A personnel researcher has designed a questionnaire and she would like to estimate the average time to complete the questionnaire. Suppose she samples 100 employees and finds that the mean time to take the test is 27 minutes with a standard deviation of 4 minutes. Construct a 90% confidence interval for the mean time to complete the questionnaire. Also, write a short explanation about the findings to the human resources director of your company summarizing the results. Use Excel for this analysis.

Answer:So on this case the 90% confidence interval would be given by (26.336;27.664)    We are 90% confident that the mean time to complete the questionnaire is between (26.336;27.664) Step-by-step explanation:1) Previous concepts A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval". The margin of error is the range of values below and above the sample statistic in a confidence interval. Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean". [tex]\bar X=27[/tex] represent the sample mean   [tex]\mu[/tex] population mean (variable of interest) s=4 represent the sample standard deviation n=100 represent the sample size  2) Confidence interval The confidence interval for the mean is given by the following formula: [tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]   (1) In order to calculate the critical value [tex]t_{\alpha/2}[/tex] we need to find first the degrees of freedom, given by: [tex]df=n-1=100-1=99[/tex] Since the Confidence is 0.90 or 90%, the value of [tex]\alpha=0.1[/tex] and [tex]\alpha/2 =0.05[/tex], and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-T.INV(0.05,99)".And we see that [tex]t_{\alpha/2}=1.66[/tex] Now we have everything in order to replace into formula (1): [tex]27-1.66\frac{4}{\sqrt{100}}=26.336[/tex]    In excel would be "=27-1.66*(4/SQRT(100))"[tex]27+1.66\frac{4}{\sqrt{100}}=27.664[/tex] In excel would be "=27+1.66*(4/SQRT(100))"So on this case the 90% confidence interval would be given by (26.336;27.664)    We are 90% confident that the mean time to complete the questionnaire is between (26.336;27.664)