Question

Bob the Agricultural Engineer is studying the masses of the apples grown in Tallula's orchard. He wants to test the null hypothesis that the population mean mass of the apples is 120 g against the alternative hypothesis that the population mean mass of the apples is not 120 g. He studies a sample of 49 apples and finds the sample mean mass to be 123.5 g with a sample standard deviation of 14 g. He will test the hypothesis at a 5% level of significance using a Z-test. (a) State the criterion for rejection as an inequality involving the test statistic. [1 mark] (b) What is the value of the test statistic? [2 marks] (c) Interpret the results. [2 marks]

Answer 1

Given that Sample Size (m) 49 Sample mean (x) = 123.5. Sample 9.D (5) 14 Pobulation me an (u)= 120 level of significance (a) = 0.05 mass of Null hypothesis (Ho): The Population mean apples is the 120 g' 120 mass of the ip Alternative hypothesis (H) : The Population mean apples not 120 g: ie u + 120 This corresponds to two-tailed z. test box onc mean Pro Rejection Region : the Gritical for Zc =1.96 Given 2 20.05 5, two-tailed test Value a is The rejection region tor this two-tailed test R : { 7:171 >1.967 is ie Reject Ho ib Izl >1.96 Cs Scanned with CamScanner

(b The za statistic is computed Test statistic follows: os -u N(o,) Z slon Under Ho 123:5-120 Z 14/049 3.5 2 Z = 1.75 1.75 The Value of test statistic is Ho Decision about that it is observed Since Izl=1.75< Zc=1.96, it . is the null hypothesis is then Concluded that not dejected. Interpretakan the Fail to reject mull hy bothesis (Ho). Conclusion: to enough evidence not there is Therefore of that claim Population mass the abbles 120 g at O OS Significance lewe mean is not cs Scanned with CamScanner