Answer to Question #154310 in Statistics and Probability for Ali Ahmed

Question

The Greater Pittsburgh Area Chamber of Commerce wants to estimate the mean time workers who are employed in the downtown area spend getting to work. A sample of 15 workers reveals the following number of minutes spent traveling. 29 38 38 33 38 21 45 34 40 37 37 42 30 29 35 a. Develop a 95 percent confidence interval for the population mean. Interpret the result. 

Answer 1

Sample mean

$μ= \frac{Sum \;of\; all \; the \; observations}{Number \; of \; observations} \\ = \frac{29+38+38+33+38+21+45+34+40+37+37+42+30+29+35}{15} \\ = \frac{526}{15} \\ = 35.067$

Standard deviation (SD) is formulated as follows:

$SD = \sqrt{\frac{1}{n-1}\sum(x_i-μ)^2}$

$SD = \sqrt{\frac{507}{15-1}} \\ = \sqrt{36.21} \\ = 6.017$

Now we will develop a 95 confidence interval.

Use the z-value for 95%: z = 1.96

Standard error is given as:

$SE = \frac{z \times SD}{\sqrt{n}} \\ = \frac{1.96 \times 6.017}{\sqrt{15}} \\ = 3.045$

Confidence interval is:

$(μ-SE, μ+SE) \\ (35.067-3.045, 35.067+3.045) \\ (32.022, 38.112)$

The mean time workers who are employed in the downtown area spend getting to work is between 32.022 and 38.112.