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 22 16 15 19 7 8 14 10 Money 81 55 41 60 41 21 35 54 Find the correlation coefficient: r=r= Round to 2 decimal places. The null and alternative hypotheses for correlation are: H0:H0: ? ρ r μ ? = 0 H1:H1: ? μ r ρ ? ≠ 0 The p-value is: _______ (Round to four decimal places) 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 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. 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.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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	22	16	15	19	7	8	14	10
Money	81	55	41	60	41	21	35	54

Find the correlation coefficient: r=r= Round to 2 decimal places.
The null and alternative hypotheses for correlation are:
H0:H0: ? ρ r μ ? = 0
H1:H1: ? μ r ρ ? ≠ 0
The p-value is: _______ (Round to four decimal places)
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 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.
- 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.
r2 = _______ (Round to two decimal places)
Interpret r2 :
- Given any group that spends a fixed amount of time at the store, 60% of all of those customers will spend the predicted amount of money at the store.
- There is a 60% 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.
- 60% of all customers will spend the average 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 60%.
The equation of the linear regression line is:
ˆy =_______ +_______x (Please show your answers to two decimal places)
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.)

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