A random sample of 15 customers in two different banks were selected and their w
ID: 3180838 • Letter: A
Question
A random sample of 15 customers in two different banks were selected and their wait times (in minutes) are given below. Use this data to complete parts (a) through (d).
Bank A
Bank B
3.54
9.68
3.18
5.88
4.38
8.12
6.12
5.89
0.34
8.78
5.05
3.74
6.56
8.14
6.11
8.37
3.83
10.47
4.19
6.66
5.46
5.56
3.04
4.02
5.06
6.22
4.74
9.93
2.31
5.49
a.
Is there evidence of a difference in the variability of the waiting time between the two banks? (Use =0.01).
Determine the hypotheses. Choose the correct answer below.
A.
H0: 1 less than or equal to 2
H1: 1 greater than 2
B.
H0: 1 not equal to 2
H1: 1 equal to 2
C.
H0: 1 equal to 2
H1: 1 not equal to 2
D.
H0: 1 greater than or equal to 2
H1: 1 less than 2
Compute the FSTAT test statistic.
FSTAT = ____
(Round to two decimal places as needed.)
Determine the critical value.
F/2 = ____
(Round to two decimal places as needed.)
b.
Determine the p-value in (a) and interpret its meaning.
The p-value in part (a) is ____
(Round to three decimal places as needed.)
What does the p-value mean?
A. The p-value is the probability of falsely rejecting the null hypothesis.
B. The p-value is the probability of rejecting the null hypothesis if the test were repeated for different samples.
C. The p-value is the probability of obtaining a result at least as extreme as the one obtained with this sample given that the null hypothesis is true.
D. The p-value is the probability that the null hypothesis is true.
c.
What assumption about the population distribution of the two banks is necessary in (a)? Is the assumption valid for these data?
What assumption about the population distribution of the two banks is necessary in (a)?
A. Each of the two populations must be normally distributed.
B. There is enough information given that no assumptions need to be made.
C. The sample sizes taken from the population are independent and identically distributed.
D. The populations do not contain any extreme outliers.
Is the assumption valid for these data?
A. The assumption is not valid because histograms of the data do not appear to be bell shaped, which is a good indication of possible non-normality.
B. The assumption is not valid because both populations contain outliers.
C. The assumption is not valid because the sample sizes are not independent.
D. The assumption is valid because histograms of the data appear to be bell shaped, which is a good indication of possible normality.
d.
Assume the results of part (a) are valid. Based on the results of (a), is it appropriate to use the pooled-variance t test to compare the means of the two banks?
A. No, because the population variances cannot be assumed to be equal.
B. Yes, because the samples are randomly and independently selected from populations that are assumed to be normally distributed and the population variances can be assumed to be equal.
C. No, because the samples are not randomly and independently selected from populations that are assumed to be normally distributed.
Bank A
Bank B
3.54
9.68
3.18
5.88
4.38
8.12
6.12
5.89
0.34
8.78
5.05
3.74
6.56
8.14
6.11
8.37
3.83
10.47
4.19
6.66
5.46
5.56
3.04
4.02
5.06
6.22
4.74
9.93
2.31
5.49
Explanation / Answer
let X denotes the waiting time for bank A and Y denottes the same for bank B
assumption is X~N(u1,sigma12) and Y~N(u2,sigma22) independently
with all the parameters unknown.
we have n=15 observations from both the populations and
let sx2 be the variance of the first sample which is 2.689 and sy2 be the same for second sample which is 4.445
we want to test Is there evidence of a difference in the variability of the waiting time between the two banks?
with alpha=0.01
a) the correct set of hypothesis are
H0: 1 equal to 2
H1: 1 not equal to 2 [option C]
then test statistic is Fstat=sx2/sy2 which under H0 follows an F distribution with df 15-1 and 15-1
value of Fstat is =2.689/4.445=0.60 [answer]
since the alternative hypothesis is both sided hence the critial value is
F0.01/2;14,14=4.299 [answer]
b) hence p value is p=2*min{P[F>0.60],P[F<0.60]}=2*0.175196=0.350 [answer]
hence p value > alpha
so H0 is accepted. hence the conclusion is that both the variances are same
p value means
The p-value is the probability of obtaining a result at least as extreme as the one obtained with this sample given that the null hypothesis is true. [answer] [option C]
c)the F test is valid only if the parent population is normal
hence
What assumption about the population distribution of the two banks is necessary in (a)?
A. Each of the two populations must be normally distributed.
Is the assumption valid for these data?
D. The assumption is valid because histograms of the data appear to be bell shaped, which is a good indication of possible normality.
otherwise the above would not be valid
d)
Assume the results of part (a) are valid. Based on the results of (a), is it appropriate to use the pooled-variance t test to compare the means of the two banks?
B. Yes, because the samples are randomly and independently selected from populations that are assumed to be normally distributed and the population variances can be assumed to be equal.
as H0 is accepted
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