1. A sample of 8 customers from internet provider A was obtained and their ages
ID: 3263564 • Letter: 1
Question
1. A sample of 8 customers from internet provider A was obtained and their ages recorded below. A sample of 10 customers from internet provider B and their ages were also obtained. Using the .05 level of significance, is it possible to conclude that the average age of provider A customers is significantly larger than the average age of provider B? The results of the test of variances and means (using two different methods) are presented below. Using alpha = .05, please answer the questions below. the .05 level of significance, is it possible to conclude that the average age of provider A customers is significantly larger than the average age of provider B? The results of the test of variances and means (using two different methods) are presented below. Using alpha = .05, please answer the questions below.
Ages of Customers: Provider A Provider B F Test Two Sample for Variances
65 53 Provider B Provider A
75 59 Mean 45.9 58.375
63 27 Variance 146.9889 88.839
55 58 Observations 10 8
57 51 df 9 7
49 45 F 1.654548
45 53 P value 0.2597
58 26 F Critical 4.823221
51
36
Mean 58.375 45.9
Median 57.5 51
Standard Deviation 9.425459 12.1239
Sample Variance 88.83929 146.9889
t-Test: Two Sample Assuming Equal Variances t-Test: Two Sample Assuming Unequal Variances
Provider A Provider B Provider A Provider B
Mean 58.375 45.9 Mean 58.375 45.9
Variance 88.83929 146.9889 Variance 88.83929 146.9889
Observations 8 10 Observations 8 10
Pooled Variance 121.5484
Hypothesized mean difference 0 Hypothesized Mean difference 0
Df 16 Df 16
t-Stat 2.385474 t-Stat 2.455832
P(T<=t) one-tail 0.014883 P(T<=t) one tail 0.012934
t Critical one-tail 1.745884 t Critical one-tail 1.745884
P(T<=t) two tail 0.029767 P(T<=t) two tail 0.025869
t Critical two tail 2.119905 t Critical two tail 2.119905
You must conduct two tests with this problem. First use the F-test to determine if your variances are equal or not equal. (Parts a – g)
Then conduct the appropriate test of means. The output s provided for both the equal variance t-test and the unequal variance t-test. You must decide which test is appropriate based on your answer to questions f and g. The test of means begins with question h and goes through question k.
a. What statistical test must you use before you can test the means? _____________________
b. What are your null and alternative hypotheses for that first test?
____________________________________________________________________
c. What is your calculated test statistic? _________________
d. What is your critical value? ____________
e. What is your decision rule? ________________________________________________________
f. What is your conclusion? ______________________________________
g. Which test of means should be used? ______________________________
h. State your null and alternative hypotheses for testing the means_________________________________________
i. What is your calculated test statistic?_____________________
j What is your decision rule? ______________________________________________________
k. What can you conclude about the average ages of the two internet providers? ____________________________________________________________________________________
Explanation / Answer
a. What statistical test must you use before you can test the means?
Answer: F-test for Variances
b. What are your null and alternative hypotheses for that first test?
H0: There is no significance difference between the variance of Provider A and Provider B
H1: There is significance difference between the variance of Provider A and Provider B
c. What is your calculated test statistic?
Answer :F - 146.9889/ 88.839= 1.6545
d. What is your critical value?
Answer: F-Critical value = 4.823221
e. What is your decision rule?
Answer: Reject H0 if F value > F-critical value
Here F value < F critical value, so we accept H0 There is no significance difference between the variance of Provider A and Provider B
f. What is your conclusion?
Answer: we have to use T-test for equal variance
h. State your null and alternative hypotheses for testing the means
Answer:
H0: the average age of provider A customers is not significantly larger than the average age of provider B
H1: the average age of provider A customers is significantly larger than the average age of provider B
i. What is your calculated test statistic?
Answer: t-stat = 2.385474
j What is your decision rule?
Answer: Reject H0 if t-stat >t - critical one -tail (1.745884)
k. What can you conclude about the average ages of the two internet providers?
Here t value > t - Critical value one-tail, so we reject H0
thus we conclude that the average age of provider A customers is significantly larger than the average age of provider B
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.