A random sample of 175 items is drawn from a population whose standard deviation

Question

A random sample of 175 items is drawn from a population whose standard deviation is known to be sigma = 50. The sample mean is x = 920. (a) Construct an interval estimate for mu with 95 percent confidence. (Round your answers to 1 decimal place.) The 95% confidence interval is from (b) Construct an interval estimate for mu with 95 percent confidence, assuming that sigma = 100. (Round your answers to 1 decimal place.) The 95% confidence interval is from (c) Construct an interval estimate for mu with 95 percent confidence, assuming that or sigma = 200. (Round your answers to 1 decimal place.) The 95% confidence interval is from (d) Describe how the confidence interval changes as sigma increases. The interval stays the same as sigma increases. The interval gets wider as sigma increases. The interval gets narrower as sigma increases. The interval gets wider as sigma decreases.

Explanation / Answer

a) The statistical software output for this problem is:

One sample Z confidence interval:
: Mean of population
Standard deviation = 50

95% confidence interval results:

Hence,

The 95% confidence interval is from 912.6 to 927.4

b) The statistical software output for this problem is:

One sample Z confidence interval:
: Mean of population
Standard deviation = 100

95% confidence interval results:

Hence,

The 95% confidence interval is from 905.2 to 934.8

c) The statistical software output for this problem is:

One sample Z confidence interval:
: Mean of population
Standard deviation = 200

95% confidence interval results:

Hence,

The 95% confidence interval is from 890.4 to 949.6

d) Option B is correct.

Mean n Sample Mean Std. Err. L. Limit U. Limit 175 920 3.7796447 912.59203 927.40797

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