Question

2) In addition to meeting the Randomization Condition and the Independence Assumption, a1 Sample t-Test must also meet the Nearly Normal Condition. We check the Nearly Normal Condition by making a histogram of the distribution. Describe what the histogram must look like to meet the Nearly Normal Condition for each scenario below. (3 points) ) The sample size is very small les than 15). b) The sample size is moderate (between 15 and 40) c) The sample size is large (above 40)

Answer 1

First try to make histogram of the data and check
its distribution is unimodal and symmetric with no outliers.

We can also make a Normal probability plot to
see that it’s reasonably straight.

a) The smaller the sample size (n less than 15 ),
the more closely the data should follow a Normal model.

b) For moderate sample sizes (between 15 and 40),
the t works well as long as the data are unimodal and reasonably symmetric.

c) For larger sample sizes(above 40),
the t test is safe to use unless the data are extremely skewed.