A researcher wants to calculate a 95% confidence interval for the unknown true proportion of defective resistors off an assembly line. They take a random sample of 50 resistors, and find that 2 of them are defective. Are the needed assumptions for the confidence interval satisfied? No, because the sample size is still too small. No, because they should be use the T distribution No, because they took a random sample Yes, because the sample size is larger than 30
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- 27. Bob selects independent random samples from two populations and obtains the values î1 0.700 and p2 = 0.500. He constructs the 95% confidence interval for p1 – P2 and gets: 0.200 + 1.96(0.048) = 0.200 ± 0.094. Note that 0.048 is called the estimated standard error of pi – p2 (the ESE of the estimate). Tom wants to estimate the mean of the success rates: Pi +P2 2 (a) Calculate Tom's point estimate. (b) Given that the estimated standard er- ror of (p1 + P2)/2 is 0.024, calculate the 95% confidence interval estimate of (Pi + P2)/2. Hint: The answer has our usual form: Pt. est. +1.96 × ESE of the estimate.We would like to compute a 95% confidence interval for the difference of proportions of men and women who are frequent binge drinkers. Of 534 males, 26% admitted to frequent binge drinking as opposed to 20.6% of 847 women. The 95% confidence interval for the difference of proportions (proportion of males - proportion of females) is (0.0179, 0.1001). Based on this confidence interval, can we conclude that men are more likely to frequently binge drink than women? (4)A sample of size n= 60 is drawn from a population whose standard deviation is o = 33. Part 1 of 2 (a) Find the margin of error for a 90% confidence interval for µ. Round the answer to at least three decimal places. The margin of error for a 90% confidence interval for u is Part 2 of 2 X (b) If the sample size were n=82, would the margin of error be larger or smaller? because the sample size is (Choose one) (Choose one) x Ś Ś
- A statistics professor wants to compare today's students with those 25 years ago. All of his current students' marks are stored on a computer so that he can easily determine the population mean. However, the marks 25 years ago reside only in his musty files. He does not want to retrieve all the marks and will be satisfied with a 98% confidence interval estimate of the mean mark 25 years ago. If he assumes that the population standard deviation is 11, how large a sample should he take to estimate the mean to within 4 marks? Sample Size =An ecologist randomly samples 13 plants of a specific species and measures their heights. He finds that this sample has a mean of 18 cm and a standard deviation of 4 cm. If we assume that the height measurements are normally distributed, find a 90% confidence interval for the mean height of all plants of this species. Then find the lower limit and upper limit of the 90% confidence interval. Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place. (If necessary, consult a list of formulas.) Lower limit: |I| Upper limit:Shea wants to estimate the difference between two population means and plans to use data collected from two independent = simple random samples of sizes n₁ 30 and n₂ = :35. She does not know the population standard deviations, so she plans to construct a two-sample t-confidence interval for the difference in the two means. Use a t-distribution table to determine the positive t-critical value needed to construct a 99% confidence interval using a conservative estimate of the number of degrees of freedom. Enter the positive critical value precise to three decimal places. t =
- Mr. Roby is trying to estimate the difference in the proportion of his male students who on average sleep fewer than 6 hours per night compared with his female students. He selects a random sample of 20 of his 75 male students and finds that 5 of them sleep fewer than 6 hours per night. He selects another random sample of 17 of his 100 female students and finds that 8 of them sleep fewer than 6 hours a night. Check the conditions for constructing a confidence interval for the difference in proportions. Random condition: A) metB) not metC) does not apply 10% condition: A) metB) not metC) does not apply Large Counts condition: A) metB) not metC) does not apply Are all the conditions for inference met? A) YesB) NoC) Not enough informationA sample of size n=77 is drawn from a population whose standard deviation is 0= 33. Part 1 of 2 (a) Find the margin of error for a 95% confidence interval for µ. Round the answer to at least three decimal places. The margin of error for a 95% confidence interval for µ is Part 2 of 2 (b) If the confidence level were 90%, would the margin of error be larger or smaller? (Choose one) ▼ because the confidence level is (Choose one) ▼Jelly beans are packed in boxes of 50, and the overall proportion of black jelly beans is set by the manufacturer to be 0.2. Suppose that 10 boxes of jelly beans are selected at random, and the proportion of black jelly beans in each box determined. a Use your calculator to generate 10 values of the sample proportidn p of black jelly beans in a box. b Use your calculator to find an approximate 80% confidence interval for the population proportion p from each of these values of the sample proportion p. c How many of these intervals contain the value of the population proportion p? d How many of these intervals would you expect to contain the value of the population proportion p? e Suppose that we generate 50 approximate 80% confidence intervals for p. How many of these intervals would you expect to contain the value of the population proportion p?
- An ecologist randomly samples 16 plants of a specific species and measures their heights. He finds that this sample has a mean of 17 cm and a standard deviation of 2 cm. If we assume that the height measurements are normally distributed, find a 99% confidence interval for the mean height of all plants of this species. Then find the lower limit and upper limit of the 99% confidence interval. Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place.A sample of size n=89 is drawn from a population whose standard deviation is a 16. Part 1 of 2 (a) Find the margin of error for a 90% confidence interval for μ. Round the answer to at least three decimal places. The margin of error for a 90% confidence interval for μ is. Part 2 of 2 (b) If the sample size were n=87, would the margin of error be larger or smaller? (Choose one) , because the sample size is (Choose one)A random sample of 100 students is taken from a larger population of students in a multi-lecture course and the sample mean (average) of their final grades is found to be 62.25. Suppose that the population standard deviation is known to be 3. Which of the following is correct? A 90% Z confidence interval for the true population mean that is calculated from this sample data of 100 students will be wider than a 95% Z confidence interval for the true population mean that is calculated from this sample data of 100 students. b. A 95% Z confidence interval for the true population mean that is calculated from this sample data of 100 students will be narrower than a 90% Z confidence interval for the true population mean that is calculated from this sample data of 100 students. c. A 90% Z confidence interval for the true population mean that is calculated from this sample data of 100 students would be narrower than a 90% Z confidence interval for the true population mean that is…