Question

The table below gives the percent of married women with children ages 6 to 17 in the labour force in the United States from 1950 to 1994.

a. Draw a scatterplot of these data with year on the horizontal axis. To simplify data entry, enter the number of years after 1900. For instance, enter 50 instead of 1950.

b. Use a statistics utility to find a linear model to fit the data. Graph the line on the scatterplot.

c. According to your answer in part b, about what percent of married women, with children ages 6 to 17, were in the labor force in the year 1982?

d. According to your answer in part b, in about what year will 85% of married women with children ages 6 to 17 be in the labor force?

e. What is the correlation coefficient for this data?

f. Write a sentence which explains the direction and strength of the correlation.

Answer 1

As the number of years increases, the percentage of married women with children ages 6 to 17 in labor force increases

a. Draw a scatter plot of these data with year on the horizontal axis.

To do this, we enter the number of years after 1900 and the percentage of labor force on a graphing calculator

See attachment for the scatter plot

b. Use a statistics utility to find a linear model to fit the data

Using the graphing calculator, we can find a linear model to fit the data

From the line on the scatter plot, the equation is

y = 1.12x - 28.48

c. The percentage in the labor force in the year 1982?

This means that x = 82

So, we have:

y = 1.12 * 82 - 28.48

Evaluate

y = 63.36

Hence, the percentage in the labor force in the year 1982 is 63.36%

d. About what year will 85% be in the labor force?

This means that y = 85

So, we have:

85 = 1.12x - 28.48

This gives

1.12x = 113.48

Divide by 1.12

x = 101.32

Approximate

x = 101

Year = 1900 + 101

Year = 2001

Hence, the year is 2001

What is the correlation coefficient for this data?

To do this, we enter the number of years after 1900 and the percentage of labor force on a graphing calculator

Using the graphing tool;

The value of correlation coefficient for this data is 0.9962.

f. Write a sentence which explains the direction and strength of the correlation.

This is a strong positive correlation, which means that as the number of years increases, the percentage of married women with children ages 6 to 17 in labor force increases

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