Question 17 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 15 15 27 12 5 25 26 24 22 Money 43 51 81 53 28 100 77 65 73 Find the correlation coefficient: r=r= Round to 2 decimal places. The null and alternative hypotheses for correlation are: H0:H0: Correct == 0 H1:H1: Correct ≠≠ 0 The p-value is: (Round to four decimal places) 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. 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. 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. 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.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. r2r2 = (Round to two decimal places)

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
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Chapter4: Equations Of Linear Functions
Section4.5: Correlation And Causation
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Question 17

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 15 15 27 12 5 25 26 24 22
Money 43 51 81 53 28 100 77 65 73

 

  1. Find the correlation coefficient:  r=r=    Round to 2 decimal places.
  2. The null and alternative hypotheses for correlation are:
    H0:H0:     Correct == 0
    H1:H1:     Correct  ≠≠ 0    
    The p-value is:    (Round to four decimal places)

    • 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.
    • 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.
    • 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.
    • 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.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.
  3.  r2r2 =  (Round to two decimal places)  
    • There is a 80% 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.
    • 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 80%.
    • 80% of all customers will spend the average amount of money at the store.
    • Given any group that spends a fixed amount of time at the store, 80% of all of those customers will spend the predicted amount of money at the store. Interpret r2r2 :  
  4. The equation of the linear regression line is:   
    ˆyy^ =  + xx   (Please show your answers to two decimal places)  

  5. Use the model to predict the amount of money spent by a customer who spends 18 minutes at the store.
    Dollars spent =  (Please round your answer to the nearest whole number.)  
  6.  Interpret r2r2 :  
    • There is a 80% 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.
    • 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 80%.
    • 80% of all customers will spend the average amount of money at the store.
    • Given any group that spends a fixed amount of time at the store, 80% of all of those customers will spend the predicted amount of money at the store.
    Correct
  7. The equation of the linear regression line is:   
    ˆyy^ =  + xx   (Please show your answers to two decimal places)  

  8. Use the model to predict the amount of money spent by a customer who spends 18 minutes at the store.
    Dollars spent =  (Please round your answer to the nearest whole number.)

 

Question 18

A study was done to look at the relationship between number of movies people watch at the theater each year and the number of books that they read each year. The results of the survey are shown below.

 

Movies 8 1 9 9 4 4 5 9 7 5 4 0
Books 6 12 4 5 11 10 5 3 7 9 7 8

 

  1. Find the correlation coefficient:  r=r=    Round to 2 decimal places.
  2. The null and alternative hypotheses for correlation are:
    H0:H0:      == 0
    H1:H1:       ≠≠ 0    
    The p-value is:      Round to 4 decimal places.
  3.  r2r2 =  (Round to two decimal places)
  4. The equation of the linear regression line is:   
    ˆyy^ =   + xx    (Please show your answers to two decimal places)  
  5. Use the model to predict the number of books read per year for someone who watches 3 movies per year.
    Books per year =  (Please round your answer to the nearest whole number.) 

 

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