Question

Question was provided via image upload.

Explanation:

State the hypotheses

To test if the bags contain less than twenty (20) ounces, we formulate the hypotheses. Using the Null Hypothesis and Alternative Hypothesis concepts:

• Null Hypothesis \(H_0\): \(\mu \ge 20\)
• Alternative Hypothesis \(H_a\): \(\mu < 20\)

Select the test statistic

Using the Test Statistic Selection concept, since we are testing a single population mean \(\mu\) with an unknown population standard deviation \(\sigma\), we use a one-sample \(t\)-test. The test statistic is:

$$t = \frac{\bar{x} - \mu_0}{s / \sqrt{n}}$$

Identify missing data

The problem states to "Use the results from the hypothesis test in the Excel worksheet". However, the Excel worksheet data, sample mean \(\bar{x}\), sample standard deviation \(s\), and sample size \(n\) are not visible in the provided image.

Formulate the general solution

Without the specific numerical values from the Excel worksheet, the exact value of the test statistic cannot be computed. The final value is expressed symbolically as:

$$t = \frac{\bar{x} - 20}{s / \sqrt{n}}$$

where:

• \(\bar{x}\) is the sample mean from the Excel sheet.
• \(s\) is the sample standard deviation from the Excel sheet.
• \(n\) is the sample size from the Excel sheet.

Answer:

What is the Value of Test Statistic? <blank>\(t = \frac{\bar{x} - 20}{s / \sqrt{n}}\)</blank>