"Critical Thinking. In Exercises 17–28, use the data and confi...

Question

"Critical Thinking. In Exercises 17–28, use the data and confidence level to construct a confidence interval estimate of p, then address the given question.

Internet Use A random sample of 5005 adults in the United States includes 751 who do not use the Internet (based on three Pew Research Center polls). Construct a 95% confidence interval estimate of the percentage of U.S. adults who do not use the Internet. Based on the result, does it appear that the percentage of U.S. adults who do not use the Internet is different from 48%, which was the percentage in the year 2000?"

Accepted Answer

Welcome back everyone. In Nepal of 3500 college students, 420 reported that they do not own a laptop. Construct a 95% confidence interval for the proportion of college students who do not own a laptop. Is this proportion significantly different from 25%, which was the value a decade ago? So first of all, we want to construct the confidence interval for the proportion, right? We have to recall that it is equal to the sample proportion Pha plus or minus the margin of error E. Now what we can do is simply express E. And we have to recall that it is equal to the critical C value, C critical, multiplied by the standard error, and how do we express our standard error as E. Well, essentially, We have to Take our critical value, see critical and multiply it by square root. Of Phat multiplied by 1 minus p hat. And divide that by the sample size and. This is how we get our standard error. So let's identify each parameter. Let's begin with our sample proportion that would be. 420 divided by the total number of students 3500. When we divide these numbers, we get 0.12. Our sample size N is 3500. Our critical Z value for 95% confidence is 1.960. So our confidence interval becomes he had 0.12. Plus or minus 1.960 multiplied by square root of 0.12. Multiplied by 1 minus 0.12. Divided by 3500. So now we can simplify our margin of error so that the confidence interval becomes 0.12 plus or minus. 0.01077 Now what we can do is simply add and subtract this value to identify our bounds, right? Let's suppose that our confidence interval is between A and B. So A is the lower bound. It is equal to 0.12 minus 0.01077. And when we subtract, we get 0.109. In its percentage form, that would be 10.9%. Our upper bound is 0.12, plus the margin of error, 0.01077. And this gives us a 0.131. Which is 13.1%. So we can state that our confidence interval is between 10.9%. And 13.1%. That's our first answer, and now we can compare. Now, a decade ago. The proportion was 25%, right? And because it is above the upper bound of the confidence interval, we can say that the proportion is significantly lower now, right? So we can say that. Since 25%. Is above. The upper bounds. The proportion. Yes Significantly Lower Now Those be our final answers, we can label them. And to conclude the video. Thank you for watching.

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Key Concepts

Confidence Interval

Sample Proportion

Hypothesis Testing

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