The mean time taken to design a house plan by 38 architects was found to be 22 h

Question

The mean time taken to design a house plan by 38 architects was found to be 22 hours with a standard deviation of 3.65 hours. a. Construct a 95% confidence interval for the population mean .

Round your answers to two decimal places.

__________to _________hours

b. Suppose the confidence interval obtained in part a is too wide. Select all of the ways the width of this interval can be reduced.

a.Lowering the sample size

b.Increasing the sample size

c.Lowering the confidence level

d.Increasing the confidence level

Explanation / Answer

Given that sample size i.e n = 38

sample mean = 22

sample standard deviation = 3.65

mean of populatio mean i.e = 22

standard deviation of population mean = sample standard deviation/n = 3.65/38 = 0.5921

95% confidence interval is (mean- 1.645*sd, mean +1.645*sd)

95% confidence interval for the population mean is (22- 1.645*0.5921, 22+1.645*0.5921) i.e (21.03, 22.97)

95% confidence interval for the population mean is (21.03, 22.97)

b)

- as sample size increseases the standard deviation of population mean decrease hence width of interval decreases

- lower is the confidence interval lower is the width of the interval

so answers are (b),(c) i.e increasing the sample size and Lowering the confidence level

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