Suppose that 20% of the residents in a certain state suppor an increase in the property tax. An opinion poll will randomly sample 400 state residents and will then compute the proportion in the sample that support a property tax increase. How likely is the resulting sample proportion to be within 0.04 of the true proportion (i.e., between 0.16 and 0.24)?
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- A conservative radio talk show host with a large audience is interested in the proportion p ofadults in his listening area who think the drinking age should be lowered to eighteen. To findthis out, he poses the following question to his listeners: “Do you think that the drinking ageshould be reduced to eighteen in light of the fact that eighteen year‐olds are eligible for militaryservice?” He asks listeners to phone in and vote “Yes” if they agree the drinking age should belowered and “No” if not. Of the 100 people who phoned in, 70 answered “Yes.” a. List one source of sampling bias (i.e. bias based on the people included in the sample). b. List another source of bias (sampling or non-sampling).A mayor running for re-election claims that during his term, average municipal taxes have fallen by $125. A conscientious statistician wants to test this claim. He surveys 37 of his neighbors and finds that their taxes decreased (in dollars) as follows: 121, 139, 121, 125, 118, 145, 141, 91, 127, 136, 144, 154, 131, 139, 139, 125, 108, 130, 125, 106, 137, 148, 154, 134, 137, 112, 96, 114, 114, 126, 133, 129, 94, 129, 148, 163, 121 The statistician assumes a population standard deviation of $19. Do you think the statistician should reject the mayor's claim? Why or why not? Step 1: State the hypothesis. ?v= Step 2: Determine the Features of the Distribution of Point Estimates Using the Central Limit Theorem. By the Central Limit Theorem, we know that the point estimates are [Select an answer with distribution mean and distribution standard deviation Step 3: Assuming the Claim is True, Find the Probability of Obtaining the Point Estimate. P? ✓ ? ♥ = P(? ? ♥According to Pew Research Center surveys, 79% of U.S. adults were using the Internet in January 2011 and 83% were using it in January 2012 (USA TODAY, January 26, 2012). Suppose that these percentages are based on random samples of 1720 U.S. adults in January 2011 and 1970 in January 2012. a. Let p, and p, be the proportions of all U.S. adults who were using the Internet in January 2011 and January 2012, respectively. Construct a 95% confidence interval for p, - P2- Round your answers to three decimal places. to i
- Suppose that we have a random sample of 8 students with final exam scores: 43, 55, 96, 33, 37, 78, 62 and 20. Find the point estimate of the population proportion by taking into account the values higher than 60In a Gallup poll of 1236 adult respondents, 6% said that bad luck follows breaking a mirror. That percentage has a margin of error of 1.5 percentage points. Why is it misleading to state that the percentage is 6% with a margin of error of 1.5%?About 4% of the population has a particular genetic mutation. 300 people are randomly selected.Find the mean for the number of people with the genetic mutation in such groups of 300. (Remember that means should be rounded to one more decimal place than the raw data.)
- Suppose the manager of a shoe store wants to determine the current percentage of customers who are males. How many customers should the manager survey in order to be 92% confident that the estimated (sample) proportion is within 8 percentage points of the true population proportion of customers who are males? z0.10 z0.05 z0.04 z0.025 z0.01 z0.005 1.282 1.645 1.751 1.960 2.326 2.576 Use the table of values above.A researcher wants to determine the percentage of American teenagers who send or receive text messages while doing homework. Which of the following techniques would likely be the MOST efficient way of obtaining an accurate estimate for this percentage? 1. Randomly select teenagers from the list of all teenage students in every state in America and mail surveys to those teens, asking them if they send or receive text messages while doing homework. 2. Send a survey to every teenager in America and ask them if they send or receive text messages while doing homework. 3. Randomly select teenagers from the list of all teenage students in one state and mail surveys to those teens, asking them if they send or receive text messages while doing homework.Many states are carefully considering steps that would help them collect sales taxes on items purchased through the Internet. How many randomly selected sales transactions must be surveyed to determine the percentage that transpired over the Internet? Assume that we want to be 99% confident that the sample percentage is within two percentage points of the true population percentage for all sales transactions. n = (Round up to the nearest integer.)
- The state education commission wants to estimate the fraction of tenth grade students that have reading skills at or below the eighth grade level. Step 1 of 2: Suppose a sample of 333 tenth graders is drawn. Of the students sampled, 260 read above the eighth grade level. Using the data, estimate the proportion of tenth graders reading at or below the eighth grade level. Enter your answer as a fraction or a decimal number rounded to three decimal places. Step 2 of 2: Suppose a sample of 333 tenth graders is drawn. Of the students sampled, 260 read above the eighth grade level. Using the data, construct the 80% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level. Round your answers to three decimal places.Suppose a company wants to determine the percentage of customers who shop online. How many customers should the company survey in order to be 92% confident that the estimated (sample) proportion is within 3 percentage points of the true population proportion of customers who shop online? z0.16 z0.08 z0.04 z0.02 z0.01 0.994 1.405 1.751 2.054 2.326A mayor running for re-election claims that during his term, average municipal taxes have fallen by $150. A conscientious statistician wants to test this claim. She surveys 45 of her neighbors and finds that their taxes decreased (in dollars) as follows: 149, 135, 147, 147, 160, 146, 165, 144, 142, 159, 138, 185, 143, 164, 143, 154, 163, 151, 171, 156, 133, 145, 180, 172, 166, 167, 149, 144, 154, 172, 138, 168, 179, 151, 131, 165, 114, 140, 162, 151, 136, 152, 157, 154, 136 The statistician assumes a population standard deviation of $13. Do you think the statistician should reject the mayor's claim? Why or why not? Step 1: State the hypothesis. ? Step 2: Determine the Features of the Distribution of Point Estimates Using the Central Limit Theorem. By the Central Limit Theorem, we know that the point estimates are [Select an answer distribution mean with and distribution standard deviation Step 3: Assuming the Claim is True, Find the Probability of Obtaining the Point Estimate. P? ✓ ? ✓…