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.


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\}


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.

    pingbacks / trackbacks

    Leave a Comment

    Contact Us

    CONTACT US We would love to hear from you. Contact us, or simply hit our personal page for more contact information

    Not readable? Change text. captcha txt

    Start typing and press Enter to search