Question

Demographers have been interested in studying the causes of adolescent fertility. A demographer hypothesizes that the minimum wage in states might be negatively correlated with adolescent fertility rates, because teens will have more resources to obtain contraception and more opportunities to invest in their economic futures in states with higher minimum wages. The researcher collects data on the minimum wage (dollars) and the adolescent fertility rate (births per 1,000 women age15-19) in a random sample of 8 U.S. States. State Minimum Wage Fertility Rate Washington 13.50 37 Texas 7.25 58 Pennsylvania 7.25 35 Oregon 12.00 36 Georgia 7.25 47 West Virginia 8.75 54 Montana 8.75 41 Kansas 7.25 40 a. Calculate the Pearson's correlation coefficient for the association between minimum wage and the adolescent fertility rate in the sample of U.S. states. b. Provide an interpretation for the correlation coefficient. c. Do the sample data provide sufficient evidence to conclude that a real negative association exists in the population from which this sample was drawn, using a 95% confidence level? (To answer this question, you will need to perform a hypothesis test.) Explain your answer and show all necessary work. You should write out the research and null hypotheses in Greek notation.

Answer 1

To calculate the Pearson's correlation coefficient, use the formula r = ((x - mean_x)(y - mean_y)) / sqrt((x - mean_x)^2 * (y - mean_y)^2). Plug in the values for minimum wage and fertility rate and calculate the mean for each variable. Then, calculate the correlation coefficient.

Step-by-step explanation:

To calculate the Pearson's correlation coefficient for the association between minimum wage and adolescent fertility rate, use the following formula:

r = Σ((x - μx)(y - μy)) / sqrt(Σ(x - μx)^2 × Σ(y - μy)^2)

Plug in the values for minimum wage and fertility rate from the data:

• Washington: Minimum Wage = 13.50, Fertility Rate = 37
• Texas: Minimum Wage = 7.25, Fertility Rate = 58
• Pennsylvania: Minimum Wage = 7.25, Fertility Rate = 35
• Oregon: Minimum Wage = 12.00, Fertility Rate = 36
• Georgia: Minimum Wage = 7.25, Fertility Rate = 47
• West Virginia: Minimum Wage = 8.75, Fertility Rate = 54
• Montana: Minimum Wage = 8.75, Fertility Rate = 41
• Kansas: Minimum Wage = 7.25, Fertility Rate = 40

Calculate the mean for each variable, then calculate the correlation coefficient.