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. Minutes Rating   4 16   8 12   1 17   6 10   7 13   1 17   10 15   3 19   7 15   3 13   R2=0.274   α=0.05​   The ​F-test statistic is 3.02. The​ p-value is 0.121 ​   Because the​ p-value is greater than α​, do not reject the null hypothesis. There is not enough evidence to conclude that the coefficient of determination is significant.   c. Construct a​ 95% confidence interval for the average rating given by a customer who waits 8 minutes.   UCL = 15.88 ​(Round to two decimal places as​ needed.) LCL = 10.74 ​(Round to two decimal places as​ needed.)   d. Construct a​ 95% prediction interval for the rating given by a customer who waits 8 minutes.   UPL =   ​(Round to two decimal places as​ needed.) LPL =   ​(Round to two decimal places as​ needed.)

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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.

Minutes
Rating
 
4
16
 
8
12
 
1
17
 
6
10
 
7
13
 
1
17
 
10
15
 
3
19
 
7
15
 
3
13
 
R2=0.274
 
α=0.05​
 
The ​F-test statistic is 3.02.

The​ p-value is 0.121
 
Because the​ p-value is greater than α​, do not reject the null hypothesis. There is not enough evidence to conclude that the coefficient of determination is significant.
 
c. Construct a​ 95% confidence interval for the average rating given by a customer who waits 8 minutes.
 
UCL
=
15.88
​(Round to two decimal places as​ needed.)
LCL
=
10.74
​(Round to two decimal places as​ needed.)
 
d. Construct a​ 95% prediction interval for the rating given by a customer who waits 8 minutes.
 
UPL
=
 
​(Round to two decimal places as​ needed.)
LPL
=
 
​(Round to two decimal places as​ needed.)
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