When is unknown and the sample is of size n 230, there are two methods for...
When σ is unknown and the sample is of size n ≥ 30, there are two methods for computing confidence intervals for μ. Method 1: Use the Student's t distribution with d.f. = n − 1. This is the method used in the text. It is widely employed in statistical studies. Also, most statistical software packages use this method. Method 2: When n ≥ 30, use the sample standard deviation s as an estimate for σ, and then use the...
Consider a 90% confidence interval for µ not known. For which sample size, n = 10 or n = 20, is the confidence interval longer? Critical Thinking Lorraine computed a confidence interval for µ based on a sample of size 41. Since she did not know α, she used s in her calculations. Lorraine used the normal distribution for the confidence interval instead of a Student's t distribution. Was her interval longer or shorter than one obtained by using an...
If sample size is 15, below please fill the UPPER and LOWER critical values of the standard normal distribution and t distribution under the various confidence levels. (20%) Confidence level standard normal distribution t distribution 80% _______________ _______________ 90% _______________ _______________ 95% _______________ _______________ 98% _______________ _______________ 99% _______________ _______________
2. Assume that the observed value of the sample mean X and of the sample variance S2 of a random sample of size n from a normal population is 81.2 and 26.5, respectively Find %90,%95, %99 confidence intervals for the population mean μ 2. Assume that the observed value of the sample mean X and of the sample variance S2 of a random sample of size n from a normal population is 81.2 and 26.5, respectively Find %90,%95, %99 confidence...
simple random sample of size n is drawn from a population that is normally distributed. The sample mean, X. is found to be 111, and the sample standard deviation is found to be 10. a) Construct a 95% confidence interval about if the sample size, n, is 28. b) Construct a 95% confidence interval about if the sample size, n, is 11 c) Construct a 90% confidence interval about if the sample size, n, is 28 ) Could we have...
A simple random sample of size n is drawn. The sample mean, x, is found to be 19.4, and the sample standard deviation, s, is found to be 4.9. Click the icon to view the table of areas under the t-distribution. (a) Construct a 95% confidence interval about if the sample size, n, is 35. Lower bound: :Upper bound: (Use ascending order. Round to two decimal places as needed.) (b) Construct a 95% confidence interval about if the sample size,...
A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x, is found to be 113, and the sample standard deviation, s, is found to be 10 (a) Construct a 95% confidence interval about if the sample size, n, is 25. (b) Construct a 95% confidence interval about if the sample size, n, is 13 (c) Construct a 90% confidence interval about if the sample size, n, is 25. (d) Could...
A simple random sample of size n is drawn. The sample mean, x, is found to be 19.4, and the sample standard deviation, s, is found to be 4.9. Click the icon to view the table of areas under the t-distribution. OC. The margin of error decreases. (c) Construct a 99% confidence interval about if the sample size, n, is 35. Lower bound: 17.14; Upper bound: 21.66 (Use ascending order. Round to two decimal places as needed.) Compare the results...
A simple random sample of size n is drawn. The sample mean, X, is found to be 17.9, and the sample standard deviation, s, is found to be 4.8. Click the icon to view the table of areas under the t-distribution. (a) Construct a 95% confidence interval about us if the sample size, n, is 34. Lower bound: upper bound: (Use ascending order. Round to two decimal places as needed.) (b) Construct a 95% confidence interval about if the sample...
In a 95% confidence interval. i 1-0.0s is called the confidence coefficient. A) True lB) False If a 95% confidence interval on the mean has a lower limit of 10 and an upper limit that 95% of the time the true value of the mean is between 10 and 15. ) True B) False For a fixed value of the standard deviation and a fixed sample size, a confidence inte population mean will get longer as the level of confidence...