Question

Question was provided via image upload.

Explanation:

Identify the missing information

The problem asks to conduct a hypothesis test using results from an Excel worksheet. However, the Excel worksheet containing the sample data, sample size, sample mean, sample standard deviation, or the pre-calculated test results is not visible in the provided image.

Formulate the hypothesis test structure

Using the Hypothesis Testing knowledge point, we define the null and alternative hypotheses to test the claim that the bags contain less than 20 ounces:

• Null Hypothesis: \(H_0: \mu \ge 20\)
• Alternative Hypothesis: \(H_a: \mu < 20\) (left-tailed test)

Select the appropriate test statistic

Using the Test Statistic Selection knowledge point, since we are testing a single population mean and the population standard deviation \(\sigma\) is typically unknown, we use a one-sample \(t\)-test:

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

where \(\bar{x}\) is the sample mean, \(s\) is the sample standard deviation, and \(n\) is the sample size.

Determine the critical value

Using the Critical Value Calculation knowledge point, for a left-tailed \(t\)-test at a significance level \(\alpha\) with degrees of freedom \(df = n - 1\), the critical value is:

$$ t_{\text{crit}} = -t_{\alpha, df} $$

To provide the exact numerical values for the test statistic and the critical value, the data from the referenced Excel worksheet is required.

Answer:

Question 1

To find the value of the test statistic, the sample data or summary statistics (sample mean \(\bar{x}\), sample standard deviation \(s\), and sample size \(n\)) from the Excel worksheet are required.

Question 2

To find the critical value, the significance level \(\alpha\) and the sample size \(n\) (to determine degrees of freedom \(df = n - 1\)) from the Excel worksheet are required.