Recall that the cigarette industry requires that models in cigarette ads must appear to be at least 25 years old. Also recall that a sample of 50 people is randomly selected at a shopping mall. Each person in the sample is shown a "typical cigarette ad" and is asked to estimate the age of the model in the ad. The p-value for testing H0 versus Ha can be calculated to be 0.0044.

 

Determine whether H0 would be rejected at each of α = .10, α = .05, α = .01, and α = .001. (Round your answer to 4 decimal places.)

 





To determine whether the null hypothesis \(H_0\) should be rejected at each significance level (\(\alpha\)), we compare the p-value (0.0044) to the given \(\alpha\) levels. The null hypothesis is rejected if the p-value is less than \(\alpha\).

Here are the comparisons:

1. **At \(\alpha = 0.10\):**
   \[ \text{p-value} = 0.0044 < 0.10 \]
   Since the p-value is less than 0.10, we reject \(H_0\).

2. **At \(\alpha = 0.05\):**
   \[ \text{p-value} = 0.0044 < 0.05 \]
   Since the p-value is less than 0.05, we reject \(H_0\).

3. **At \(\alpha = 0.01\):**
   \[ \text{p-value} = 0.0044 < 0.01 \]
   Since the p-value is less than 0.01, we reject \(H_0\).

4. **At \(\alpha = 0.001\):**
   \[ \text{p-value} = 0.0044 > 0.001 \]
   Since the p-value is greater than 0.001, we do not reject \(H_0\).

### Summary:
- At \(\alpha = 0.10\), reject \(H_0\).
- At \(\alpha = 0.05\), reject \(H_0\).
- At \(\alpha = 0.01\), reject \(H_0\).
- At \(\alpha = 0.001\), do not reject \(H_0\).

Would you like any further details or explanations on these results? Here are five questions you might ask:

1. Can you explain more about the concept of p-value and its importance in hypothesis testing?
2. How do significance levels (\(\alpha\)) influence the decision to reject or not reject \(H_0\)?
3. What are Type I and Type II errors in the context of hypothesis testing?
4. How would you interpret the results of this test in practical terms for the cigarette industry?
5. Can you provide an example of a situation where the p-value might lead to different decisions at different significance levels?

Tip: Always ensure that the sample size and the data collection methods are appropriate for the hypothesis test to ensure valid results.

Explore the application of p-values in hypothesis testing through a case study. Learn how to determine if the null hypothesis should be rejected at various significance levels (α) including 0.10, 0.05, 0.01, and 0.001. This example is ideal for high school students studying statistics.

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