A random sample of 15 items is drawn from a population whose standard deviation

Question

A random sample of 15 items is drawn from a population whose standard deviation is unknown. The sample mean is 760 and the sample standard deviation is s 20. Use Appendix D to find the values of Student's t. (a) Construct an interval estimate of with 99% confidence. (Round your answers to 3 decimal places.) The 99% confidence interval is from to (b) Construct an interval estimate of with 99% confidence, assuming that s = 40, (Round your answers to 3 decimal places.) The 99% confidence interval is from (c) Construct an interval estimate of with 99% confidence, assuming that s-80. (Round your answers to 3 decimal places.) The 99% confidence interval is from to

Explanation / Answer

we know that the confidence interval is given as ,

mean +- z*SD/sqrt(n)

we check the value of z for 99% CI is 2.58

760 +- 2.58*20/sqrt(15)

, solving this

746.676, 773.3 23

using the same equation above , changing the value of s = 40

760 +- 2.58*40/sqrt(15)

, solving this

733.353, 786.646

again changing s = 80

760 +- 2.58*80/sqrt(15)

706.707 , 813.292

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