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Two individuals are running for mayor of your town. You conduct an election survey a week before the election and find that 51% of the respondents prefer candidate A. Can you predict a winner? Use the 99% level. (HINT: In a two-candidate race, what percentage of the vote would the winner need? Does the confidence interval indicate that candidate A has a sure margin of victory? Remember that while the population parameter is probably [
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- Reynir examines the difference in the amount of carbon dioxide in two types of mineral water. He performs a two-group t-test to compare the average carbon dioxide levels in the two groups. His hypotheses are H0 : μ1 - μ2 = 0 og H1 : μ1 - μ2 ≠ 0. Reynir also calculated a confidence interval for the difference between the means of the two groups α and in the hypothesis test). Reynir rejected the null hypothesis. Which of the following applies to the safety margin calculated by Reynir?a) It contains the value zero.b) It contains 95% of the values that can occur when the experiment is performed.c) It does not contain the value zero.d) It contains both values greater than zero and values less than zero.arrow_forwardA soft-drink manufacturer purchases aluminum cans from an outside vendor. A random sample of 70 cans is selected from a large shipment, and each is tested for strength by applying an increasing load to the side of the can until it punctures. Of the 70 cans, 59 meet the specification for puncture resistance. (a) Find a 95% confidence interval for the proportion of cans in the shipment that meet the specification. (b) How to interpret the confidence interval in part (a)? (c) Find the sample size needed for a 90% confidence interval to specify the proportion to within ±0.06. (d) If a 90% confidence interval is computed each day for 300 days, what is the probability that more than 280 of the confidence intervals cover the true proportions?arrow_forwardA telephone service representative believes that the proportion of customers completely satisfied with their local telephone service is different between the South and the Northeast. The representative's belief is based on the results of a survey. The survey included a random sample of 700700 southern residents and 580580 northeastern residents. 49%49% of the southern residents and 42%42% of the northeastern residents reported that they were completely satisfied with their local telephone service. Find the 80%80% confidence interval for the difference in two proportions. Step 1 of 3: Find the critical value that should be used in constructing the confidence interval.arrow_forward
- In random, independent samples of 400 adults and 325 teenagers who watched a certain television show, 240 adults and 133 teens indicated that they liked the show. Let p1 be the proportion of all adults watching the show who liked it, and let p2 be the proportion of all teens watching the show who liked it. Find a 90% confidence interval for −p1p2 . Then complete the table below. Carry your intermediate computations to at least three decimal places. Round your responses to at least three decimal places. (If necessary, consult a list of formulas.) What is the lower limit of the 90% confidence interval? What is the upper limit of the 90% confidence interval?arrow_forwardA national opinion poll found that 44% of all American adults agree that parents should be given vouchers that are good for education at any public or private school of their choice. The result was based on a small sample. How large of a sample is required to obtain a margin of error of 0.03 in a 99% confidence interval? a. Use the national opinion poll from a previous study to find the sample size: b. Use the conservative guess of p = 0.5 to calculate the sample size:arrow_forwardBased on your confidence interval from the previous problem, can you conclude that the mean permeability coefficient at 60∘60∘C differs from that at 61∘61∘C at the 0.05 level of significance? A. Yes, because the 95% confidence interval includes 0 B. No, because the 95% confidence interval includes 0 C. Yes, because the 95% confidence interval does not include 0 D. No, because the 95% confidence interval does not include 0 E. It is impossible answer this question only using the 95% confidence interval.arrow_forward
- ANSWER ALL QUESTION 14 out of 31 American adults responded "yes" when asked if they have ever voted for a candidate in a party different from which they identify with. What is the critical value for a 99% confidence interval?2.9772.3262.752.5762.7443.012 2. The correct conclusion is that we conclude that the percent of all companies that have both Twitter and Facebook accounts IS LESSTHAN, IS DIFFRENET FROM OR OR IS MORETHAN 81,96,OR 0.2 3. A random sample of 40 commercials made since the year 2010 has an average of 24.9 seconds with a standard deviation of 9.6 seconds. What is the margin of error that corresponds to a 99% confidence interval for the average length of all commercials made since 2010? 4.11 4.1 3.91 4.106 None of the above 3B. The correct interpretation of the confidence interval is that we are 99% confident that the interval contains the length of commercials made since the year 2010. is what A similar study was conducted and found an interval of…arrow_forwardIndependent random samples from two normally distributed populations give the following results:nx = 10 x̄ = 480 sx = 30ny = 12 ȳ = 520 sy = 25a. If we assume that the unknown population variances are equal, find the 90% confidence interval for the difference of population means.b. If we do not assume that the unknown population variances are equal, find the 90% confidence interval for the difference between population means.arrow_forwardAn avid birdwatcher wants to know if the number of goslings per goose in his lake differs from the regional average of 2.58. He takes a random sample of geese, conducts a hypothesis test of H0: μ = 2.58 vs.Ha: μ ≠ 2.58, and obtains a p-value of 0.013. (a) What should you expect of a 95% confidence interval constructed from his data? ---- The interval should contain 2.58 The interval should not contain 2.58 The interval should contain 0 The interval should not contain 0 We cannot say anything about the interval because ---- the p-value is not less than the corresponding alpha. the p-value is less than the corresponding alpha. we cannot make a conclusion about a confidence interval just from a hypothesis test. . (b) Given his sample size what 74, what critical value would the birdwatcher use to make the 95% confidence interval? (3 decimal places)(c) The birdwatcher's friend says his geese have an average of 3.88 goslings, and the birdwatcher wants to know if that would be a reasonable…arrow_forward
- In random, independent samples of 225 adults and 200 teenagers who watched a certain television show, 112 adults and 138 teens indicated that they liked the show. Let p1 be the proportion of all adults watching the show who liked it, and let p2 be the proportion of all teens watching the show who liked it. Find a 95% confidence interval for −p1p2. Then find the lower limit and upper limit of the 95% confidence interval. Carry your intermediate computations to at least three decimal places. Round your responses to at least three decimal places. a.) The Lower Limit is: b.) The Upper Limit is:arrow_forward(a)A random sample of 25 college males was obtained and each was asked to report their actual height and what they wished as their ideal height. A 95% confidence interval for µd = average difference between their ideal and actual heights was 0.8" to 2.2". Based on this interval, which one of the null hypotheses below (versus a two-sided alternative) can be rejected? all the above c. H0: µd = 1.5 H0: µd = 0.5 b. H0: µd = 1.0 H0: µd = 2.0 (b)Which of the following is a correct form of an alternate hypothesis for paired data? H1: μd = p H1: μ1 ≠ μ2 H1: μd > 0 H1: μ1 = μ2 (C)Which of the following is always the null hypothesis for two sample proportions? d. H0: p1 = 3 H0: p1 < μ2 H0: p1 ≠ p2 H0: p1 = p2arrow_forwardA telephone service representative believes that the proportion of customers completely satisfied with their local telephone service is different between the South and the Midwest. The representative's belief is based on the results of a survey. The survey included a random sample of 11601160 southern residents and 12601260 midwestern residents. 43%43% of the southern residents and 56%56% of the midwestern residents reported that they were completely satisfied with their local telephone service. Find the 80%80% confidence interval for the difference in two proportions. Step 3 of 3 : Construct the 80%80% confidence interval. Round your answers to three decimal places.arrow_forward
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