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 traveled.

29 38 38 33 38 21 45 34 40 37 37 42 30 29 35

Click here for the Excel Data File

For a 98 percent confidence interval for the population mean, what are the high and low values? (Round your answers to 2 decimal places.)

Confidence interval for the population mean and .

Answer 1

Answer 2

Sample Mean = xbar = (29+38+38+33+38+21+45+34+40+37+37+42+30+29+35)/15 = 35.07
Sample Std Dev = s = sqrt (Σ (x_i-xbar)²/(n-1)) = 6.02

98%CI --> α = 0.02 --> z_α/2 = 2.330

xbar ± z_α/2s√n
35.07 ± (2.330)(6.02)/(sqrt(15))
35.07 ± 3.62
[31.45,38.69]

Answer 3

x<-c(29, 38, 38, 33, 38, 21, 45, 34, 40, 37, 37, 42, 30, 29, 35)
mean(x)
35.0666667

sd(x)
6.017435


qnorm(c(.01, .99),mean(x),sd(x))
[1] 21.06802 49.06531
98% confident between 21 and 49 mins