Question

Bank A and Bank B have each developed an improved process for serving customers. The waiting period from the moment a customer enters until he or she reaches the counter needs to be shortened. A random sample of 10 customers is selected from each bank and the results​ (in minutes) are shown in the accompanying data table

Bank A
2.18
2.38
3.02
3.02
3.11
4.57
4.29
4.37
5.28
5.83

Bank B
3.97
4.41
4.13
5.18
5.33
6.84
6.36
8.58
8.55
10.33

Assuming that the population variances from both banks are​ equal, is there evidence of a difference in the mean waiting time between the two​ branches? (Use

.α=0.01.​)

1) Reject Ho. There is insufficient evidence that means differ.

2) Do not reject Ho. There is sufficient evidence that means differ

3) Do not reject Ho. There is insufficient evidence that means differ

4) Reject Ho. There is sufficient evidence that means differ.

B) Determine the​ p-value in​ (a) and interpret its meaning.

interpret the​ p-value. Choose the correct answer below.

1) It is the probability of obtaining a sample that yields a t test statistic farther away from 0 in the negative direction than the computed test statistic if there is no difference in the mean waiting time between Bank A and Bank B.

2) It is the probability of obtaining a sample that yields a t test statistic farther away from 0 in the positive direction than the computed test statistic if there is no difference in the mean waiting time between Bank A and Bank B.

3) It is the probability of obtaining a sample that yields a t test statistic farther away from 0 in either direction than the computed test statistic if there is no difference in the mean waiting time between Bank A and Bank B.

c. In addition to equal​ variances, what other assumption is necessary in​ (a)?

1) Both sampled populations are approximately normal.

2) The sample sizes must be equal.

3) The samples are specifially chosen and not independently sampled.

4) Both sampled populations are not approximately normal.

Answer 1

Where

Substituting the variances and values  of and in the formula above we get as 3.1366. Now computing the test statistic we have T=3.2359

The degrees of freedom here in this test is

The p value for the T value at 18 degrees of freedom is 0.0046<0.05 . Reject H_0.Hence there is enough evidence from the data to believe that the two means differ

A) option 4

B) option 3 ( Since the test is two tailed, it can be either direction

C) option 1 ( Both samples are assumed to be from the normal population, t test is used since the population standard deviation is unknown)