Question

Question was provided via image upload.

Explanation:

Identify the missing data

The problem asks to conduct a hypothesis test to verify if the bags contain less than 20 ounces. It references "results from the hypothesis test in the Excel worksheet." However, the Excel worksheet, sample data, sample size, sample mean, sample standard deviation, and significance level \(\alpha\) are not visible in the provided image.

Formulate the test structure

Using the Hypothesis Testing knowledge point:

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

Define the test statistic formula

Using the Test Statistic Calculation knowledge point:

• The test statistic \(t\) is calculated as:

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

where \(\bar{x}\) is the sample mean, \(\mu_0 = 20\), \(s\) is the sample standard deviation, and \(n\) is the sample size.

Define the critical value formula

Using the Critical Value Calculation knowledge point:

• For a significance level \(\alpha\) and degrees of freedom \(df = n - 1\), the critical value \(t_{\text{crit}}\) for a left-tailed test is:

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

Answer:

The provided image is incomplete because it does not include the Excel worksheet, sample data, or summary statistics (such as the sample mean, sample standard deviation, sample size, or significance level \(\alpha\)) required to calculate the numerical values.

To find the answers once you have the data:

1. Value of Test Statistic: Calculate \(t = \frac{\bar{x} - 20}{s / \sqrt{n}}\).
2. Critical Value: Find the left-tailed critical value \(-t_{\alpha, n-1}\) using a \(t\)-distribution table or Excel formula =T.INV(alpha, n-1).