Question

A customer service department asks its customers to rate their​ over-the-phone service on a scale of​ 1-20 immediately after their service has been completed. The department then matches each​ customer's rating with the number of minutes the person waited on hold. The accompanying table shows the ratings and number of minutes on hold for 10 randomly selected customers. The regression line for the data is (^ is above the Y) Y=16.85-0.15x. Use this information to complete parts a through d.

Minutes	Rating
3	14
9	12
1	17
6	9
7	15
1	17
9	13
2	19
9	14
3	13

A. Calculate the coefficient of determination

R2=0.358

(round to three decimal places)

(this has already been found)

B. using a significance level of 0.05 test the significance of the population coefficient of determination

Determine the null and alternative hypotheses.

(this has already been solved below)

Ho:p2 < 0 (< has a line under it)

Ho:p2 > 0

*the F- Statistic is =

(round to two decimal places)

* the P-Value is=

(round to two decimal places)

Choose the correct answer below

*because the P-Value is greater than / less than/or equal to the significance level, do not reject / reject the null hypothesis / alternative hypothesis. There is not / is enough evidence to conclude that the coefficient of determination

C. construct a 95% confidence interval for the average rating by a customer who waits 8 minutes

UCL=

(round to two decimal places)

LCL=

(round both to two decimal points)

D. construct a 95% prediction interval for the rating given by a customer who waits 8 minutes

UPL=

(round to two decimal places)

LPL=

(round to two decimal places)

Answer 1

1)

	df	SS	MS	F	Significance F
Regression	1	26.5	26.5	4.46	0.0678
Residual	8	47.6	5.9
Total	9	74.1

F statisctcs = 4.46

P value = 0.07

because the P-Value is greater than the significance level, do not reject the null hypothesis There is not enough evidence to conclude that the coefficient of determination is significant.

2)

Confidence:

------------------------------------

Predicted Y at X=   8   is                  
Ŷ =   16.84902   +   -0.509804   *   8   =   12.771

standard error, S(ŷ)=Se*√(1/n+(X-X̅)²/Sxx) =    1.058              
margin of error,E=t*Std error=t* S(ŷ) =   2.3060   *   1.0582   =   2.4402
                  
Confidence Lower Limit=Ŷ +E =    12.771   -   2.440   =   10.33
Confidence Upper Limit=Ŷ +E =   12.771   +   2.440   =   15.21

PRediction:------------------------------------

standard error, S(ŷ)=Se*√(1+1/n+(X-X̅)²/Sxx) =   2.6587              
margin of error,E=t*std error=t*S(ŷ)=    2.3060   *   2.66   =   6.1309
                  
Prediction Interval Lower Limit=Ŷ -E =   12.771   -   6.13   =   6.64
Prediction Interval Upper Limit=Ŷ +E =   12.771   +   6.13   =   18.90

Please revert in case of any doubt.

Please upvote. Thanks in advance