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Paper 1 · November 2018 · Hypothesis Testing

A test of H0:μ=1.10H_0:\mu=1.10 kg against H1:μ<1.10H_1:\mu<1.10 kg for the mass of manure pockets gives a test statistic of t=−1.82t=-1.82 with 79 degrees of freedom, compared against a one-tailed 5% critical value of −1.664-1.664. What is the correct conclusion?

AReject H0H_0: there is evidence at the 5% level that the mean mass is less than 1.10 kg
BDo not reject H0H_0: there is no evidence at the 5% level that the mean mass is less than 1.10 kg
CReject H0H_0: there is evidence at the 5% level that the mean mass is greater than 1.10 kg
DDo not reject H0H_0: the sample provides no information about the population mean

Explanation

Since the calculated t = -1.82 is more negative than the critical value -1.664, it lies in the rejection region, so H0 is rejected in favour of H1: there is evidence at the 5% level that the mean mass of the pockets is less than 1.10 kg.

Derived from ZIMSEC Statistics Paper 1, November 2018, Q9

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