1 One Sample Proportion: Proportion of Smoking Students A professor gave a survey to a large random sample of college students. Of the 362 students in the sample, 43 said they smoked. b. What sample size would be needed to construct a 95% confidence interval to estimate the proportion of all students who smoke with a margin of error of ±1%? Use the observed sample proportion as an estimate for the population proportion. You will need to do hand calculations. Show all work. c. A Student Affairs professional wants to know if there is evidence that less than 15% of all college students smoke. Use the five-step hypothesis testing procedure outlined below to address this research question. The only hand calculation you will need to do will be in step 1 to check assumptions. Use Minitab Express for steps 2 and 3. Remember to include all relevant Minitab Express output and to clearly identify your test statistic and p-value from the output. Step 1: Check assumptions and write hypotheses. Step 2: Calculate the test statistic. Step 3: Determine the p value. Step 4: Decide to reject or fail to reject the null. Step 5: State a “real world” conclusion.
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We are given a large random sample of college students (n = 362), and we want to test if the proportion of students who smoke is less than 15%. We can write our null and alternative hypotheses as follows: H0: p >= 0.15 Ha: p < 0.15 Show more…
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Suppose that you are interested in determining whether the advice given by a physician during a routine physical examination is effective in encouraging patients to stop smoking. In a study of current smokers, one group of patients was given a brief talk about the hazards of smoking and was encouraged to quit. A second group received no advice pertaining to smoking. All patients were given a follow-up exam. In the sample of 114 patients who had received the advice, 11 reported that they had quit smoking; in the sample of 96 patients who had not, 7 had quit smoking. a. Write the null and alternative hypothesis for testing the difference between these two proportions. b. What are the critical values and rejection region for this test, if your alpha is 0.05? c. Calculate the test statistic for the difference between the proportions. d. What is the p-value for this test and report the number here. e. Do you reject the null hypothesis or not? Why? f. Write a meaningful conclusion for your decision about the null hypothesis. g. Construct a 95% confidence interval for the difference between these two proportions.
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