Question

At the Foremost State Bank, the average savings account balance in 2012 was $1200. A random sample of 38 savings account balances for 2013 yielded a mean of $1900 with a standard deviation of $1575. At the significance level α = 0.025, 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 H0

Fail to reject the H0
(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).

Answer 1

The average savings account balance in 2013 is different from the average savings account balance in 2012.

Step-by-step explanation:

The random variable for this study is the savings account balance.

The null hypothesis for this study is μ = $1200 and the alternative hypothesis is μ ≠ $1200.

To test the null hypothesis, we can calculate the test statistic value, which is equal to the difference between the sample mean ($1900) and the hypothesized population mean ($1200), divided by the standard deviation of the sample mean ($1575/sqrt(38)). The test statistic value should be -3.01.

Using the critical value approach, the critical value for a two-tailed test at α = 0.025 is +-1.96.

Since the test statistic value is less than the critical value, we reject the null hypothesis. This means that there is sufficient evidence to conclude that the mean savings account balance in 2013 is different from the mean savings account balance in 2012.

Based on our choice to reject the null hypothesis, we can conclude that there is sufficient evidence to warrant rejection of the claim.