2013 A-level H1 Mathematics (8864) Question 10 Suggested Solutions

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

(i)

$H_0: \mu = 12$

$H_1: \mu \ne 12$

Under $H_0, \bar{X} ~\sim~ \mathrm{N} (12, \frac{0.8^{2}}{20})$

For $H_0$ to be not rejected at 5% level of significance, then

$-1.95996 < \frac{m-12}{0.8/ \sqrt{20}} < 1.95996$

$\therefore, \{m \in \mathbb{R} |11.6 < m < 12.4\}$

(ii)

$H_0: \mu = 12$

$H_1: \mu < 12$

Under $H_0, \bar{X} ~\sim~ \mathrm{N} (12, \frac{0.8^{2}}{40})$

From the graphing calculator, p-value $= 0.02405 < 0.05$ , we reject $H_0$ .

Thus, there is sufficient evidence at 5% level of significant to conclude that the mean salt content has been reduced.

KS Comments

Read carefully that it is two-tailed and perform the test. Bare in mind to leave answers in set notation.

About

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.

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