The U.S. Bureau of Labor Statistics’ most current figures indicate the average wage for construction workers was about $19.50 an hour. Its survey suggests that construction wages can vary widely. Hartford, Connecticut, wages are approximately 38% larger and Brownsville, Texas, wages are about 30% lower than the national average. A sample of 25 construction workers in San Antonio, Texas, yielded an average wage of $13.87 and a standard deviation of $1.46.

a. Estimate the standard deviation of the nation’s construction wages. (Hint: Recall the relationship between the standard deviation and the range of a normal distribution used in the sample-size calculations in the confidence interval for a population mean.)

b. Does it appear that both the average and the standard deviation of the construction workers’
wages in San Antonio are smaller than those of the nation as a whole? Use hypotheses tests and a significance level of 0.05 to make your determination.