6) In addition to meeting the Randomization Condition and the Independence Assumption, a 1- Sample t-Test...

6) In addition to meeting the Randomization Condition and the Independence Assumption, a 1- 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)

a) The sample size is very small (less than 15).

b) The sample size is moderate (between 15 and 40).

c) The sample size is large (above 40).

Solutions

Expert Solution

Solution:-

To meet the Nearly Normal Condition for each scenario the histogram must satisfy the below mentioned points.

(a) The sample size is very small (less than 15).

1. Histogram must be symmetric.

2. Unimodal (i.e. there is only one hump)

3. Without Outliers (i.e. There should be no observation that lies outside the overall pattern of the distribution)

(b) The sample size is moderate (between 15 and 40).

1. Histogram need be symmetric and allowed to be moderately skewed.

2. Unimodal (i.e. there is only one hump).

3. Without Outliers (i.e. There should be no observation that lies outside the overall pattern of the distribution)

1. Without Outliers (i.e. there should be no observation that lies outside the overall pattern of the distribution). As the central limit theorem states that if sample size is large enough (i.e. above 40), the distribution will be approximately normal as long as we do not have outliers.

orchestra answered 1 year ago

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