Question

The mean time taken to design a house plan by 40 architects was found to be 19 hours with a standard deviation of 3.10 hours.

a. Construct a 99% confidence interval for the population mean μ . 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.

-Lowering the sample size

-Increasing the sample size

-Lowering the confidence level

-Increasing the confidence level

Answer 1

Part a.

The provided sample mean is and the sample standard deviation is s=3.10. The size of the sample is n=40 and the required confidence level is 99%.

The number of degrees of freedom is df=40−1=39, and the significance level is α=0.01.

Based on the provided information, the critical t-value for α=0.01 and df=39 degrees of freedom is tc​=2.708.

The 99% confidence for the population mean μ is computed using the following expression

Therefore, based on the information provided, the 99 % confidence for the population mean μ is

which completes the calculation.

Part b.

-Increasing the sample size

-Lowering the confidence level

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