One survey by the American Medical Association showed that among 785 randomly selected people who completed four years of college, 81.7% do not smoke. Use a 0.01 significance level to test the claim that people who completed four years of college are more likely to not smoke than people in the general population.
Incomplete
To test the claim that people who completed four years of college are more likely to not smoke than people in the general population, we can use a hypothesis test.
Step 1: State the hypotheses:
The null hypothesis (H0): The proportion of people who do not smoke among those who completed four years of college is equal to the proportion in the general population.
The alternative hypothesis (Ha): The proportion of people who do not smoke among those who completed four years of college is higher than the proportion in the general population.
Step 2: Set the level of significance:
The given significance level is 0.01. This signifies that we will reject the null hypothesis if the probability of obtaining the observed result is less than 0.01 assuming that the null hypothesis is true.
Step 3: Calculate the test statistic:
To test the hypothesis, we calculate the test statistic using the formula for a one-sample proportion test:
z = (p - P) / √(P * (1 - P) / n)
where p is the sample proportion (0.817), P is the proportion in the general population (to be determined), and n is the sample size (785).
Step 4: Determine the critical value:
Since we have a one-sided alternative hypothesis (claiming a higher proportion of non-smokers), we need to find the critical value corresponding to a 0.01 significance level from the standard normal distribution. This critical value is z = 2.33.
Step 5: Calculate the p-value:
The p-value is the probability of obtaining a test statistic as extreme as the one observed in the sample, given that the null hypothesis is true. To calculate the p-value, we use the standard normal distribution. We find the area to the right of the test statistic (z = 1.87) under the standard normal curve using a z-table or a calculator.
Step 6: Make a decision:
Compare the p-value to the significance level. If the p-value is less than the significance level (0.01), we reject the null hypothesis. If the p-value is greater than or equal to the significance level, we fail to reject the null hypothesis.
In this case, if the p-value is less than 0.01, we reject the null hypothesis. If the p-value is greater than or equal to 0.01, we fail to reject the null hypothesis.
So, the final step would involve calculating the p-value based on the test statistic and comparing it to the significance level. Unfortunately, without the proportion of non-smokers in the general population, we cannot proceed with calculating the p-value.