A random sample of 115 items is drawn from a population whose standard deviation

Question

A random sample of 115 items is drawn from a population whose standard deviation is known to be The sample mean is = 950. 40. (a) Construct an interval estimate for with 99 percent confidence. (Round your answers to 1 decimal place.) The 99% confidence interval is from (b) Construct an interval estimate for with 99 percent confidence, assuming that -80. (Round your answers to 1 decimal place.) The 99% confidence interval is from (c) Construct an interval estimate for with 99 percent confidence, assuming that -160. (Round your answers to 1 decimal place.) The 99% confidence interval is from (d) Describe how the confidence interval changes as increases. The interval stays the same as increases. The interval gets wider as increases. The interval gets narrower as increases. The interval gets wider as decreases.

Explanation / Answer

Solution:- n = 115 , = 40 , x = 950 , 99% confidence interval is 2.58

a) => x ± Z * ( /sqrt(n) = 950 ± 2.58 * (40/sqrt(115)) = 950 ± 2.58 * 3.7300

= ( 940.4 , 959.6)

b) = 80 =>   950 ± 2.58 * (80/sqrt(115)) = 950 ± 2.58 * 7.4600

= ( 930.8 , 969.2)

c)   = 160 =>   950 ± 2.58 * (160/sqrt(115)) = 950 ± 2.58 * 14.92

=(  911.5 , 988.5)

d) option B. The interval gets wider as   increases.

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