Question

A researcher is evaluating whether an increase in the minimum hourly wage had an effect on employment in manufacturing industry in the following three months. Taking a sample of 25 firms, 1. [3 points] what should she conclude if the mean decrease in employment is 9 percent and the standard error of the mean is 5 percent (use 5% significance level)? 2. [3 points] what should she conclude if the mean decrease in employment is 12 percent and the standard error of the mean is 5 percent (use 5% significance level)? 3. [2 points] if the mean decrease in employment is 9 percent and the standard error of the mean is 5 percent, what is the 95 percent confidence interval for the effect of an increase in the minimum wage on employment?

Answer 1

1.

The t statistic is obtained using the formula,

Where,

The p-value is obtained from t distribution table for degree of freedom = n - 1 = 25 - 1 = 24 and significance level = 0.05 for two-tailed test

Since

the null hypothesis is not rejected. Hence it can be concluded that an increase in the minimum hourly wage had no effect on employment in the manufacturing industry.

2.

The t statistic is obtained using the formula,

Where,

The p-value is obtained from t distribution table for degree of freedom = n - 1 = 25 - 1 = 24 and significance level = 0.05 for two-tailed test

Since

the null hypothesis is rejected. Hence it can be concluded that an increase in the minimum hourly wage had a significant effect on employment in the manufacturing industry.

3.

The confidence interval for the mean is obtained using the formula,

The t critical value is obtained from t distribution table for significance level = 0.05 and degree of freedom = n -1 = 25 - 1 = 24.