Question

A sample of the ages of 9 trees in a certain area gave the following data.

1189    1271    1267    1272    1268    1316    1275    1317    1275

Let μ= the mean age of trees in this area. The 99% confidence interval for this data is (1230.9, 1313.5).

a) Write the statistical interpretation of this interval.

b) Write the real-world interpretation of this data.

Answer 1

Solution-A:

confidence interval includes the true population parameter,mu

we are 99% confident that the true mean ages of trees lies in between 1230.9 and 1313.5.

1230.9<mu<1313.5

That is over and over with many different random samples,99% of the intervals would give correct results,containing the popualtion mean.

and in 1% of the intervals do not contain popualtion mean

Solution-B:

we can estimate the true mean ages of trees by using the confidence interval

and if the sample is random,estimates are reliable.