Last Wednesday, a random sample of 24 students were surveyed to find how long it takes to walk from the Fretwell Building to the college of education building. The survey team found a sample mean of 12.3 minutes with a standard deviation of 3.2 minutes. assuming walking time from Fretwell to College of education are normally distribution, which of the following is the correct 95% confidence interval for the population mean of walking times.
A) 12.3LaTeX: \pmLaTeX:±LaTeX:±(1.645)(LaTeX: \frac{3.2}{\sqrt{24}}LaTeX:3.224√LaTeX:3.224)
B) 12.3LaTeX: \pmLaTeX:±LaTeX:±(1.90)(LaTeX: \frac{3.2}{\sqrt{24}}LaTeX:3.224√LaTeX:3.224)
C) 12.3LaTeX: \pmLaTeX:±LaTeX:±(1.28)(LaTeX: \frac{3.2}{\sqrt{24}}LaTeX:3.224√LaTeX:3.224)
D) 12.3LaTeX: \pmLaTeX:±LaTeX:±(2.575)(LaTeX: \frac{3.2}{\sqrt{24}}LaTeX:3.224√LaTeX:3.224)
E) 12.3LaTeX: \pmLaTeX:±LaTeX:±(1.96)(LaTeX: \frac{3.2}{\sqrt{24}}LaTeX:3.224√LaTeX:3.224) A E B C

- We are to investigate the confidence interval of 95% for the population mean of walking times from Fretwell Building to the college of education building.

- The survey team took a sample of size n = 24 students and obtained the following results:

Sample mean ( x^ ) = 12.3 mins

Sample standard deviation ( s ) = 3.2 mins

- The sample taken was random and independent. We can assume normality of the sample.

- First we compute the critical value for the statistics.

- The z-distribution is a function of two inputs as follows:

Significance Level ( α / 2 ) = ( 1 - CI ) / 2 = 0.05/2 = 0.025

Compute: z-critical = z_0.025 = +/- 1.96

- The confidence interval for the population mean ( u ) of walking times is given below:

[ x^ - z-critical*s / √n , x^ + z-critical*s / √n ]

Answer: [ 12.3 - 1.96*3.2 / √24 , 12.3 + 1.96*3.2 / √24 ]