Question

First National Bank and City National Bank are competing for customers who would like to open IRAs (individual retirement accounts). Thirty-two weeks were randomly selected for First National Bank and another (different) 32 weeks were randomly selected for City National. The total amount deposited into IRAs is noted for each week. A summary of data (deposits are recorded in thousands of dollars) from the survey is as follows: First National: x-bar = 4.1, sigma = 1.2 City National: x-bar = 3.5, sigma = 0.9.

The appropriate null hypothesis to test for differences in customer deposits is:

a) H₀: µ_FN = µ_CN

b) H₀: µ_FN > µ_CN

c) H₀: µ_FN ≠µ_CN

d) H₀: p_FN = p_CN

A good point estimate of the difference in weekly amount deposited into IRAs for these two banks is ____

a) 4.1-3.5 = 0.6

b) 4.1/3.5

c) 0.265

d) 1.2/0.9

The appropriate test statistic is

a) chi-square

b) F

c) z

d) t

Say that the appropriate distribution to use for finding the critical value is z; furthermore, say that the appropriate level of significance is α = 0.05. Finally, assume that you want to know if there are differences in average IRA deposits between the two banks. What is the critical value from the table?

a) 1.96

b) 1.28

c) 2.575

d) not the answer

Answer 1

a) H₀: µ_FN = µ_CN

A good point estimate of the difference in weekly amount deposited into IRAs for these two banks is __

a) 4.1-3.5 = 0.6

The appropriate test statistic is

c) z

The critical value from the table

a) 1.96

We have

= 4.1 , = 1.2

= 3.5, = 0.9

test statistics.

p value = 0.02364

Conclusion:

p value (0.02364) < 0.05

or

test statistics(2.263) > 1.96

Reject H0

So we conclude that

There are differences in average IRA deposits between the two banks.