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

Question

2 years ago

10

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.

Mathematics

1 answer:

Vesna [10] · Answer 1 · 2023-07-31T09:48:44+03:00

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

<h3>a. Draw a scatter plot of these data with year on the horizontal axis. </h3>

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

<h3>b. Use a statistics utility to find a linear model to fit the data</h3>

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

<h3>c. The percentage in the labor force in the year 1982?</h3>

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%

<h3>d. About what year will 85% be in the labor force?</h3>

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

<h3>What is the correlation coefficient for this data?</h3>

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.

<h3>f. Write a sentence which explains the direction and strength of the correlation.</h3>

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