10.71 According to the U.S. Bureau of Labor Statistics, 7.0% of female hourly workers who are 16 to 24 years old are being paid minimum wage or less. (Note that some workers in some industries are exempt from the minimum wage requirement of the Fair Labor Standards Act and, thus, could be legally earning less than the “minimum” wage.) A prominent politician is interested in how young working women within her county compare to this national percentage, and selects a simple random sample of 500 female hourly workers who are 16 to 24 years old. Of the women in the sample, 42 are being paid minimum wage or less. From these sample results, and using the 0.10 level of significance, could the politician conclude that the percentage of young female hourly workers who are low-paid in her county might be the same as the percentage of young women who are low-paid in the nation as a whole? Determine and interpret the p-value for the test.

Source: Statistical Abstract of the United States 2009, p. 413.