Further Math A2s 4.2.3 Two-sample tests

[Maximum number: 8]

Scientists are studying the effects of exercise on LDL blood cholesterol levels. Over a three-month period, a large group of people exercised for 20 minutes each day. For a randomly chosen sample of 10 of these people, the LDL blood cholesterol levels were measured at the beginning and the end of the three-month period. The results, measured in suitable units, are as follows.

Table for Question CAIE A-Level Further Math A2 4.2.3 Hypothesis Tests Questions question 1 — CAIE A-Level Further Math A2

(a)

Test, at the 2.5% significance level, whether there is evidence that the population mean LDL blood cholesterol level has reduced by more than 2 units after the three-month period.

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$\mathrm{H}_{0}: \mu_{B}-\mu_{E}=2 \quad \mathrm{H}_{1}: \mu_{B}-\mu_{E}>2$
May use $\mu_{d}$ , but must be consistent with direction of
differences found.

8 & 8 & 15 & -2 & -3 & 20 & -3 & 0 & 5 & 4
Differences, at most 2 errors.

$\sum d=52, \sum d^{2}=816, s^{2}=\frac{1}{9}\left(816-\frac{52^{2}}{10}\right)\left[=\frac{2728}{45}=60.62\right]$
Their values but must see 9 and 10 used correctly.

$t=\frac{\frac{52}{10}-2}{\sqrt{\frac{s^{2}}{10}}}$ $t=1.29967, \quad 1.30$
Tabular value =2.262. '1.30' <2.262, accept $\mathrm{H}_{0}$
Allow 'not significant'.

Insufficient evidence to suggest that cholesterol level has reduced by more
than 2.
CWO. Correct conclusion in context, following correct work, level of uncertainty in language.

A0 if hypotheses wrong way round or missing.

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(b)

State any assumption that you have made in part (a).

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CAIE A-Level Further Math A2 4.2.3 Hypothesis Tests Questions question 1

Question (a)

Question (b)