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 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.

Identify the correct alternative hypothesis.
a) μ > $1200
b) μ = $1200
c) μ < $1200
d) μ ≠ $1200

Answer 1

To test the claim that the mean savings account balance in 2013 is different from the mean savings account balance in 2012, a two-sample t-test can be used at the α=0.025 significance level. The correct alternative hypothesis is μ ≠ $1200.

Step-by-step explanation:

To test the claim that the mean savings account balance in 2013 is different from the mean savings account balance in 2012, we can use a hypothesis test. The null hypothesis, denoted as H0, assumes that the mean savings account balance in 2013 is equal to the mean savings account balance in 2012. The alternative hypothesis, denoted as Ha, assumes that the mean savings account balance in 2013 is not equal to the mean savings account balance in 2012.

Since we are comparing two means, we can use a two-sample t-test. With a sample mean of $1900 and a sample standard deviation of $1575, we can calculate the test statistic:

t = (sample mean - population mean) / (sample standard deviation / √sample size)

Comparing the test statistic to the t-distribution with (sample size - 1) degrees of freedom and a significance level of α = 0.025, we can determine the critical t-value and make a decision about the null hypothesis. If the test statistic falls in the rejection region, we reject the null hypothesis and conclude that the mean savings account balance in 2013 is different from the mean savings account balance in 2012. Otherwise, we fail to reject the null hypothesis.

The correct alternative hypothesis is d) μ ≠ $1200.