grocery store manager did a study to look at the relationship

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 15PPS
icon
Related questions
Topic Video
Question

I AM RESUBMITTING THIS QUESTION FOR MORE SUBPARTS. I NEED HELP FROM NUMBER 7 DOWN. THANK YOU. 

 

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 27 22 17 30 17 19 12 23 22
Money 117 72 53 106 66 93 53 83 95

 

  1. Find the correlation coefficient:  r=    Round to 2 decimal places.
  2. The null and alternative hypotheses for correlation are:
    H0:H0: ? μ r ρ  == 0
    H1:H1: ? r ρ 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 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 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 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.
  4.  r2 =  (Round to two decimal places)  
  5.  Interpret r2 :
    • There is a 73% 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.
    • 73% 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, 73% of all of those customers will spend the predicted amount of money 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 73%.
  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 amount of money spent by a customer who spends 13 minutes at the store.
    Dollars spent = _____ (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 what any individual customer will spend.
    • As x goes up, y goes up.
    • For every additional minute customers spend at the store, they tend to spend on averge $3.54 more money at the store.


  9. Interpret the y-intercept in the context of the question:
    • The average amount of money spent is predicted to be $7.63.
    • The y-intercept has no practical meaning for this study.
    • The best prediction for a customer who doesn't spend any time at the store is that the customer will spend $7.63.
    • If a customer spends no time at the store, then that customer will spend $7.63.

 

Expert Solution
steps

Step by step

Solved in 2 steps

Blurred answer
Knowledge Booster
Discrete Probability Distributions
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Glencoe Algebra 1, Student Edition, 9780079039897…
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
Holt Mcdougal Larson Pre-algebra: Student Edition…
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Algebra
ISBN:
9781680331141
Author:
HOUGHTON MIFFLIN HARCOURT
Publisher:
Houghton Mifflin Harcourt
Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell
Elementary Algebra
Elementary Algebra
Algebra
ISBN:
9780998625713
Author:
Lynn Marecek, MaryAnne Anthony-Smith
Publisher:
OpenStax - Rice University
College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning