SAJC 2021 H1 Chapter 6 Math Hypothesis Testing Check your understanding_Teacher_v1

2021 SAJC JC1 H2 Maths Chapter 6 : Hypothesis Testing 1 Check Your Understanding (Hypothesis Testing) Formulating Null and Alternative Hypothesis ( No need to perform the hypothesis testing) 1. For each of the following parts, justify why a z -test (z-test means a test where the test statistic is normally distributed) can be used by writing down the following (i) The null and alternative hypotheses; (ii) If the sample size is considered large or small; (iii) The population variance , or if unavailable, the unbiased estimate of the population variance ; (iv) If the population is normally distributed or not (if not, also indicate whether an assumption for the population to be normally distribu ted is needed to complete the test); (v) If the Central Limit Theorem is to be used when performing the hypothesis test. You do NOT need to actually perform the hypothesis test (a) The heights of boys in SAJC are normally distributed with a mean 𝜇 cm and standard deviation 5 cm. It is claimed that 𝜇 = 171. However, a random sample of 50 SAJC boys has mean height 173 cm. Test, at the 2% significance level, whether the mean height of SAJC boys in general is above 171 cm. (b) The heights of boys in SAJC are distributed with a mean μ cm and standard deviation 5 cm. It is claimed that μ = 171. However, a random sample of 50 SAJC boys has mean height 169 cm. Test, at the 2% significance level, whether the mean height of SAJC boys in general is below 171 cm. (c) The heights of boys in SAJC are normally distributed with a mean μ cm. It is claimed that μ = 171. However, a random sample of 50 SAJC boys has mean height 173 cm with standard deviation 5 cm. Test, at the 2% significance level, whether the mean height of SAJC boys in general is not equal to 171 cm. (d) The heights of boys in SAJC are normally distributed with a mean μ cm and standard deviation 5 cm. It is claimed that μ = 171. However, a random sample of 5 SAJC boys has mean height 173 cm. Test, at t he 2% significance level, whether the mean height of SAJC boys in general is above 171 cm. (e) The heights of boys in SAJC are distributed with a mean μ cm. It is claimed that μ = 171. However, a random sample of 50 SAJC boys has mean height 173 cm with st andard deviation 5 cm. Test, at the 2% significance level, whether the mean height of SAJC boys in general is not equal to 171 cm. (f) The heights of boys in SAJC are distributed with a mean μ cm and standard deviation 5 cm. It is claimed that μ = 171. However, a random sample of 5 SAJC boys has mean height 169 cm. Test, at the 2% significance level, whether the mean height of SAJC boys in general is not equal to 171 cm. 2 2s

2021 SAJC JC1 H2 Maths Chapter 6 : Hypothesis Testing 2 Solution: (a) , Large sample size, Population is normally distributed, use a z-test, do not need to use CLT (b) , Large sample size, Population is not stated to be normally distribu