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 a 96% confidence interval about u if the sample size, n, is 15.(b) Construct a 96% confidence interval about u if the sample size, n, is 11.(c) Construct an 80% 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?Click 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 15.μLower bound: 109.47; Upper bound: 120.53(Use ascending order. Round to one decimal place as needed.)

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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 simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x, is found to be 19.4, and the sample standard deviation, s, is found to be 4.3. (a) Construct a 95% confidence interval about μ if the sample size, n, is 31. (b) Construct a 95% confidence interval about μ if the sample size, n, is 63. How does increasing the sample size affect the margin of error, E? (c) Construct a 98% confidence interval about μ if the sample size, n, is 31.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?
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…
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.)
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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 bound www
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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 with n = 52 provided a sample mean of 24.0 and a sample standard deviation of 4.6. a. Develop a 90% confidence interval for the population mean (to 1 decimal). b. Develop a 95% confidence interval for the population mean (to 1 decimal). c. Develop a 99% confidence interval for the population mean (to 1 decimal). d. What happens to the margin of error and the confidence interval as the confidence level is increased? V - Select your answer - They increase They decrease They stay the same It cannot be determined from the given data The margin of error increases and the confidence interval becomes narrower The margin of error decreases and the confidence interval becomes wider
A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, ×, is found to be 110, and the sample standard deviation, s, is found to be 8. (a) Construct a 99% confidence interval about u if the sample size, n, is 24. (b) Construct a 99% confidence interval about u if the sample size, n, is 13. (c) Construct a 96% confidence interval about u if the sample size, n, is 24. (d) Should the confidence intervals in parts (a)(c) have been computed if the population had not been normally distributed? An example was provided with additional pictures.
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A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x, is found to be 109, and the sample standard deviation, s, is found to be 10. (a) Construct a 95% confidence interval about if the sample size, n, is 14. (b) Construct a 95% confidence interval about if the sample size, n, is 18. H (c) Construct a 99% confidence interval about u if the sample size, n, is 14. (d) Could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed? Lower bound: Upper bound: (Use ascending order. Round to one decimal place as needed.) COLL Save

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