Q172 · Practice questionTechnology-freeComplex familiar1 mark
QUESTION 172
A random sample consists of 36 independent measurements from a normal population with unknown mean and known standard deviation . The sample mean is .
A spreadsheet accidentally records every measurement twice, producing 72 rows. Using , which statement gives the valid 95% confidence interval for and the reason?
(A)
, because the spreadsheet has 72 rows.
(B)
, because duplication doubles uncertainty.
(C)
, because the standard deviation is 12.
(D)
, because there are only 36 independent observations.
WORKED SOLUTION
1 markAnswer D
ANSWER
D. ; there are still only 36 independent observations.
Worked solution
Duplicating every observation leaves the sample mean exactly 100. If the original observations are , the new spreadsheet mean is
Its sampling variance is therefore unchanged at . The standard error is 2, and the interval is
The duplicated rows are perfectly dependent pairs and add no independent information. A incorrectly treats 72 rows as 72 independent observations; B doubles the standard error; C uses the population standard deviation as the standard error.
Equivalent mathematically justified methods accepted.
Exact answers unless a decimal accuracy is specified.
Select D.
Practice question aligned to the current QCAA syllabus; review the worked solution and marking criteria.
View the QCAA syllabus