On a farm, it took an average of 50 minutes for new workers to learn how to use a new
machine. Recently a new agricultural machine was introduced. The farmer wants to find out if
the mean time taken by new workers to learn to use the machine is different from 50 minutes.
A sample of 40 workers showed that it took, on average, 47 minutes for them to learn to use
the machine with a standard deviation of 7 minutes. Test the farmer’s claim at the 0.05
significance level:
(a) Formulate appropriate null and alternative hypotheses for this claim. [2 marks]
(b) Is this a left-tailed test, a right-tailed test or a two-tailed test? [1 mark]
(c) Find the value of the test statistic. [3 marks]
(d) Find the critical value for this test. [2 marks]
(e) Based on the test statistic and critical value, would you accept or reject the null hypothesis?
Explain why you would accept or reject the null hypothesis.