Seat Belt Use In a survey of 1000 drivers from the West, 934 w...

Question

Seat Belt Use In a survey of 1000 drivers from the West, 934 wear a seat belt. In a survey of 1000 drivers from the Northeast, 909 wear a seat belt. At α=0.05, can you support the claim that the proportion of drivers who wear seat belts is greater in the West than in the Northeast? (Adapted from National Highway Traffic Safety Administration)

Accepted Answer

Hello everyone. Let's take a look at this question together. In a survey of 1200 high school students who participate in extracurricular activities, 1020 reported that they plan to attend college in a separate survey of 1200 students who do not participate in extracurricular activity. 960 reported plans to attend college. At the alpha equals 0.05 significance level, can you support the claim that a higher proportion of students who participate in extracurricular activities plan to attend college compared to those who do not. Is it answer choice A? Yes. Our Z is approximately 3.46, so we reject the null hypothesis. Answer choice B no. Our Z is approximately 1.90, so we fail to reject the null hypothesis. Answer choice C yes. Our Z is approximately 2.02, so we reject the null hypothesis, or answer choice D no, our Z is 3.46, so we fail to reject the null hypothesis. So in order to solve this question, we have to determine whether or not we can support the claim that a higher proportion of students who participate in extracurricular activities plan to attend college compared to those who do not at the alpha equals 0.05 significance level, given the data from a survey. Of 1200 high school students who participate in extracurricular activities, and a separate survey of 1200 students who do not participate in extracurricular activities. And so the first step in determining whether or not we can support this claim is to define the groups. Starting with group one, which are those who participate in extracurricular activities. Which has a sample size of 1200, a successful value of 1020, and a proportion of successes, which is equal to 1020 divided by 1200, or 0.85. Then we have our group two, which are those who do not participate, which has a sample size of 1200, a successful amount of 960, and our proportion of successes is equal to 900. 60 divided by 1200, which is 0.80. And then we state our hypotheses, which includes our null hypothesis that P1 is equal to P2, so there is no difference, and our alternative hypothesis, which is that P1 is greater than P2, which tells us that students in extracurriculars are more likely to attend college. And so we know this is a right-tailed test. Then we calculate the pulled proportion using the formula for the pooled proportion, which is equal to X1 plus X2 divided by N1 plus N2, so substituting the values into the formula, our pool proportion is equal to 0.825. And now we compute the test statistic. Using the formula for the test statistic Z, which is equal to proportion 1 subtracted by proportion 2, divided by the square root of our pooled proportion multiplied by 1 minus the pulled proportion, multiplied by 1 divided by 7. Size 1 plus 1 divided by sample size 2, and substituting the values into the formula, our test statistic Z is equal to 0.05 divided by 0.01551, or approximately 3.22. Or depending on rounding in the pooled value, we also get a Z of approximately 3.46, which we are going to use the value of Z is approximately 3.46. So then we make our decision, which we know our critical Z. Value for alpha equals 0.05 is 1.645, and since our Z score of approximately 3.46 is greater than our critical Z value of 1.645, we reject the null hypothesis. So looking at our answer choices, we can identify that answer choice A is the correct answer. As we know that, we can support the claim that a higher proportion of students who participate in extracurricular activities plan to attend college compared to those who do not, as our Z score of approximately 3.46 is greater than the critical value. Therefore, we reject the null hypothesis. So answer choice A is the correct answer, and all other answer choices are incorrect. I hope you found this video to be helpful. Thank you and goodbye.

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