DA 5 - Confidence Intervals-1

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Oregon State University, Corvallis *

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314

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Economics

Date

Jan 9, 2024

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pdf

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4

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Confidence Intervals In this data analysis, you will investigate confidence intervals to gain a deeper understanding of how and why they're constructed. You may find it useful to review the notes from week 5 before proceeding with this assignment. I f you haven’t already done so, work through the tutorial provided on the Data Analysis 5 Canvas page. Once you’ve worked through the tutorial, write up your responses to the questions listed throughout the tutorial. The same questions are included below to help you format your submissions. Submit a PDF copy of your responses to Gradescope by the deadline stated on Canvas. Part 1: Confidence Interval for a Proportion Question 1 (1 point) What proportion of the adults in your sample think climate change affects their local community? Hint: Just like we did with the population, we can calculate the proportion of those in this sample who think climate change affects their local community. 62% of the adults in my sample think climate change affects their local community. Question 2 (2 points) Would you expect another student’s sample proportion to be identical to yours? Would you expect it to be similar? Why or why not? I wouldn t expect another’s student sample proportion to be comparable to mine, because I took a random sample from the population, and because it s random each sample is going tio have a higher chance of being different. Question 3 (2 points) Check that the success-failure conditions needed to apply the Central Limit Theorem to the sample proportion are met in this case. Show your work. Question 4 (3 points) Suppose you instead wanted to construct a confidence interval with a different confidence level. How can you determine the necessary critical values in R for the following confidence levels? Your answers must include the R code used to find the critical value. a. A 95% confidence interval b. An 85% confidence interval
c. A 99% confidence interval Code: Answers: Question 5 (2 points) Using the point estimate from the sample of size n=180 you generated earlier, construct a 95% confidence interval for the true population proportion p. Show your work. Code: Answer: Question 6 (1 point) Does your confidence interval capture the true population proportion of US adults who think climate change affects their local community, p=0.62? My confidence interval does capture the TRUE population of US adults who think climate change affects their local community. Question 7 (1 point) There are 280 students enrolled in ST 314 this term. Each student should have gotten a slightly different 95% confidence interval due to random sampling. How many of 280 confidence intervals constructed do you expect to have captured the true population proportion p=0.62? Using the following reasoning, we can determine the number of confidence intervals that are anticipated to capture the true population proportion, p=0.62. A 95% confidence interval suggests that there is a 95% chance that it contains the true population parameter, so we would anticipate that 95% of the intervals will capture the true proportion. Thus, we would anticipate that about 0.95 × 280 intervals would capture the actual fraction out of 280 intervals.
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