Question

What is the relationship between the number of minutes per day a woman spends talking on the phone and the woman's weight? The time on the phone and weight for 7 women are shown in the table below.

Time40601737774652

Pounds139196127150208176182

Find the correlation coefficient: r=r=    Round to 2 decimal places.

The null and alternative hypotheses for correlation are:
H0:H0: ? ρ μ r  == 0
H1:H1: ? ρ r μ   ≠≠ 0
The p-value is:    (Round to four decimal places)

Use a level of significance of α=0.05α=0.05 to state the conclusion of the hypothesis test in the context of the study.

There is statistically significant evidence to conclude that a woman who spends more time on the phone will weigh more than a woman who spends less time on the phone.

There is statistically significant evidence to conclude that there is a correlation between the time women spend on the phone and their weight. Thus, the regression line is useful.

There is statistically insignificant evidence to conclude that a woman who spends more time on the phone will weigh more than a woman who spends less time on the phone.

There is statistically insignificant evidence to conclude that there is a correlation between the time women spend on the phone and their weight. Thus, the use of the regression line is not appropriate.

r2r2 =  (Round to two decimal places)

Interpret r2r2 :

Given any group of women who all weight the same amount, 89% of all of these women will weigh the predicted amount.

89% of all women will have the average weight.

There is a 89% chance that the regression line will be a good predictor for women's weight based on their time spent on the phone.

There is a large variation in women's weight, but if you only look at women with a fixed weight, this variation on average is reduced by 89%.

The equation of the linear regression line is:   
ˆyy^ =  + xx   (Please show your answers to two decimal places)

Use the model to predict the weight of a woman who spends 47 minutes on the phone.
Weight =  (Please round your answer to the nearest whole number.)

Interpret the slope of the regression line in the context of the question:

The slope has no practical meaning since you cannot predict a women's weight.

For every additional minute women spend on the phone, they tend to weigh on averge 1.51 additional pounds.

As x goes up, y goes up.

Interpret the y-intercept in the context of the question:

If a woman does not spend any time talking on the phone, then that woman will weigh 97 pounds.

The y-intercept has no practical meaning for this study.

The best prediction for the weight of a woman who does not spend any time talking on the phone is 97 pounds.

The average woman's weight is predicted to be 97.

Answer 1

X	y	(x-xbar)^2	(y-ybar)^2	(x-xbar)(y-ybar)
40 60 17 37 77 46 52	139 196 127 150 208 176 182	49.000 169.000 900.000 100.000 900.000 1.000 25.000 Sum: 2144.000	857.653 768.082 1704.510 334.367 1577.224 59.510 188.082 Sum: 5489.429	205.000 360.286 1238.571 182.857 1191.429 -7.714 68.571 Sum: 3239.000