A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
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In a population where 63% of voters prefer Candidate A, how many voters must be sampled for the distribution of voters that prefer candidate A to be
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- In a random sample for 56 professional actors, it was found that 46 were extrovert.let p represent the proportion of all actors who were extroverts. Find a point estimate for parrow_forwardAn adventure company runs two obstacle courses, Fundash and Coolsprint, with similar designs. Since Fundash was built on rougher terrain, the designer of the courses suspects that the mean completion time of Fundash is greater than the mean completion time of Coolsprint. To test this, she selects 235 Fundash runners and 275 Coolsprint runners. (Consider these as independent random samples of the Fundash and Coolspring runners.) The 235 Fundash runners complete the course with a mean time of 78.1 minutes and a standard deviation of 6.7 minutes. The 275 individuals complete Coolsprint with a mean time of 76.4 minutes and a standard deviation of 8.1 minutes. Assume that the population standard deviations of the completion times can be estimated to be the sample standard deviations, since the samples that are used to compute them are quite large. At the 0.01 level of significance, is there enough evidence to support the claim that the mean completion time, u,, of Fundash is greater than…arrow_forwardin a random sample of 56 professional actors,it wa sfound that 46 were extroverts. let p represent the proportion of all actors who are extroverts. find a point estimate for parrow_forward
- An airline claims that luggage is rarely lost (does not arrive at the destination at the same time as the passenger). The airline claims that if luggage is lost, in 87% of cases the airline is able to recover and deliver the luggage within 24 hours. A consumer watchdog group found a random sample of 125 people whose luggage was lost and found that 99 of them had their luggage recovered and returned within 24 hours. The Sample proportion p-hat is 99/125 = 0.792. The watchdog group wants to perform a hypothesis test against the claim that the airline is able to recover 87% of lost luggage in 24 hours. What is the test statistic?arrow_forwardA study is conducted in a large high school to determine if the proportion of students who plan to come to the upcoming football game differs across the grades. A random sample of 50 ninth graders, 50 tenth graders, 50 eleventh graders, and 50 twelfth graders was selected. The responses are displayed in the table. The principal would like to know if these data provide convincing evidence that the distribution of responses differs across the grades in the population of all students in her school. The random and 10% conditions are met, and this table of expected counts shows that all expected counts are at least 5. What is the value of the chi-square test statistic for this test? χ‑2 = 0.49 χ‑2 = 0.70 χ‑2 = 0.84 χ‑2 = 200arrow_forwardWhen two births are randomly selected, the sample space for genders is bb, bg. gb, and gg. Assume that those four outcomes are equally likely. Construct a table that describes the sampling distribution of the sample proportion of girls from two births. Does the mean of the sample proportions equal the proportion of girls in two births? Does the result suggest that a sample proportion an unbiased estimator of a population proportion? For the entire population, assume the probability of having a boy is the probability of having a girl is , and this is not affected by how many boys or girls have previously been born. 2 Determine the probabilities of each sample proportion. Probability Sample proportion of girls Tune intanare or cimnlifiad frartinnearrow_forward
- A sample of 300 items was selected. compute the p-valuearrow_forwardSuppose that Mairin has knit a collection of wool‑blend infinity scarves that she wants to sell in her Etsy shop for $28.00 each. However, she is worried that if the average price of comparable scarves is less than $28.00, hers would be less likely to sell. Mairin selected a random sample of 9 similar hand‑knit, wool‑blend infinity scarves, and their prices are as follows. $21.75,$24.00,$27.25,$29.95,$23.00,$26.00,$27.80,$33.50,$27.00$21.75,$24.00,$27.25,$29.95,$23.00,$26.00,$27.80,$33.50,$27.00 Use a left‑tailed one‑sample ?t‑test to determine whether the average price of hand‑knit, wool‑blend infinity scarves sold on Etsy is less than $28.00. Assume that the prices of all comparable scarves are normally distributed. Mairin should (reject, accept, fail to accept) her null hypothesis. There is (sufficient, no, insufficient) evidence that the mean price of hand‑knit, wool‑blend infinity scarves is (greater than, different from, less than, equal two) $28.00.arrow_forwardA manufacturing company that produces laminate for countertops is interested in studying the relationship between the number of hours of training that an employee receives and the number of defects per countertop produced. Ten employees are randomly selected. The number of hours of training each employee has received is recorded and the number of defects on the most recent countertop produced is determined. The results are as follows. Hours of Training Defects per Countertop 1 5 4 1 7 0 3 3 2 5 2 4 5 1 5 2 1 8 6 2 Copy Data The estimated regression line and the standard error are given. Defects per Countertop=6.717822−1.004950(Hours of Training)se=1.229787se=1.229787 Suppose a new employee has had 5 hours of training. What would be the 90% prediction interval for the number of defects per countertop? Round your answer to two decimal places.arrow_forward
- The records of a light bulb manufacturer show that, when the manufacturing machinery is working correctly, the defect rate (due to imperfections in the material used) is 1%. The manufacturer's control department periodically tests samples of the bulbs, and when 1.25% or more are defective, they call repair technicians for service. The control department is going to take a random sample of 4400 light bulbs. Let p be the proportion of defective light bulbs in the sample assuming the machinery is working correctly. A) find the mean of p b)find the standard deviation of p c)Compute an approximation for P≥p0.0125, which is the probability that, assuming the machinery is working correctly, the repair technicians will be called. Round your answer to four decimal places.arrow_forwardThe records of a light bulb manufacturer show that, when the manufacturing machinery is working correctly, the defect rate (due to imperfections in the material used) is 1%. The manufacturer's control department periodically tests samples of the bulbs, and when 1.25% or more are defective, they call repair technicians for service. The control department is going to take a random sample of 4400 light bulbs. Let p be the proportion of defective light bulbs in the sample assuming the machinery is working correctly. Answer the following. (If necessary, consult a list of formulas.) (a) Find the mean of p. (b) Find the standard deviation of p. (c) Compute an approximation for P(P ≥ 0.0125), which is the probability that, assuming the machinery is working correctly, the repair technicians will be called. Round your answer to four decimal places.arrow_forwardIn 1992, Canadians voted in a referendum on a new constitution. In the province of Quebec, 42.3% of those who voted were in favor of the new constitution. A random sample of 110 voters from the province was taken. Complete parts a through d below. What is the mean of the distribution of the sample proportion in favor of a new constitution? a) The mean of the distribution of the sample proportion in favor of a new constitution is b) what is the variance of the sample proportion? c) what is the standard error of the sample proportion? d) what is the probability that the sample proportion is more than 0.51?arrow_forward
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- A First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON
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