Commercial Bank and Trust Company is studying the use of its automatic teller ma
ID: 3132546 • Letter: C
Question
Commercial Bank and Trust Company is studying the use of its automatic teller machines (ATMs). Of particular interest is whether young adults (under 25 years) use the machines more than senior citizens. To investigate further, samples of customers under 25 years of age and customers over 60 years of age were selected. The number of ATM transactions last month was determined for each selected individual, and the results are shown below.
(Under 25) 10 10 11 15 7 11 10 9
(Over 60) 4 8 7 7 4 5 1 7 4 10 5
(1) Find the degrees of freedom for unequal variance test. (Round down answer to nearest whole number.)
Degrees of freedom ___________
(2) State the decision rule for 0.01 significance level: H0 ?under ? ?over; ?under > ?over. (Round your answer to 3 decimal places.)
Reject H0 if t > __________
(3) Compute the value of the test statistic. (Round your answer to 2 decimal places.)
Value of the test statistic ____________
4.At the .01 significance level, can the bank management conclude that younger customers use the ATMs more?
Explanation / Answer
Solution:
1) Degrees of freedom = 15
2) Reject H0 if t > 2.603
3) Value of test statistic = t = 4.34
4) The two sample t test for checking the claim whether the younger customers use the ATMs more or not given as below:
Null hypothesis: H0: There is no any significant difference in the use of ATMs by younger and older customers.
Alternative hypothesis: Ha: The younger customers use the ATMs more than the older customers.
The test is given as below:
Calculations Area
Pop. 1 Sample Variance
5.1250
Pop. 2 Sample Variance
6.0545
Pop. 1 Sample Var./Sample Size
0.6406
Pop. 2 Sample Var./Sample Size
0.5504
For one-tailed tests:
TDIST value
0.0003
1-TDIST value
0.9997
Separate-Variances t Test for the Difference Between Two Means
(assumes unequal population variances)
Data
Hypothesized Difference
0
Level of Significance
0.01
Population 1 Sample
Sample Size
8
Sample Mean
10.375
Sample Standard Deviation
2.2638
Population 2 Sample
Sample Size
11
Sample Mean
5.636363636
Sample Standard Deviation
2.4606
Intermediate Calculations
Numerator of Degrees of Freedom
1.4186
Denominator of Degrees of Freedom
0.0889
Total Degrees of Freedom
15.9526
Degrees of Freedom
15
Standard Error
1.0913
Difference in Sample Means
4.7386
Separate-Variance t Test Statistic
4.3420
Upper-Tail Test
Upper Critical Value
2.6025
p-Value
0.0003
Reject the null hypothesis
Here, we get the p-value as 0.0003 which is less than the given level of significance or alpha value 0.01, so we reject the null hypothesis that there is no any significant difference in the use of ATMs by younger and older customers. This means, we conclude that the younger customers use the ATMs more than the older customers.
Calculations Area
Pop. 1 Sample Variance
5.1250
Pop. 2 Sample Variance
6.0545
Pop. 1 Sample Var./Sample Size
0.6406
Pop. 2 Sample Var./Sample Size
0.5504
For one-tailed tests:
TDIST value
0.0003
1-TDIST value
0.9997