Question

Five hundred randomly selected working adults living in Calgary, Canada were asked how long, in minutes, their typical daily commute was (Calgary Herald Traffic Study, Ipsos, September 17, 2005). The resulting sample mean and standard deviation of commute time were 28.5 minutes and 24.2 minutes, respectively. Construct and interpret a 90% confidence interval for the mean commute time of working adult Calgary residents.

Answer 1

Answer:

90% confidence interval for the mean commute time of working adult Calgary residents is between a lower limit of 26.72 minutes and an upper limit of 30.28 minutes.

Step-by-step explanation:

Confidence Interval = Mean + or - Error margin (E)

mean = 28.5 minutes

sd = 24.2 minutes

n = 500

degree of freedom = n - 1 = 500 - 1 = 499

confidence level = 90%

t-value corresponding to 499 degrees of freedom and 90% confidence level = 1.64801

E = t × sd/√n = 1.64801 × 24.2/√500 = 1.78

Lower limit = mean - E = 28.5 - 1.78 = 26.72 minutes

Upper limit = mean + E = 28.5 + 1.78 = 30.28 minutes

90% confidence interval is between 26.72 and 30.28 minutes.