedures are not recommended in any of these cases.

Answer 1

ANSWER::

From the given information, the dot plots for the two samples were drawn for checking the normality assumption. From the assumptions of t distribution, the data represents no outliers and moreover, the data is distributed as roughly symmetric. Hence, the options (b), (c), (d), (e) and (f) are incorrect.

Explanation::

The incorrect options are identified by observing whether the data contains outliers or not and symmetric or not.

**From the given information, the dot plots for the two samples were drawn for checking the normality assumption. From the assumptions of t distribution, the data is collected for constructing 90% confidence interval having no outliers and symmetrically distributed. Here, the dot plot of sample 1 is roughly symmetric and the dot plot of sample 2 moderately skewed left. Moreover, there are no outliers. Hence, the correct option is (a).

The correct description for t-procedures is I only.

Explanation

The correct option is identified by observing whether the data contains outliers or not and moreover, symmetric or not.

Answer

The correct description for t-procedures is I only.

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