Moderate -0.3 This is a straightforward two-tail z-test with known population standard deviation. Students must state hypotheses, calculate the sample mean (35 minutes), compute the test statistic using z = (x̄ - μ)/(σ/√n), and compare with critical values at 10% significance. While it requires correct application of the normal distribution test procedure, it's a standard textbook exercise with small sample size (n=3) making calculations simple. Slightly easier than average due to minimal computation and being a direct application of a learned technique.
2 The times taken for the pupils in Ming's year group to do their English homework have a normal distribution with standard deviation 15.7 minutes. A teacher estimates that the mean time is 42 minutes. The times taken by a random sample of 3 students from the year group were 27, 35 and 43 minutes. Carry out a hypothesis test at the \(10 \%\) significance level to determine whether the teacher's estimate for the mean should be accepted, stating the null and alternative hypotheses.
2 The times taken for the pupils in Ming's year group to do their English homework have a normal distribution with standard deviation 15.7 minutes. A teacher estimates that the mean time is 42 minutes. The times taken by a random sample of 3 students from the year group were 27, 35 and 43 minutes. Carry out a hypothesis test at the $10 \%$ significance level to determine whether the teacher's estimate for the mean should be accepted, stating the null and alternative hypotheses.
\hfill \mbox{\textit{CAIE S2 2008 Q2 [5]}}