Paper 2 · November 2018 · Hypothesis Testing
A sample of 10 toothpick lengths (cm): 4.99, 4.96, 5.00, 4.98, 5.01, 4.95, 4.96, 4.97, 4.99, 4.97 gives a sample mean of 4.978 cm and standard deviation of about 0.107 cm. Testing H0: mu = 5 against H1: mu is not equal to 5 at the 1% significance level gives a t-statistic of about -0.649, compared with a critical value of t(9) = 3.250. What is the conclusion?
AReject H0 because the sample mean is exactly equal to 5 cm.
BThe test is inconclusive and must be repeated with a larger sample.
CReject H0; the machine is not producing toothpicks of the correct length.
DDo not reject H0; there is insufficient evidence the machine is faulty.
Explanation
Since |t| = 0.649 is well below the critical value of 3.250, the test statistic does not fall in the rejection region, so there is insufficient evidence at the 1% level to say the machine is out of order.
Derived from ZIMSEC Statistics Paper 2, November 2018, Q10