Question

2. Cash withdrawals from a college credit union for a random sample of 30 Fridays and 30 Mondays are shown. At α = .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
   • First test to determine if the variances in cash withdrawals differ between Friday and Monday. Show and follow the 7 steps.  
   • Verify your results in part (a) using Minitab.
   • 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.  
   • Refer to part c, give and interpret the p-value.  
   • 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

Answer 1

(a)

(b) Minitab output:

Test and CI for Two Variances: Firday, Monday

Method

Null hypothesis         Sigma(Firday) / Sigma(Monday) = 1
Alternative hypothesis Sigma(Firday) / Sigma(Monday) not = 1
Significance level      Alpha = 0.05

Statistics

Variable   N   StDev Variance
Firday    30 81.684 6672.299
Monday    30 71.631 5131.034

Ratio of standard deviations = 1.140
Ratio of variances = 1.300

95% Confidence Intervals

                                   CI for
Distribution   CI for StDev       Variance
of Data            Ratio           Ratio
Normal        (0.787, 1.653) (0.619, 2.732)
Continuous    (0.213, 4.795) (0.045, 22.994)

Tests

                                               Test
Method                          DF1 DF2 Statistic       P-Value
F Test (normal)                  29   29       1.30           0.484
Levene's Test (any continuous)    1   58       0.04    0.847

(c)

(d)

Minitab output:

Two-Sample T-Test and CI: Firday, Monday

Two-sample T for Firday vs Monday

                           SE
         N Mean StDev Mean
Firday 30 50.3   81.7    15
Monday 30 50.0   71.6    13

Difference = mu (Firday) - 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 = 76.8223