Question

Once a month samples of sea level from Key West, FL in 2016 had a mean level of 0.113m and standard deviation of 0.0492m. Ten years earlier, once a month samples of sea level in the same location had mean of 0.014m and standard deviation 0.0373m. Researchers wish to estimate the change in mean sea level in Key West from 2006 to 2016 with 95% confidence.
Year: Jan, Feb    ...Dec Mean SD

2006 0.010 0.120 ... 0.104 0.133 0.0492

2016 0.010 0.101 ... 0.082 0.014 0.0373

Diff 0.000 0.019    ... 0.022 0.099 0.0380

(a) Explain why this is considered paired data.

(b) What is the point estimate for the average difference?

(c) What is the standard error of the difference in means?

(d) What is the margin of error?

(e) Construct and interpret the confidence interval for the mean difference in sea level between 2006 and 2016.

Answer 1

a) The data is paired since it arises from the same location at different points in time.

b) The point estimate for the average difference is

c)The sample standard deviation/error of the difference in means is (here )

d) The margin of error is

e) The 95% confidence interval for the mean difference in sea level between 2006 and 2016 is

We are 95% confident that the mean difference in sea level between 2006 and 2016 lies in the interval .