11 (i) 16.2, 27.36 (ii) H,: H = 15, H,:H> 15 %3D (iii) z= 1.986, not significant

Question and answer key

Extracted text: 11 (i) 16.2, 27.36 (ii) H,: H = 15, H,:H> 15 %3D (iii) z= 1.986, not significant


Extracted text: 11 A random sample of 75 eleven-year-olds performed a simple task and the time taken, t minutes, was noted for each. You may assume that the distribution of these times is normal. The results are summarised as follows. n=75, Σt= 1215, Et2 = 21 708 (i) Calculate unbiased estimates for the population mean and variance. (ii) State suitable null and alternative hypotheses to test whether there is evidence that the mean time taken to perform this task is greater than 15 minutes. (iii) Carry out the test, at the 1% significance level, stating your conclusions carefully.