Question

1. A real estate office conducted a survey on the commute distance in a certain town. They interviewed a random sample of 80 persons in the town, and they found that the sample mean of the commute distance is 8.7 miles and the sample standard deviation is 9.5 miles.

a) What's the point estimate of the mean commute distance for all persons in the town?

b) What's the standard error of the point estimate?

c) Construct a 99% upper one-sided confidence interval for the mean commute distance.

d) construct a 99% two-sided confidence interval for the mean commute distance.

Answer 1

Answer)

As the population s.d is not mentioned here we will use t distribution to estimate the interval

n = 80

Mean = 8.7

S.d = 9.5

A)

Point estimate = 8.7

B)

Standard error = s.d/√n = 9.5/√80 = 1.06

Degrees of freedom is = n-1 = 79

For 79 dof and 99% confidence level, critical value t from t distribution is = 2.64

Margin of error (MOE) = 2.64*9.5/√80 = 2.804

Interval is given by

(Mean - MOE, Mean + MOE)

[5.896, 11.504].

You can be 99% confident that the population mean (μ) falls between 5.896 and 11.504.

C)

Upper sided = 11.504

D)

[5.896, 11.504].

You can be 99% confident that the population mean (μ) falls between 5.896 and 11.504.