Given below are two statements. In the light of the above statements, choose the most appropriate answer from the options given below.
Statement I:The null hypothesis for testing the difference between means is generally stated as the two population means being not equal.
Statement II:When samples are small and population variances are unknown but assumed equal, a Z-test is employed for testing the null hypothesis.
ABoth Statement I and Statement II are true
BBoth Statement I and Statement II are false ✓ Correct
CStatement I is true but Statement II is false
DStatement I is false but Statement II is true
Correct answer: (B) Both Statement I and Statement II are false
Explanation
The null hypothesis for a difference between means states that the two population means are equal, so Statement 1 is false, and small samples with unknown equal variances call for a t-test, so Statement 2 is false.
The null always asserts no difference, leaving inequality to the alternative hypothesis.
Statement 1 confuses the null with the alternative it is tested against.
A Z-test needs known population variances or very large samples.
With small samples and estimated variances the t-test is the correct choice.
Pooled-variance t-tests handle the assumption of equal population variances.
Want more like this? Create a free account to practise a full test, track your progress, and get spaced-repetition review.
Practise on Mcqkart →🎓 Book an expert →