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In recent poling, it has been suggested that the approval rating of a certain politician (the proportion of people polled that approve of his performance in office) is 40%. 1) Suppose we conduct a new poll consisting of 30 people. Assuming the suggested approval rating is correct, and the independence of people polled, if X was the number of people in this new poll who approve of the politician, what kind of distribution would x have and what are its parameters? 2) Assuming the facts in the previous problem, how many people would we expect to see in the new poll who approve of the candidate? Suppose the approval rating in the new poll is 30%. How many people would approve of the candidate in this case? 3) Again, given the facts in problem 1, what is the probability of seeing a higher approval rating in the new poll (more than expected in problem 2)?

In recent poling, it has been suggested that the approval rating of a certain politician (the proportion of people polled that approve of his performance in office) is 40%. 1) Suppose we conduct a new poll consisting of 30 people. Assuming the suggested approval rating is correct, and the independence of people polled, if X was the number of people in this new poll who approve of the politician, what kind of distribution would x have and what are its parameters? 2) Assuming the facts in the previous problem, how many people would we expect to see in the new poll who approve of the candidate? Suppose the approval rating in the new poll is 30%. How many people would approve of the candidate in this case? 3) Again, given the facts in problem 1, what is the probability of seeing a higher approval rating in the new poll (more than expected in problem 2)?

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section11.4: Collecting Data
Problem 2E
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In recent poling, it has been suggested that the approval rating of a certain politician (the proportion of people polled that approve of his performance in office) is 40%. 1) Suppose we conduct a new poll consisting of 30 people. Assuming the suggested approval rating is correct, and the independence of people polled, if X was the number of people in this new poll who approve of the politician, what kind of distribution would x have and what are its parameters? 2) Assuming the facts in the previous problem, how many people would we expect to see in the new poll who approve of the candidate? Suppose the approval rating in the new poll is 30%. How many people would approve of the candidate in this case? 3) Again, given the facts in problem 1, what is the probability of seeing a higher approval rating in the new poll (more than expected in problem 2)? 4) After taking the new poll, we find that 9 out of the 30 people polled approve of the politician's performance in office. Calculate a 95% confidence interval for the true approval rating (or rather, the population proportion of people who approve of the politician's performance). 5) If we want the margin of error in the previous interval to be less than 2%, how many people should we poll in total? 6) Does 40% fall into the confidence interval in problem 4? Does this suggest that the politician's approval rating has fallen significantly, or do we nee more data?
Transcribed Image Text:In recent poling, it has been suggested that the approval rating of a certain politician (the proportion of people polled that approve of his performance in office) is 40%. 1) Suppose we conduct a new poll consisting of 30 people. Assuming the suggested approval rating is correct, and the independence of people polled, if X was the number of people in this new poll who approve of the politician, what kind of distribution would x have and what are its parameters? 2) Assuming the facts in the previous problem, how many people would we expect to see in the new poll who approve of the candidate? Suppose the approval rating in the new poll is 30%. How many people would approve of the candidate in this case? 3) Again, given the facts in problem 1, what is the probability of seeing a higher approval rating in the new poll (more than expected in problem 2)? 4) After taking the new poll, we find that 9 out of the 30 people polled approve of the politician's performance in office. Calculate a 95% confidence interval for the true approval rating (or rather, the population proportion of people who approve of the politician's performance). 5) If we want the margin of error in the previous interval to be less than 2%, how many people should we poll in total? 6) Does 40% fall into the confidence interval in problem 4? Does this suggest that the politician's approval rating has fallen significantly, or do we nee more data?
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