Statistical inference — Question 2

QCAA 2023, Paper 2 · 1 mark

Q2 · 2023 · Technology-activeSimple familiar1 mark

QUESTION 2

The standard deviation for the scores of 1000 students completing an entry test at a certain university is 13. A researcher takes repeated random samples of the test results, with each sample comprising 40 scores, and calculates the mean score for each sample. Determine the standard deviation of the distribution of the sample mean scores.

(A)

3.08

(B)

2.06

(C)

0.41

(D)

0.33

ABCD

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WORKED SOLUTION

Answer B

1 mark

ANSWER

Worked solution

The standard deviation of the sampling distribution of the mean is

\sigma_{\bar X}=\sigma/\sqrt n=13/\sqrt{40}\approx2.06

Selects option B.

[1 mark]

Worked explanation by QCE Vault; correct option verified against the QCAA answer key.

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