The Virginia Department of Social Services collected information on 25

Virginia Supplemental Nutrition Assistance Program (SNAP, formerly Food
Stamps) beneficiaries and found that their average monthly food expenditure
was $160. The average monthly food expenditure for SNAP beneficiaries
nationwide is assumed to be $136. Assume that the SNAP beneficiaries’
expenditures are normally distributed and have a standard deviation of
$15.40. If you were to test the claim that Virginia SNAP beneficiaries have a
monthly expenditure different from that of $136, using a 0.05 significance
level, what would be the test statistic?
a) 1.56
b) 7.79
c) 1.96
d) -7.79
e) -1.56

I used a t-test and got b)7.79

To test the claim that Virginia SNAP beneficiaries have a monthly expenditure different from $136, you can use a t-test since the sample size is small (<30).

Here is how you can calculate the test statistic using a t-distribution:

1. Set up the hypotheses:
- Null hypothesis (H0): The average monthly food expenditure of Virginia SNAP beneficiaries is $136.
- Alternative hypothesis (Ha): The average monthly food expenditure of Virginia SNAP beneficiaries is different from $136.

2. Determine the significance level (alpha). In this case, it is given as 0.05.

3. Calculate the test statistic:
- The formula for the t-test statistic is: t = (x̄ - μ) / (s / √n)
- x̄ is the sample mean (average monthly expenditure), which is $160.
- μ is the population mean (hypothesized average monthly expenditure), which is $136.
- s is the sample standard deviation, which is $15.40.
- n is the sample size, which is 25.

- Plugging in the values, we get: t = (160 - 136) / (15.40 / √25) ≈ 7.79

4. Determine the critical value:
- Since we are using a t-test and have 24 degrees of freedom (df = n - 1), and a significance level of 0.05, we need to find the critical t-value from the t-distribution table or using a calculator. For a two-tailed test at alpha = 0.05, the critical t-value is approximately ±1.96.

5. Make a decision:
- If the absolute value of the test statistic is greater than the critical value (|7.79| > 1.96), we reject the null hypothesis (H0) in favor of the alternative hypothesis (Ha). This means that the average monthly food expenditure of Virginia SNAP beneficiaries is significantly different from $136.

Therefore, the correct test statistic for this problem is b) 7.79.