2010 A-level H2 Mathematics (9740) Paper 2 Question 6 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions.

Unbiased estimate of population mean $= \bar{x} = 41.3$

Unbiased estimate of population variance $= s^2 = 1.584$

Let $\mu$ be the population mean time required by an employee to complete a task.
$H_0: \mu = 42$ against

$H_1: \mu \neq 42$ at 10% level of significance

Reject $H_0$ if p-value $\textless 0.10$

Test Statistic, $T = \frac{\bar{x}-\mu_0}{\frac{s}{\sqrt{n}}} \sim t(10)$
Applying t-test with $\bar{t} = 41.3, n = 11, s^2 = 1.584$

From GC, $p-value = 0.09487 \textless 0.10$ , reject $H_0$ .

Thus, there is sufficient evidence at 10% significance level that there has been a change in the mean time required by an employee to complete the task.

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KS Teng

KS has been teaching H2/H1 Mathematics and IB mathematics for the more than 10 years. Having taught students from all various Junior Colleges, KS adapts to students' abilities and help them better understand the topics. As someone who loves to teach mathematics and sees it as a truly useful tool in life, KS seeks to enable students to appreciate math. Therefore, his tuition mission is to motivate and cultivate students to be independent and confident thinkers.

2010 A-level H2 Mathematics (9740) Paper 2 Question 6 Suggested Solutions

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