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 30 14 23 25 21 28 8 Money 127 80 98 123 77 106 32   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: ? r ρ μ   ≠≠ 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 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.

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.

1. Find the correlation coefficient:  r=r=    Round to 2 decimal places.
2. The null and alternative hypotheses for correlation are:
   H0:H0: ? ρ r μ  == 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.  r2r2 =  (Round to two decimal places)  
5.  Interpret r2r2 :  
   • 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 85%.
   • Given any group that spends a fixed amount of time at the store, 85% of all of those customers will spend the predicted amount of money at the store.
   • 85% of all customers will spend the average amount of money at the store.
   • There is a 85% 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.
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 12 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.
   • For every additional minute customers spend at the store, they tend to spend on averge $3.85 more money at the store.
   • As x goes up, y goes up.
   
   
   
9. Interpret the y-intercept in the context of the question:
   • The average amount of money spent is predicted to be $9.98.
   • 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 $9.98.
   • If a customer spends no time at the store, then that customer will spend $9.98.