Question

(28 pts) 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: 18 24 9 32 12 17 22 28 15 21 19

Money: 31 30 26 79 24 37 45 88 22 35 25

(4 pts) What is the value of the correlation coefficient?

(12 pts) Test the significance of the correlation coefficient.

(3 pts) Hypotheses:

(3 pts) P-value:

(3 pts) Decision:

(3 pts) Conclusion:

(4 pts) What is the equation of the regression line?

(4 pts) What is the predicted amount of money, on average, that someone will spend if they’re in the store for 20 minutes?

(4 pts) What is the predicted amount of time, on average, that someone will spend in a store when they end up spending $50?

Answer 1

Test for significance of the correlation coefficient :

Hypothesis :

Test statistic is given as :

P value :

P-value = P(t > 7.238) = 0.00005

P value can be found by using Excel function " TDIST(Test statistic, df= n-2,1 = one tail | 2 = two tail)"

df = n-2 - 11-2 = 9

P-value = TDIST(7.238,9,2) = 0.00005

Decision : Since, P-value = 0.00005 < 0.05 , we reject null hypothesis Ho

Conclusion : We conclude that there is significant correlation between amount of time (in minutes) customers spend in the store and the amount of money (in dollars) they spend.

Now,

Now, we are given X = 20

Y = -13.5466 + 2.7236*20 = 40.925

Predicted amount of money, on average, that someone will spend if they’re in the store for 20 minutes = $ 40.925

Now, we are given Y = 50

50 = -13.5466 + 2.7236*X

X = 23.332

predicted amount of time, on average, that someone will spend in a store when they end up spending $50 = 23.332 minutes