Question

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 Money 12 49 24 115 6 23 28 100 6 25 14 46 15 76 a. Find the correlation coefficient: r = Round to 2 decimal places. b. The null and alternative hypotheses for correlation are: H: ? = 0 H:? 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. 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 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 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. d. r? (Round to two decimal places) e. Interpret ? : 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 89%. Given any group that spends a fixed amount of time at the store, 89% of all of those customers will spend the predicted amount of money at the store. 89% of all customers will spend the average amount of money at the store. There is a 89% 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. 1. The equation of the linear regression line is: (Please show your answers to two decimal places)

Answer 1

f. ŷ = = 4.0521 x + 1.218 9. If time x=20 minute ŷ - 4.0521 * 10+1.218 y = 42.7393 h Interpret of slope: - for every additional minute at stoere customer spend at stoure, they tend to spend on average $4.05 more money at the store Interpret of y-intercep The best prediction for a customer who does't spend any time at the store is that customer will spend $ 1.22