Subjects statistics

Hypothesis Testing Fbce80

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Use the AI math solver

1. **State the problem for the first scenario:** A fast-food chain claims the average service time is 3 minutes. You suspect it is not true (it seems longer). 2. **Formulate hypotheses:** - Null hypothesis $H_0$: The average service time is 3 minutes, i.e., $\mu = 3$. - Alternative hypothesis $H_a$: The average service time is not 3 minutes, i.e., $\mu \neq 3$. 3. **State the problem for the second scenario:** An airline claims the average delay is less than 10 minutes. You suspect delays are longer. 4. **Formulate hypotheses:** - Null hypothesis $H_0$: The average delay is less than or equal to 10 minutes, i.e., $\mu \leq 10$. - Alternative hypothesis $H_a$: The average delay is greater than 10 minutes, i.e., $\mu > 10$. 5. **Draw conclusions based on claim and decision:** - For the first problem, if the test rejects $H_0$, conclude the average service time is not 3 minutes (claim is false). If fail to reject, claim stands. - For the second problem, if the test rejects $H_0$, conclude the average delay is significantly longer than 10 minutes (claim is false). If fail to reject, claim stands. **Summary:** - Problem 1 hypotheses: $H_0: \mu=3$, $H_a: \mu \neq 3$. - Problem 2 hypotheses: $H_0: \mu \leq 10$, $H_a: \mu > 10$. - Conclusions depend on test results: reject or fail to reject $H_0$. No numerical data or test statistics were provided, so no further calculations can be done.