Question

Is sea level the same along all coastal regions? To examine this a sample of 12 coastal locations in the Gulf Coast had mean sea level 5.3953m and standard deviation 2.2559m. A sample of 17 locations along the eastern seaboard had mean 3.4028m and standard deviation 1.036m.
(a) What is the point estimate for the dierence in mean sea level?

(b) What is the standard error of the dierence in means?

(c) What is the margin of error for a 99% condence interval?

(d) Construct and interpret the condence interval for the dierence in mean sea level between the Gulf Coast and the eastern seaboard.

(e) Based on the interval, do you expect there to be evidence or little to no evidence for Ha : μ1 = μ2? Explain without conducting the hypothesis test.

Answer 1

Part a)

Part b)

Standard Error =

Part c)

Margin of Error =

Part d)

Confidence interval :-

DF = 14



Lower Limit =
Lower Limit = -0.0854
Upper Limit =
Upper Limit = 4.0704
99% Confidence interval is ( -0.0854 , 4.0704 )

We are 99% confident that the population mean difference  in sea level between the Gulf Coast and the eastern seaboard lies in the interval  ( -0.0854 , 4.0704 ) .

part e)

Since value 0 lies in the interval, hence we can conclude that  sea level the same along all coastal regions

i.e   μ1 = μ2