## Understanding Confidence Intervals in Poll ResultsA newspaper article about the results of a poll states:"In theory, the results of such a poll, in 99 cases out of 100, should differ by no more than 5 percentage points in either direction from what would have been obtained by interviewing all voters in the United States."To analyze this, we need to find the sample size suggested by this statement.### Task**a.** Shade and label the missing parts in the graph for a 99% confidence interval. You may use Excel or a calculator to find the *z*-score. Round the *z*-score to two decimal places.### DiagramThe diagram is a standard normal distribution curve:- **Area to the left = ____**- **Area in the middle = ____**- **Area to the right = ____**- **z = ____****b.** Determine the sample size.This exercise involves understanding the concept of confidence intervals, critical values (*z*-scores), and using them to determine the sample size needed to ensure the poll's accuracy within a specified margin of error (5 percentage points in this case).

Answered: 9) A newspaper article about the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Suppose a 90 percent confidence interval to estimate a population proportion was calculated from a sample proportion of 18 percent and a margin of error of 4 percent. What is the width of the confidence interval?
7. A company that has many department stores in the southern states wanted to find at two such stores the percentage of sales for which at least one of the items was returned. A sample of 800 sales randomly selected from Store A showed that for 280 of them at least one item was returned. Another sample of 900 sales randomly selected from Store B showed that for 279 of them at least one item was returned. a. Construct a 98% confidence interval for the difference between the proportions of all sales at the two stores for which at least one item is returned. b. Using the 10% significance level, can you conclude that the proportions of all sales for which at least one item is returned is higher for Store A than for Store B?
A political scientist claims that 38% of first-year college students characterize themselves as being “moderate” or “middle of the road” as far as their political affiliation is concerned. Believing this claimed value is too high, you survey a random sample of 400 first-year college students and find that 120 characterize themselves as being “moderate” or “middle of the road.” Based on this information, what will the test statistic be? Choose the answer below that is closest to what you calculate, and try not to do a lot of rounding until you get to the very end of your calculations. 1. -0.3 2. -1.2 3. -2.6 4. -3.3 5. None of the other answer options are correct because the test statistic should be positive, not negative.
3. In a recent poll of 900 randomly selected adults, 333 reported that they could not swim 24 yards (the length of a typical gymnasium lap pool). We want to construct a 95% confidence interval for the proportion of adults that cannot swim 24 yards. [Note: Assume the conditions required for this procedure have been satisfied.] a. Calculate the margin of error for the 95% confidence interval. Round to the nearest thousandth (third decimal place). b. Construct the 95% confidence interval for the proportion of adults who cannot swim 24 yards. Round to the nearest thousandth (third decimal place). c. A life guard claims that 30% of all adults cannot swim 24 yards. Does the confidence interval in part (c) support that claim? Explain.
4) Consider a confidence level of 90%. If n=68 and ?̂ = 0.42 Calculate the margin of error. 5) Consider a confidence level of 87%, let ? = 0.02 and ?̂ = 0.42. Find the sample size ?.
A 95% confidence interval for how much time on average GRC students spend doing homework every day is 75 to 105 minutes.Choose a correct interpretation of the statement above. A. If random sampling is repeated, 95% of the confidence intervals created will capture the true mean. B. If random sampling is repeated, 95% of the samples will have a mean that is between 75 and 105 minutes. C. 95% of GRC students study between 75 and 105 minutes on average every day. D. There is 95% chance that the true mean is between 75 and 105 minutes.
A newspaper article reported that 400 people in one state were surveyed and 70% were opposed to a recent court decision. The same article reported that a similar survey of 500 people in another state indicated opposition by only 40%. Construct a 95% confidence interval of the difference in population proportions based on the data.
2. Bob draws a simple random sample from an extremely large population of lemons. The sample size is n=700 and in the sample 250 lemons turn out to be good and 450 lemons turn out to be bad. Find the 95% confidence interval for the population proportion p of good lemons.
The president’s policy on domestic affairs received a 45% approval rating in a recent poll. The margin of error was given as 0.035. What sample size was used for this poll if we assume a 95% confidence level?
5.) A genetic experiment with peas resulted in one sample of offspring that consisted of 410 green peas and 151 yellow peas. a. Construct a 90% confidence interval to estimate of the percentage of yellow peas. b. It was expected that 25% of the offspring peas would be yellow. Given that the percentage of offspring yellow peas is not 25%, do the results contradict expectations?
In the Star and Tribune newspaper, there is an article entitled "1 in 8 school buses fail tests." The article says that the overall statewide proportion of school buses that fail safety tests is 9%. However, one bus company has a higher rate of over 12%. Assume that we want a new estimate for the statewide proportion of school buses that fail the safety inspection. How large a sample would you have to take in order to construct a 95% confidence interval estimate for the true proportion of buses that fail the inspection and achieve a margin of error of plus or minus 2%? (your answer should be an integer)
3. Bob draws a simple random sample from an extremely large population of lemons. The sample size is n=925 and in the sample 576 lemons turn out to be good and 349 lemons turn out to be bad. Find the 99% confidence interval for the population proportion P of good lemons.

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