The CEO of the Jen and Benny's ice cream company is concerned about the net weight of ice cream in their 50 ounce ice cream tubs. He decides that he wants to be fairly sure that the mean weight of these ice cream tubs (μ) is greater than 52 ounces. A hypothesis test is conducted with the following hypotheses: H0: μ = 52 Ha: μ > 52 The level of significance used in this test is α = 0.05. A random sample of 26 ice cream tubs are collected and weighed. The sample mean weight is calculated to be x = 54.98 and the sample standard deviation is s = 8.43. a)Calculate the test statistic (t) for this test. Give your answer to 4 decimal places.

To calculate the test statistic (t) for this hypothesis test, we will use the formula for the t-test statistic when the population standard deviation is unknown:

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

Where: - \(\bar{x}\) is the sample mean, - \(\mu_0\) is the hypothesized population mean under the null hypothesis, - \(s\) is the sample standard deviation, and - \(n\) is the sample size.

Given the values: - Sample mean (\(\bar{x}\)) = 54.98 ounces, - Hypothesized population mean (\(\mu_0\)) = 52 ounces (under \(H_0\)), - Sample standard deviation (\(s\)) = 8.43 ounces, - Sample size (\(n\)) = 26 ice cream tubs,

the t-test statistic can be calculated as:

\[ t = \frac{54.98 - 52}{8.43 / \sqrt{26}} \]

Now we find the denominator, \(8.43 / \sqrt{26}\):

\[ 8.43 / \sqrt{26} = 8.43 / 5.099 = 1.654 \]

And substitute this into the equation to calculate \(t\):

\[ t = \frac{54.98 - 52}{1.654} = \frac{2.98}{1.654} \]

\[ t \approx 1.802 \]

Rounding to four decimal places:

\[ t \approx 1.8024 \]

So, the t-test statistic is approximately 1.8024.