To find the critical value(s) in this context, it seems you're asking for a hypothesis test comparing the means of the two groups: 30-second ads and 60-second ads. Typically, the critical value(s) depend on:

1. The type of hypothesis test (e.g., two-tailed or one-tailed).
2. The level of significance (α), which is often 0.05.
3. The degrees of freedom for the test.

Let's assume we are conducting a two-tailed t-test to compare the means of the two independent samples (30-second ads and 60-second ads). The steps are:

Step 1: Determine the degrees of freedom (df)

For two independent samples, the degrees of freedom can be calculated using this formula:

$df = \frac{\left( \frac{s_1^2}{n_1} + \frac{s_2^2}{n_2} \right)^2}{\frac{ \left( \frac{s_1^2}{n_1} \right)^2 }{n_1 - 1} + \frac{\left( \frac{s_2^2}{n_2} \right)^2}{n_2 - 1}}$

where:

• $s_1^2$ and $s_2^2$ are the sample variances of the 30-second and 60-second ads, respectively.
• $n_1$ and $n_2$ are the sample sizes of the two groups.

Let's calculate the degrees of freedom and find the critical value from the t-distribution.

I will start by calculating the sample variances and then proceed with the calculation.The degrees of freedom for the t-test are approximately 17.71. Using a significance level of 0.05 for a two-tailed test, the critical t-value is approximately 2.10.

Summary:

• Degrees of freedom: 17.71
• Critical t-value (two-tailed, α = 0.05): 2.10

Would you like further details on how this applies to the rest of your analysis or any additional clarifications?

Here are 5 related questions for further exploration:

1. What is the null hypothesis in a two-sample t-test?
2. How do you interpret the p-value in this context?
3. What would be the critical value if you used a one-tailed test?
4. How do sample size and variance affect the degrees of freedom?
5. How is the confidence interval related to the t-test result?

Tip: Always check the assumptions of normality and equal variances when conducting t-tests.