A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x, is found to be 110, and the sample standard deviation, s, is found to be 10.(a) Construct a 95% confidence interval about µ if the sample size, n, is 24.(b) Construct a 95% confidence interval about µ if the sample size, n, is 16.p(c) Construct a 90% confidence interval about if the sample size, n, is 24.(d) Could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed?Click the icon to view the table of areas under the t-distribution.(a) Construct a 95% confidence interval about u if the sample size, n, is 24.Lower bound: Upper boundwww

It is given that X̄ = 110 s = 10 Note: According to Bartleby expert guidelines, we can answer…

Answered: A simple random sample of size n is…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The law of large numbers states that as the number of observations drawn at random from a population with finite mean increases, the mean of the observed values: a. tends to get closer and closer to the population mean . b. gets smaller and smaller. c. gets larger and larger. d. fluctuates steadily between 1 standard deviation above and 1 standard deviation below the mean. I collect a random sample of size n from a population and compute a 95% confidence interval for the proportion I observe from the population. What could I do to produce a new confidence interval with a larger width (larger margin of error) based on these same data? a. I could use the same confidence level but compute the interval n times; approximately 5% of these intervals will be larger. b. Nothing can guarantee absolutely that I will get a larger interval; I can only say the chance of obtaining a larger interval is 0.05. c. I could use a smaller confidence…
Tina catches a 14-pound bass. She does not know the population mean or standard deviation. So she takes a sample of five friends and they say the last bass they caught was 9, 12, 13, 10, and 10 pounds. Find the t and calculate a 95% (α = .05) confidence interval.
A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x, is found to be 19.6, and the sample standard deviation, s, is found to be 5.6. (a) Construct a 98% confidence interval about u if the sample size, n, is 32. (b) Construct a 98% confidence interval about µ if the sample size, n, is 58. How does increasing the sample size affect the margin of error, E? (c) Construct a 99% confidence interval about u if the sample size, n, is 32. How does increasing the level of confidence affect the size of the margin of error, E? (d) If the sample size is 21, what conditions must be satisfied to compute the confidence interval? (a) Construct a 98% confidence interval about µ if the sample size, n, is 32. Lower bound:; Upper bound: (Round to two decimal places as needed.) C...
A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x, is found to be 115, and the sample standard deviation, s, is found to be 10. (a) Construct an 80% confidence interval about μ if the sample size, n, is 25. (b) Construct an 80% confidence interval about μ if the sample size, n, is 12. (c) Construct a 70% confidence interval about μ if the sample size, n, is 25. (d) Could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed?
Professor Nord stated that the mean score on the final exam from all the years he has been teaching is a 79%. Colby was in his most recent class, and his class’s mean score on the final exam was 82%. Colby decided to run a hypothesis test to determine if the mean score of his class was significantly greater than the mean score of the population. α = .01. What is the mean score of the population? What is the mean score of the sample? Is this test one-tailed or two-tailed? Why?
Suppose we are making predictions of the dependent variable y for specific values of the independent variable x using a simple linear regression model holding the confidence level constant. Let Width (C.I) = the width of the confidence interval for the average value y for a given value of x, and Width (P.I) = the width of the prediction interval for a single value y for a given value of x. Which of the following statements is true? Width (C.I) = 0.5 Width (P.I) Width (C.I) = Width (P.I) Width (C.I) > Width (P.I) Width (C.I) < Width (P.I)
Allen's hummingbird (Selasphorus sasin) has been studied by zoologist Bill Alther.t Suppose a small group of 20 Allen's hummingbirds has been under study in Arizona. The average weight for these birds is x = 3.15 grams. Based on previous studies, we can assume that the weights of Allen's hummingbirds have a normal distribution, with o = 0.32 gram. (a) Find an 80% confidence interval for the average weights of Allen's hummingbirds in the study region. What is the margin of error? (Round your answers to two decimal places.) lower limit upper limit margin of error (b) What conditions are necessary for your calculations? (Select all that apply.) O normal distribution of weights Oo is known O n is large O o is unknown O uniform distribution of weights (c) Interpret your results in the context of this problem. O The probability that this interval contains the true average weight of Allen's hummingbirds is 0.20. O we are 80% confident that the true average weight of Allen's hummingbirds falls…
A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x, is found to be 110, and the sample standard deviation, s, is found to be 10. (a) Construct a 98% confidence interval about μ if the sample size, n, is 15. (b) Construct a 98% confidence interval about μ if the sample size, n, is 24. (c) Construct a 99% confidence interval about μ if the sample size, n, is 15. (d) Could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed?
A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x, is found to be 104, and the sample standard deviation, s, is found to be 8. (a) Construct a 95% confidence interval about u if the sample size, n, is 22. (b) Construct a 95% confidence interval about u if the sample size, n, is 16. (c) Construct a 90% confidence interval about u if the sample size, n, is 22. (d) Should the confidence intervals in parts (a)-(c) have been computed if the population had not been normally distributed? (a) Construct a 95% confidence interval about u if the sample size, n, is 22. Lower bound: 100.5; Upper bound: 107.5 (Round to one decimal place as needed.) (b) Construct a 95% confidence interval about u if the sample size, n, is 16. Lower bound: Upper bound: (Round to one decimal place as needed.)
A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x, is found to be 108, and the sample standard deviation, s, is found to be 10. (a) Construct a 96% confidence interval about µ if the sample size, n, is 13. (b) Construct a 96% confidence interval about µ if the sample size, n, is 29. (c) Construct a 99% confidence interval about μ if the sample size, n, is 13. (d) Could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed? FClick the icon to view the table of areas under the t-distribution. (a) Construct a 96% confidence interval about μ if the sample size, n, is 13. Lower bound: Upper bound: (Use ascending order. Round to one decimal place as needed.)
Use the bootstrap distributions in Figure 1 to estimate the value of the sample statistic and standard error, and then use this information to give a 95 % confidence interval. In addition, give notation for the parameter being estimated. The bootstrap distribution in Figure 1, generated for a sample correlation to 0.25 0.30 0.35 0.40 0.45 0.50 0.55 Figure 1 Bootstrap distribution (a) Give the sample statistic for the parameter being estimated. Round your answer to one decimal place. Sample statistic = eTextbook and Media (b) Estimate the standard error. Round your answer to two decimal places. standard error = i eTextbook and Media (c) Give the 95 % confidence interval. Round your answers to two decimal places, if necessary. The 95 % confidence interval is i to i e Textbook and Media

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