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A grocery store manager did a study to look at the relationship between the amount of time (in minutes) customers spend in the store and the amount of money (in dollars) they spend. The results of the survey are shown below. Time 12 21 14 27 10 19 10 16 Money 42 87 56 86 31 87 32 56 a. Find the correlation coefficient: r = Round to 2 decimal places. b. The null and alternative hypotheses for correlation are: Ho: = 0 + 0 o o H1: The p-value is: (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. O There is statistically insignificant evidence to conclude that there is a correlation between the amount of time customers spend at the store and the amount of money that they spend at the store. Thus, the use of the regression line is not appropriate. O There is statistically significant evidence to conclude that there is a correlation between the amount of time customers spend at the store and the amount of money that they spend at the store. Thus, the regression line is useful. O There is statistically significant evidence to conclude that a customer who spends more time at the store will spend more money than a customer who spends less time at the store. O There is statistically insignificant evidence to conclude that a customer who spends more time at the store will spend more money than a customer who spends less time at the store.

A grocery store manager did a study to look at the relationship between the amount of time (in minutes) customers spend in the store and the amount of money (in dollars) they spend. The results of the survey are shown below. Time 12 21 14 27 10 19 10 16 Money 42 87 56 86 31 87 32 56 a. Find the correlation coefficient: r = Round to 2 decimal places. b. The null and alternative hypotheses for correlation are: Ho: = 0 + 0 o o H1: The p-value is: (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. O There is statistically insignificant evidence to conclude that there is a correlation between the amount of time customers spend at the store and the amount of money that they spend at the store. Thus, the use of the regression line is not appropriate. O There is statistically significant evidence to conclude that there is a correlation between the amount of time customers spend at the store and the amount of money that they spend at the store. Thus, the regression line is useful. O There is statistically significant evidence to conclude that a customer who spends more time at the store will spend more money than a customer who spends less time at the store. O There is statistically insignificant evidence to conclude that a customer who spends more time at the store will spend more money than a customer who spends less time at the store.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
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 11PPS
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A grocery store manager did a study to look at the relationship between the amount of time (in minutes) customers spend in the store and the amount of money (in dollars) they spend. The results of the survey are shown below, Time 12 21 14 27 10 19 10 16 Money 42 87 56 86 31 87 32 56 a. Find the correlation coefficient: r = Round to 2 decimal places. b. The null and alternative hypotheses for correlation are: Ho: pv H1: pv 手0 。 The p-value is: (Round to four decimal places) c. Use a level of significance of a of the study. 0.05 to state the conclusion of the hypothesis test in the context O There is statistically insignificant evidence to conclude that there is a correlation between the amount of time customers spend at the store and the amount of money that they spend at the store. Thus, the use of the regression line is not appropriate. O There is statistically significant evidence to conclude that there is a correlation between the amount of time customers spend at the store and the amount of money that they spend at the store. Thus, the regression line is useful. O There is statistically significant evidence to conclude that a customer who spends more time at the store will spend more money than a customer who spends less time at the store. O There is statistically insignificant evidence to conclude that a customer who spends more time at the store will spend more money than a customer who spends less time at the store. d. r2 (Round to two decimal places) e. Interpret r : O There is a 84% chance that the regression line will be a good predictor for the amount of money spent at the store based on the time spent at the store. O 84% of all customers will spend the average amount of money at the store. O There is a large variation in the amount of money that customers spend at the store, but if you only look at customers who spend a fixed amount of time at the store, this variation on average is reduced by 84%. O Given any group that spends a fixed amount of time at the store, 84% of all of those customers will spend the predicted amount of money at the store. 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 amount of money spent by a customer who spends 20 minutes at the store. Dollars spent = (Please round your answer to the nearest whole number.) h. Interpret the slope of the regression line in the context of the question: As x goes up, y goes up. O The slope has no practical meaning since you cannot predict what any individual customer will spend. OFor every additional minute customers spend at the store, they tend to spend on averge $3.74 more money at the store. i. Interpret the y-intercept in the context of the question: O The y-intercept has no practical meaning for this study. O The best prediction for a customer who doesn't spend any time at the store is that the customer will spend $-0.75. O The average amount of money spent is predicted to be $-0.75. O If a customer spends no time at the store, then that customer will spend $-0.75.
Transcribed Image Text:A grocery store manager did a study to look at the relationship between the amount of time (in minutes) customers spend in the store and the amount of money (in dollars) they spend. The results of the survey are shown below, Time 12 21 14 27 10 19 10 16 Money 42 87 56 86 31 87 32 56 a. Find the correlation coefficient: r = Round to 2 decimal places. b. The null and alternative hypotheses for correlation are: Ho: pv H1: pv 手0 。 The p-value is: (Round to four decimal places) c. Use a level of significance of a of the study. 0.05 to state the conclusion of the hypothesis test in the context O There is statistically insignificant evidence to conclude that there is a correlation between the amount of time customers spend at the store and the amount of money that they spend at the store. Thus, the use of the regression line is not appropriate. O There is statistically significant evidence to conclude that there is a correlation between the amount of time customers spend at the store and the amount of money that they spend at the store. Thus, the regression line is useful. O There is statistically significant evidence to conclude that a customer who spends more time at the store will spend more money than a customer who spends less time at the store. O There is statistically insignificant evidence to conclude that a customer who spends more time at the store will spend more money than a customer who spends less time at the store. d. r2 (Round to two decimal places) e. Interpret r : O There is a 84% chance that the regression line will be a good predictor for the amount of money spent at the store based on the time spent at the store. O 84% of all customers will spend the average amount of money at the store. O There is a large variation in the amount of money that customers spend at the store, but if you only look at customers who spend a fixed amount of time at the store, this variation on average is reduced by 84%. O Given any group that spends a fixed amount of time at the store, 84% of all of those customers will spend the predicted amount of money at the store. 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 amount of money spent by a customer who spends 20 minutes at the store. Dollars spent = (Please round your answer to the nearest whole number.) h. Interpret the slope of the regression line in the context of the question: As x goes up, y goes up. O The slope has no practical meaning since you cannot predict what any individual customer will spend. OFor every additional minute customers spend at the store, they tend to spend on averge $3.74 more money at the store. i. Interpret the y-intercept in the context of the question: O The y-intercept has no practical meaning for this study. O The best prediction for a customer who doesn't spend any time at the store is that the customer will spend $-0.75. O The average amount of money spent is predicted to be $-0.75. O If a customer spends no time at the store, then that customer will spend $-0.75.
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