1. A manager is interested in estimating the mean time (in minutes) required to complete a job. His assistant uses a sample of 100 observations to report the confidence interval as [14.355, 17.645]. The population standard deviation is known to be equal to 10 minutes.[You may find it useful to reference thez table.] a.Find the sample mean time used to compute the confidence interval.

Sample mean

b.Determine the confidence level used for the analysis.(Round "z" value to 3 decimal places and final answer to the nearest whole number.)

Confidence level

2.) We use thetdistribution to construct a confidence interval for the population mean when the underlying population standard deviation is not known. Under the assumption that the population is normally distributed, findt_/2,dffor the following scenarios.(You may find it useful to reference thet table.Round your answers to 3 decimal places.)

		t/2,df
a.	A 95% confidence level and a sample of 19 observations.
b.	A 90% confidence level and a sample of 19 observations.
c.	A 95% confidence level and a sample of 9 observations.
d.	A 90% confidence level and a sample of 9 observations.

3.) A random sample of 26 observations is used to estimate the population mean. The sample mean and the sample standard deviation are calculated as 125.4 and 26.50, respectively. Assume that the population is normally distributed.[You may find it useful to reference thet table.] a.Construct the 95% confidence interval for the population mean.(Round intermediate calculations to at least 4 decimal places. Round "t" value to 3 decimal places and final answers to 2 decimal places.)

b.Construct the 99% confidence interval for the population mean.(Round intermediate calculations to at least 4 decimal places. Round "t" value to 3 decimal places and final answers to 2 decimal places.)

c.Use your answers to discuss the impact of the confidence level on the width of the interval. multiple choice

• As the confidence level increases, the interval becomes wider.
• As the confidence level increases, the interval becomes narrower.