Question

Bob the Quality Control Engineer is studying the heights of the apple trees grown in Tallula's orchard. He wants to test the null hypothesis that the population mean height of the trees is 18 m against the alternative hypothesis that the population mean height of the trees is less than 18 m. He studies a sample of 6 trees and finds the sample mean height to be 16.4 m with a sample standard deviation of 1.1 m. He will test the hypothesis at a 1% level of significance using a t-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

Answer:

Standard error = standard deviation /sqrt(sample size) =1.1/sqrt(6) = 0.4490

As we don't have the population standard deviation so we wil choose the one sample t test

t = sample mean - population mean / standard error

t =16.4-18/0.4490 = -3.5629

Answer a)

at degree of freedom of 5(6-1) t test for 99 % for left side test is -3.3647

so lower level = 18-3.3647*(0.4490) = 16.48 m

so if height of sample tree is more than 16.48, we fail to reject the null hypothesis and states that height of the sample tree is greater than or equal to height of the population tree

So rejectio criteria is less than 16.48 m height of tree ( t value less than -3.3649)

Answer b)

As calculated above test statistics is -3.5629

Answer c:

As the calculate t value is lower than the critical t value, we reject the null hypothesis and accep the alternate hypothesis and states that mean height of the sample tree is significantly less than the population mean height of the tree(18 m)