Question 12A 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 surveyare shown below.TTime 15 21 6 23 16 15 26 6Money 47 75 39 67 69 42 8131< >a. Find the correlation coefficient: r =b. The null and alternative hypotheses for correlation are:Ho: ? = 0H₁: ?v #0The p-value is:80F3(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 contextof the study.O There is statistically significant evidence to conclude that a customer who spends more timeat 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 timeat 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 theamount of time customers spend at the store and the amount of money that they spend at thestore. Thus, the use of the regression line is not appropriate.O There is statistically significant evidence to conclude that there is a correlation between theamount of time customers spend at the store and the amount of money that they spend at thestore. Thus, the regression line is useful.(Round to two decimal places)d. ²e. Interpret ²:O There is a 81% chance that the regression line will be a good predictor for the amount ofmoney spent at the store based on the time spent at the store.Round to 2 decimal places.481% of all customers will spend the average amount of money at the store.O Given any group that spends a fixed amount of time at the store, 81% of all of those customerswill spend the predicted amount of money at the store.F4O There is a large variation in the amount of money that customers spend at the store, but if youonly look at customers who spend a fixed amount of time at the store, this variation onaverage is reduced by 81%.deF5MacBook AirAF6&F7*DIIF8DDF9 Spend the predicted 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 youonly look at customers who spend a fixed amount of time at the store, this variation onaverage is reduced by 81%.f. The equation of the linear regression line is:ŷ =+Pe, 81% of all of those customers(Please show your answers to two decimal places)g. Use the model to predict the amount of money spent by a customer who spends 20 minutes at thestore.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 For every additional minute customers spend at the store, they tend to spend on averge $2.30more money at the store.O The slope has no practical meaning since you cannot predict what any individual customer willspend.O As x goes up, y goes up.1. Interpret the y-intercept in the context of the question:Olf a customer spends no time at the store, then that customer will spend $19.57.The average amount of money spent is predicted to be $19.57.The best prediction for a customer who doesn't spend any time at the store is that thecustomer will spend $19.57.O The y-intercept has no practical meaning for this study.

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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 15 21 6 23 16 15 26 6 Money 47 75 39 67 69 42 81 31 a. Find the correlation coefficient: r = b. The null and alternative hypotheses for correlation are: Ho: ? = 0 H₁: ?0 The p-value is: Round to 2 decimal places. (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 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. 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.

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P