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 8 women are shown in the table below.

Time	61	80	32	38	74	71	33	59
Pounds	131	132	109	124	130	125	102	128

1. Find the correlation coefficient: r=r=    Round to 2 decimal places.
2. 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)
   
3. 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 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.
   • 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 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.
4. r2r2 =  (Round to two decimal places)
5. Interpret r2r2 :
   • There is a 68% 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 time on the phone , this variation on average is reduced by 68%.
   • 68% of all women will have the average weight.
   • Given any group of women who all weight the same amount, 68% of all of these women will weigh the predicted amount.
6. The equation of the linear regression line is:   
   ˆyy^ =  + xx   (Please show your answers to two decimal places)
   
7. Use the model to predict the weight of a woman who spends 38 minutes on the phone.
   Weight =  (Please round your answer to the nearest whole number.)
   
8. 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 0.47 additional pounds.
   • As x goes up, y goes up.
   
   
9. 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 96 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 96 pounds.
   • The average woman's weight is predicted to be 96.

Answer 1