At Least As Extreme A random sample of 860 births in New York ...

Question

At Least As Extreme A random sample of 860 births in New York State included 426 boys, and that sample is to be used for a test of the common belief that the proportion of male births in the population is equal to 0.512.

b. For random samples of size 860, what sample proportions of male births are at least as extreme as the sample proportion of 426/860?

Accepted Answer

Hello everyone. Let's take a look at this question together. A survey of 780 college students showed that 410 prefer online classes. If the proportion of students who favor online classes was 0.52, what sample proportions from groups of 780 students would be as or more extreme than the proportion found in our survey? Is it answer choice A, 0.5260, answer choice B, 0.5200, answer choice C 0.7338, or answer choice D 0.3669? So using the data that we are provided in the question, we need to determine what sample proportions from groups of 780 students would be as or more extreme than the proportion found in our survey, which is 410 out of 780. So from the given information in the question, we have our population proportion of P, which is equal to 0.52, our sample size of N, which is equal. 780 and the sample proportion, which was 410 divided by 780 of 0.526. And using this data, we can compute the standard error using the formula for the standard error, which is the square root of P multiplied by 1 minus P in parentheses divided by N, which plugging in our values into the formula, we get 0.0179. As the standard error value, and then we can compute the Z score for the sample proportion of 0.52 using the formula of Z is equal to the sample proportion minus the population proportion divided by the standard error, which plugging in our values we get 0.34 as the Z score value, and then we need to find the probability for the extreme values. Which we want to find the probability of getting a value as or more extreme than 0.526. Which is deviations from 0.52 that are greater than or equal to 0.006 in either direction. And since the normal distribution is symmetric, we can compute the value for the probability of getting a value as or more extreme than 0.526 using the following probability formula, which is equal to 2 multiplied. By the probability of Z being greater than or equal to 0.34, and from the standard normal table or a calculator, we know that the probability of Z being greater than or equal to 0.34 is equal to 0.3669. Therefore, the probability as or more extreme is equal to 0.7338. Which this value tells us that approximately 73.38% of sample proportions from groups of 780 students would be as or more extreme than 410 out of 780 if the true proportion was 0.52. And looking at our answer choices, we can identify that 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

Sample Proportion

Hypothesis Testing

At Least As Extreme

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