MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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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
19
27
10
20
10
30
Money
23
92
87
27
69
58
124
a. Find the correlation coefficient: r =
Round to 2 decimal places.
b. The null and alternative hypotheses for correlation are:
Ho: ? = 0
H1: ? + 0
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.
d. r2
(Round to two decimal places)
e. Interpret r2 :
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 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.
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%.
f. The equation of the linear regression line is:
=
x (Please show your answers to two decimal places)
g. Use the model to predict the amount of money spent by a customer who spends 14 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:
O The slope has no practical meaning since you cannot predict what any individual customer will
spend.
O As x goes up, y goes up.
O For every additional minute customers spend at the store, they tend to spend on averge $3.56
more money at the store.
i. Interpret the y-intercept in the context of the question:
O The average amount of money spent is predicted to be $6.99.
O The best prediction for a customer who doesn't spend any time at the store is that the
customer will spend $6.99.
O If a customer spends no time at the store, then that customer will spend $6.99.
O The y-intercept has no practical meaning for this study.
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