3. Mr. Guo selects a random sample of size n = 16 from a populationthat is normally distributed. The sample is found to have x = 78 and0² = 4.I(a) Mr. Guo wishes to construct a 98% confidence interval for fly thepopulation mean. Are all conditions met? If not, explain why.(b) Find an appropriate critical number associated with a central 98%confidence interval. Hint: Which distribution should we use?(c) Construct a central 98% confidence interval for u.

Sample size, n = 16 Sample mean x̅ = 78 Population variance σ2 = 4 So, Population standard deviation…

Answered: 3. Mr. Guo selects a random sample of…

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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A sample of size 59 from a population having standard deviation o = 56 produced a mean of 269.00. The 95% confidence interval for the population mean (rounded to two decimal places) is: The lower limit is i The upper limit is i
Two random samples were selected independently from populations having normal distributions. The statistics given below were extracted from the samples. Complete parts a through c. X₁ = 38.8 X₂ = 30.2 a. If o, 5 and o₂ =3 and the sample sizes are n₁ = 40 and n = 40, construct a 99% confidence interval for the difference between the two population means. The confidence interval is 6.23 s (H₁-H₂) ≤ 10.98 (Round to two decimal places as needed.) b. If o, 0₂, S₁ =5, and s₂ =3, and the sample sizes are n₁ = 20 and n., =20, construct a 99% confidence interval for the difference between the two population means. The confidence interval is ≤ (H₁-H₂) = (Round to two decimal places as needed.).
A simple random sample of size n = 40 is drawn from a population. The sample mean is found to be x = 121.2 and the sample standard deviation is found to be s = 12.6. Construct a 99% confidence interval for the population mean. The lower bound is (Round to two decimal places as needed.) The upper bound is . (Round to two decimal places 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 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?
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 98% confidence interval about μ if the sample size, n, is 16. (b) Construct a 98% confidence interval about µ if the sample size, n, is 12. (c) Construct a 70% confidence interval about u if the sample size, n, is 16. (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 98% confidence interval about μ if the sample size, n, is 16. Lower bound:; Upper bound: (Use ascending order. 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 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?
2. Assume that AUM body temperatures are normally distributed with o = collected a sample with the sample mean 98° F among n = mean body temperature in AUM. 1.5° F. We 9 this year. Let u be the (a) Find a two-sided 95% confidence interval for u. (b) Find an upper bounded one-sided 95% confidence interval for u. (c) Find a lower bounded one-sided 95% confidence interval for u.
Use the given statistics to complete parts (a) and (b). Assume that the populations are normally distributed. (a) Test whether u1 > H2 at the a = 0.01 level of significance for the given sample data. Population 1 Population 2 24 25 49.6 4.1 (b) Construct a 95% confidence interval about u1 - H2. 45.8 12.7 (a) Identify the null and alternative hypotheses for this test. B. Ho: H1 = H2 H1: H1>H2 O A. Ho: H1 = H2 O C. Ho: H1 + H2 H1: H1 = H2 H1: H1 #H2 O D. Ho: H1 H2 H1: H1 = H2 Find the test statistic for this hypothesis test. (Round to two decimal places as needed.)

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