Afraid to Fly According to a study conducted by the Gallup org...

Question

Afraid to Fly According to a study conducted by the Gallup organization, the proportion of Americans who are afraid to fly is 0.10. A random sample of 1100 Americans results in 121 indicating that they are afraid to fly. Explain why this is not necessarily evidence that the proportion of Americans who are afraid to fly has increased since the time of the Gallup study.

Accepted Answer

Hello, everyone, let's take a look at this question together. A national health survey reports that 65% of adults aged 25 to 40 eat breakfast every day. You randomly select a sample of 220 adults in this age group and find that only 120 of them report eating breakfast daily. After performing a one sample proportion Z test, you calculate a Z score of -5.0. 3. Based on the Z score, can you conclude that this sample is representative of the population at the alpha equals 0.05 level? Is it answer choice A? Yes, the Z score falls within the acceptance region, so the sample is representative. Answer choice B, no, the Z score is too small to support the claim, but it is not statistically significant. Answer choice C. No, the Z score falls in the rejection region, so the sample is not representative, or answer choice D yes, although the Z score is negative, it still supports the population claim. So in order to solve this question, we have to recall what we have learned about a one sample proportion C test to determine based on the calculated Z score of -5.03, can we conclude that this sample is representative of the population at the alpha equals 0.05 level, given our sample of 220 adults who are aged 25 to 40, with only 120 of those adults reporting that they eat breakfast daily. And so, in order to conclude whether this sample is representative of the population, we have to look at the data that we are given. Which includes our population claim that 65% of adults who are aged 25 to 40 eat breakfast daily. Our sample size, which is N, is equal to 220. Our sample count tells us that 120 adults say they eat breakfast daily out of the sample of 220 adults. We have our given Z score from that one sample proportion Z test, which is equal to -5.03, and then lastly, our significance level is alpha equals 0.05. So then using this information, we can define our hypotheses. Starting with our null hypothesis, which is P is equal to 0.65 and represents that the sample follows population proportion, as well as our alternative hypothesis, which is P does not equal 0.65 and represents that the sample does not follow population proportion. Therefore, we know that this is a two-tailed test, and then we use our Z score that we are given from the information in the question. Which is our calculated Z score of -5.03, and then we can determine our critical Z value, which at alpha equals 0.05 for a two-tail test. We know that our critical values are positive and negative 1.96. So then using this information, we can Make our decision by comparing the Z score to our critical value, which -5.03 is less than our critical value of -1.96, which tells us that the Z score is far into the rejection region. Therefore, we can conclude that the sample is not representative of the population at the alpha equals 0.05 level, since the Z score falls in the rejection region. So looking at our answer choices, we can identify That answer choice C is the correct answer, as we can conclude that the sample is not representative of the population at the 0.05 significance level, since the Z score falls in the rejection region. So answer choice C is the correct answer, and all other answer choices are incorrect. I hope you found this video to be helpful. Thank you and goodbye.

Key Concepts

Sampling Variability

Hypothesis Testing

Confidence Intervals

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