Question 1

Based on the histogram of the American Employee Satisfaction Index (ESI), which of the following best describes the shape of the distribution?

Accepted Answer

The distribution is approximately normal but slightly skewed to the right.

Question 2

Given the histogram and summary statistics (mean = 81.44, std. dev. = 6.056, n = 25), which assumption is most important to check before performing a one-sample t-test for the mean ESI?

Accepted Answer

The data should not have strong skewness or outliers.

Question 3

If the null hypothesis is $$H_0$$: \mu = 90$$ and the sample mean is 81.44 with n = 25$ and s = 6.056$, what is the value of the test statistic for a one-sample t-test?

Accepted Answer

$$t = \frac{81.44 - 90}{6.056 / \sqrt{25}}$$

Question 4

Using the histogram, which interval contains the most frequent ESI scores?

Accepted Answer

80–85

Question 5

If the p-value for the t-test is extremely small (e.g., $$p \u003c 0.001$$), what is the most appropriate conclusion?

Accepted Answer

There is strong evidence that the mean ESI in the U.S. branches is different from 90.

Question 6

What is the formula for a 95% confidence interval for the mean ESI based on the sample statistics?

Accepted Answer

$$\bar{x} \pm t^* \frac{s}{\sqrt{n}}$$

Question 7

If the confidence interval for the mean ESI does not include 90, what does this imply?

Accepted Answer

There is evidence that the mean ESI is not 90.

Question 8

Which of the following is NOT a condition that must be checked before using the t-test for the mean?

Accepted Answer

Sample size is at least 30

Question 9

If the histogram showed a strong right skew, what would be the best course of action before performing a t-test?

Accepted Answer

Increase the sample size or use a non-parametric test.

Question 10

Suppose the union representative wants to advocate for better working conditions based on the ESI results. Which statistical evidence would best support their case?

Accepted Answer

A low p-value and a confidence interval below 90.

Statistical Inference for Employee Satisfaction Index (ESI)

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