To address the hypothesis testing problem in the image, let's first extract and understand the given information.

Given Data:

• Company 1 times (minutes): 102, 86, 93, 114
• Company 2 times (minutes): 121, 148, 97, 92, 114

Hypothesis Test:

• Claim: The problem is testing whether the average running time of films produced by Company 2 exceeds the average running time of films produced by Company 1 by 10 minutes.

Null Hypothesis ($H_0$):

The null hypothesis assumes that the average running time of films from Company 2 is either equal to or less than the average running time of films from Company 1 plus 10 minutes.

$H_0: \mu_2 \leq \mu_1 + 10$ Where:

• $\mu_2$ = Mean running time of films produced by Company 2
• $\mu_1$ = Mean running time of films produced by Company 1

Alternative Hypothesis ($H_1$):

The alternative hypothesis posits that the average running time of films from Company 2 exceeds the average running time of films from Company 1 by more than 10 minutes.

$H_1: \mu_2 > \mu_1 + 10$

These hypotheses are suitable for a one-tailed test at the significance level $\alpha = 0.1$.

Would you like to proceed with the calculation of the test statistic and conclusion? If so, I can guide you through the process.

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Questions:

1. Would you like to calculate the sample means and variances for each company?
2. Do you need help determining the appropriate test statistic for this hypothesis test?
3. Are you interested in conducting this test manually or using statistical software?
4. Would you like to discuss the assumptions needed for this hypothesis test to be valid?
5. Do you need an explanation of how the significance level $\alpha = 0.1$ impacts the decision rule?

Tip:

When conducting hypothesis tests, always clearly define your null and alternative hypotheses before beginning calculations to ensure that your test addresses the correct research question.