Cash withdrawals from a college credit union for a random sample of 30 Fridays a
ID: 3043561 • Letter: C
Question
Cash withdrawals from a college credit union for a random sample of 30 Fridays and 30 Mondays are shown. At = .05, is there a difference in the mean withdrawal on Monday and Friday? The data are shown below and may be found in the data filed named ATM. 23 points
a)First test to determine if the variances in cash withdrawals differ between Friday and Monday. Show and follow the 7 steps.
b)Verify your results in part (a) using Minitab.
c)Using the information from your results in part (a), test to determine if the average cash withdrawals differ between Friday and Monday. Follow and show the 7 steps for hypothesis testing.
e)Verify your results in part (c) using Minitab.
Randomly Chosen Cash Withdrawals ($)
Friday
Monday
250
10
10
40
30
10
20
10
30
100
70
370
110
20
10
20
20
10
40
20
40
30
50
30
70
10
10
200
20
40
20
20
400
20
30
20
10
20
10
10
20
100
50
20
10
30
40
20
100
20
20
50
10
20
20
60
70
60
10
20
Randomly Chosen Cash Withdrawals ($)
Friday
Monday
250
10
10
40
30
10
20
10
30
100
70
370
110
20
10
20
20
10
40
20
40
30
50
30
70
10
10
200
20
40
20
20
400
20
30
20
10
20
10
10
20
100
50
20
10
30
40
20
100
20
20
50
10
20
20
60
70
60
10
20
Explanation / Answer
a)First test to determine if the variances in cash withdrawals differ between Friday and Monday. Show and follow the 7 steps.
Solution:
Here, we have to use two sample F test for population variances. The null and alternative hypotheses are given as below:
Null hypothesis: H0: 1^2 = 2^2
Alternative hypothesis: Ha: 1^2 2^2
(Two tailed test)
We are given
Level of significance = = 0.05
Test statistic is given as below:
F = S1^2/S2^2
From given data, we have
Sample sizes
n1 = 30, n2 = 30
S1^2 = 6672.298851
S2^2 = 5131.034483
F = 6672.298851/ 5131.034483
F = 6672.298851/ 5131.034483 = 1.3004
Upper critical value = 2.1010
P-value = 0.4338
P-value > Level of significance =
So, we do not reject the null hypothesis.
Variances of cash withdrawals at Friday and Monday are same.
b)Verify your results in part (a) using Minitab.
Required Minitab results are given as below:
Test for Equal Variances
Level1 Friday
Level2 Monday
ConfLvl 95.0000
Bonferroni confidence intervals for standard deviations
Lower Sigma Upper N Factor Levels
63.0506 81.6841 114.893 30 Friday
55.2909 71.6312 100.753 30 Monday
F-Test (normal distribution)
Test Statistic: 1.300
P-Value : 0.484
Levene's Test (any continuous distribution)
Test Statistic: 0.038
P-Value : 0.847
Results in part a and b are same.
c)Using the information from your results in part (a), test to determine if the average cash withdrawals differ between Friday and Monday. Follow and show the 7 steps for hypothesis testing.
Solution:
Here, we have to use two sample t test for population means.
H0: µ1 = µ2
Ha: µ1 µ2
(Two tailed test)
Test statistic formula is given as below:
t = (X1bar – X2bar) / sqrt[Sp2*((1/n1)+(1/n2))]
Where Sp2 is pooled variance
Sp2 = [(n1 – 1)*S1^2 + (n2 – 1)*S2^2]/(n1 + n2 – 2)
From given data, we have
Level of significance = alpha = 0.05
X1bar = 50.33
S1 = 81.68
N1 = 30
X2bar = 50
S2 = 71.63
N2 = 30
Total degrees of freedom = N1 + N2 – 2 = 30 + 30 – 2 = 58
Critical values = -2.0017 and 2.0017
Sp2 = [(n1 – 1)*S1^2 + (n2 – 1)*S2^2]/(n1 + n2 – 2)
Sp2 = [(30 – 1)*81.68^2 + (30 – 1)*71.63^2]/(30 + 30 – 2)
Sp2 = 5901.6667
t = (X1bar – X2bar) / sqrt[Sp2*((1/n1)+(1/n2))]
t = (50.33 – 50) / sqrt[5901.6667*((1/30) + (1/30))]
t = 0.0168
P-value = 0.9866
P-value > Alpha value
So, we do not reject the null hypothesis
There is insufficient evidence to conclude that average cash withdrawals differ between Friday and Monday.
e)Verify your results in part (c) using Minitab.
Required Minitab results are given as below:
Two-Sample T-Test and CI: Friday, Monday
Two-sample T for Friday vs Monday
N Mean StDev SE Mean
Friday 30 50.3 81.7 15
Monday 30 50.0 71.6 13
Difference = mu Friday - mu Monday
Estimate for difference: 0.3
95% CI for difference: (-39.4, 40.0)
T-Test of difference = 0 (vs not =): T-Value = 0.02 P-Value = 0.987 DF = 58
Both use Pooled StDev = 76.8
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.