At the Foremost State Bank the average savings account balance in 2012 was $1200. A random sample of 38 savings account balanes for 2013 yielded a mean of $1900 with a standard deviation of $1575. At the α
=
0.025
significance level test the claim that the mean savings account balance in 2013 is different from the mean savings account balance in 2012.

(a) Identify the correct alternative hypothesis.

μ
>
$
1200

μ
=
$
1200

μ
<
$
1200

μ
≠
$
1200

(b) The test statistic value is
. (Round your answer to two decimal places.)

(c) Using the critical value approach (traditional method), the critical value is
. (Round your answer to three decimal places.)

(d) Based on your answers above, do you
Reject the
H
0

Fail to reject the
H
0

(e) Explain the choice you made in (d).

(f) Based on your choice above, choose one of the following conclusions for your test.
There is not sufficient evidence to warrant rejection of the claim
The sample data supports the claim
There is not sufficient evidence to support the claim
There is sufficient evidence to warrant rejection of the claim

(g) Explain the choice you made in (f).