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(%)

9.84

14.13

15.01

23.47

19.07

21.37

19.64

22.38

26.56

22.52

23.11

18.77

32.77

(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

Probability Plot of PctSavings(96) Normal-95% Cl In minitab go to Graph>probability plot> select single then Ok enter the variable in the graph variable box select the distribution as normal then click OK we will get the normal probability plot Mean 20.66 StDev 5.781 AD 0273 P-Value 0.606 from the plot AD 0273 P- value-0.6060.05 so, we can say that the data follow the normal distribution a) in MINITAB go to STAT >Basic Statistics1-sample t 2) One-Sample T: PctSavings(96) select the column time select the perform hypothesis test enter the hypothesized value as 20 Descriptive Statistics select options the select 95% 95% Lower Bound for N Mean StDev SE Mean symbol Select the> 13 20.66 5.78 17.81 1.60 then select OK-> then Ok we will get the output 10 20 30 40 PctSavings(%) He mean of PctSavings/96) fron the output test statistics t 0.41 P-value0.343 Test Null hypothesis Alternative hypothesis H1: μ > 20 T-Value P-Value 2) given alpha 0.05 here p-value 0.343> 0.05 So, do not reject Ho 041 0.343