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. 24 76 74 87 84 Pounds 124 122 116 178 181 174 167 Time 14 40 a. Find the correlation coefficient: r = 0.93 o Round to 2 decimal places. b. The null and alternative hypotheses for correlation are: Ho: P V H1: P ] = 0 # 0 o o The p-value is: 0.0024 v o (Round to four decimal places) c. Use a level of significance of a = 0.05 to state the conclusion of the hypothesis test in the context of the study. 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 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. d. r² = (Round to two decimal places) e. Interpret r2 : O Given any group of women who all weight the same amount, 86% of all of these women will weigh the predicted amount. O 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 86%. O 86% of all women will have the average weight. O There is a 86% chance that the regression line will be a good predictor for women's weight based on their time spent on the phone. f. The equation of the linear regression line is: ŷ = * (Please show your answers to two decimal places) g. Use the model to predict the weight of a woman who spends 36 minutes on the phone. Weight = (Please round your answer to the nearest whole number.) h. Interpret the slope of the regression line in the context of the question: O For every additional minute women spend on the phone, they tend to weigh on averge 0.90 additional pounds. O The slope has no practical meaning since you cannot predict a women's weight. O As x goes up, y goes up. i. Interpret the y-intercept in the context of the question: O If a woman does not spend any time talking on the phone, then that woman will weigh 100 pounds. O The best prediction for the weight of a woman who does not spend any time talking on the phone is 100 pounds. O The average woman's weight is predicted to be 100. O The y-intercept has no practical meaning for this study.
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. 24 76 74 87 84 Pounds 124 122 116 178 181 174 167 Time 14 40 a. Find the correlation coefficient: r = 0.93 o Round to 2 decimal places. b. The null and alternative hypotheses for correlation are: Ho: P V H1: P ] = 0 # 0 o o The p-value is: 0.0024 v o (Round to four decimal places) c. Use a level of significance of a = 0.05 to state the conclusion of the hypothesis test in the context of the study. 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 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. d. r² = (Round to two decimal places) e. Interpret r2 : O Given any group of women who all weight the same amount, 86% of all of these women will weigh the predicted amount. O 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 86%. O 86% of all women will have the average weight. O There is a 86% chance that the regression line will be a good predictor for women's weight based on their time spent on the phone. f. The equation of the linear regression line is: ŷ = * (Please show your answers to two decimal places) g. Use the model to predict the weight of a woman who spends 36 minutes on the phone. Weight = (Please round your answer to the nearest whole number.) h. Interpret the slope of the regression line in the context of the question: O For every additional minute women spend on the phone, they tend to weigh on averge 0.90 additional pounds. O The slope has no practical meaning since you cannot predict a women's weight. O As x goes up, y goes up. i. Interpret the y-intercept in the context of the question: O If a woman does not spend any time talking on the phone, then that woman will weigh 100 pounds. O The best prediction for the weight of a woman who does not spend any time talking on the phone is 100 pounds. O The average woman's weight is predicted to be 100. O The y-intercept has no practical meaning for this study.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section4.5: Correlation And Causation
Problem 2CYU
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Transcribed Image Text: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.
Time
14
40
24
76
74
87
84
Pounds
124 122 116 178
181 174 167
a. Find the correlation coefficient: r = | 0.93
b. The null and alternative hypotheses for correlation are:
Ho: P V = 0
H1: p V
Round to 2 decimal places.
The p-value is: 0.0024
o (Round to four decimal places)
c. Use a level of significance of a = 0.05 to state the conclusion of the hypothesis test in the context
of the study.
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 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.
d. r? -
(Round to two decimal places)
e. Interpret r2 :
O Given any group of women who all weight the same amount, 86% of all of these women will
weigh the predicted amount.
O 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 86%.
O 86% of all women will have the average weight.
O There is a 86% chance that the regression line will be a good predictor for women's weight
based on their time spent on the phone.
f. The equation of the linear regression line is:
ŷ =
r (Please show your answers to two decimal places)
g. Use the model to predict the weight of a woman who spends 36 minutes on the phone.
Weight =
(Please round your answer to the nearest whole number.)
h. Interpret the slope of the regression line in the context of the question:
O For every additional minute women spend on the phone, they tend to weigh on averge 0.90
additional pounds.
The slope has no practical meaning since you cannot predict a women's weight.
O As x goes up, y goes up.
i. Interpret the y-intercept in the context of the question:
O If a woman does not spend any time talking on the phone, then that woman will weigh 100
pounds.
O The best prediction for the weight of a woman who does not spend any time talking on the
phone is 100 pounds.
O The average woman's weight is predicted to be 100.
O The y-intercept has no practical meaning for this study.
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