How to find p-value in this problem.
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How to find p-value in this problem.
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- From a large number of actuarial exam scores, a random sample of 275 scores is selected, and it is found that 206 of these 275 are passing scores. Based on this sample, find a 90% confidence interval for the proportion of all scores that are passing. Then complete the table below. Carry the intermediate computations to at least three decimal places. Round the answers to two decimal places. (a) What is the lower limit of the 90% confidence interval? (b) What is the upper limit of the 90% confidence interval?A yogurt company claims that it prints a free yogurt coupon under a randomly selected 20% of its lids. A loyal customer purchases 85 yogurt cups, and records whether each was a winner. After consuming all 85 cups, he is disappointed to see that only 12 (14.1%) of his yogurt cups contained coupon codes. He performs a 99% confidence interval for the proportion of yogurt cups containing coupon codes, obtaining (0.044, 0.238). What conclusion can the customer draw about the yogurt company’s claim? The company’s claim may be justified because 0.2 is in the confidence interval. The company’s claim is definitely justified because 0.2 is in the confidence interval. The company’s claim is not justified because the upper endpoint of the confidence interval is 0.238. The company’s claim is not justified because 12 out of 85 (0.141) is far less than 0.2.In a study, Group 1 was found to have an average of 53 and a population standard deviation of 13 out of a random sample of 25. Group 2 was found to have an average of 42 and a population standard deviation of 9 out of a random sample of 16. With a 99% confidence interval, what is the smaller value?
- 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:In a study of maternal cigarette smoking and bone density in newborns, 77 infants of mothers who smoked had a mean bone mineral content of 0.098 g/cm3 (s1 = 0.026 g/cm3). The 161 infants whose mothers did not smoke had a mean bone mineral content of 0.095 g/cm3 (s2 = 0.025 g/cm3). Calculate the 95% confidence interval for µ1 - µ2Suppose you surveyed a sample of 100 in-state students at public colleges in Pennsylvania and a sample of 100 in-state students at public colleges in Ohio and found that the average difference in tuition between the two groups is $2,982, 95%CIs[$1,769, $4,195]. Based on this confidence interval, would you reject the null hypothesis or fail to reject the null hypothesis if you had conducted a two-tailed hypothesis test with alpha = .05 to see if there is a significant difference between the two groups? Explain.
- A 30 month study is conducted to determine the difference in rates of accidents per month between two departments in an assembly plant. If a sample of 12 from the first department averaged 12.3 accidents per month with a standard deviation of 3.5, and a sample of 9 from the second department averaged 7.6 accidents per month with standard deviation of 3.4, find: The t-value for a 95% confidence interval is:1. The lifetime of a 75 watts lightbulb is normally distributed with mean µ hours and variance σ2. From a random sample of 20 lightbulbs, the sample mean is 1014 hours and the sample standard deviation is 25 hours.(a) Compute a 95% confidence interval for µ.(b) Suppose that σ = 25 hours. We want to re-construct a 95% confidence interval for µ with the interval length no longer that 9 hours. Determine the required sample size.A 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, 51 meet the specification for puncture resistance. a) Find the sample size needed for a 90% confidence interval to specify the proportion to within ±0.06. Round up the answer to the nearest integer. b) 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? Round the answer to three decimal places.
- An epidemiologist with the Florida Department of Health needs to estimate the proportion of Floridians who are infected with the corona virus but are asymptomatic (show no signs of the virus). The epidemiologist compiled a preliminary random sample of infected patients and found that 76% of the sample were also asymptomatic.How large a sample should be selected such that the margin of error of the estimate for a 99% confidence interval is at most 1.09%. Round the solution up to the nearest whole number.In a random sample of 1500 BA majors who are graduating from the University of Cape Town this autumn(2020), we observe that 1380 have already found a job.Question 3Calculate the 95 % Confidence interval for the proportion in Question 6 above. Round off to six decimals and show all workings.1. Does the data provide convincing evidence that the true mean body temperature in all healthy 18-40 year-olds is not 98.6 F? 2. A 95% confidence interval for the population mean is 98.123 F to 98.377 F. Explain how the confidence interval is consistent with, but gives more information than, the significance test in the previous question.
