Question

A cellular phone service provider is offering a new calling plan that it claims will result in an average savings of more than 20% for its customers who switch to the plan. To evaluate this claim, a consumer watchdog organization contacted a random sample of this provider's customers who enrolled in the new plan and computed their individual savings (as a percentage of their original monthly bill).

PctSavings(%)
33.17
21.43
19.29
24.59
29.25
24.09
21.36
14.27
26.29
16.85
19.09
27.56
25.65
15.02
18.53
17.06
21.16

1. Use Minitab to construct a normal probability plot to check the normality condition. Report the value of the Anderson-Darling statistic (AD) below.

AD =  (rounded to 3 decimal places; 2 for Minitab Express)

2. Use Minitab to conduct a test to see if there is enough evidence for the provider's claim. Report the value of the appropriate test statistic and the p-value.

Test Statistic Value =? (rounded to 2 decimal places)
p-value =? (rounded to 3 decimal places; 4 for Minitab Express)

Answer 1

1)

AD = 0.2

p-value = 0.861 > 0.05

hence normality assumption is valid

2)

One-Sample T: PctSavings

Test of μ = 20 vs > 20

Variable   N   Mean    StDev SE Mean 95% Lower Bound     T      P
PctSavings    17    22.04        5.24 1.27           19.82 1.60    0.064

TS = 1.60

p-value = 0.064 > 0.05

hence we fail to reject the null hypothesis