Question

A set of sample of 20 places of mean annual rainfall were randomly selected from a normally distributed universe that has mean annual rainfall of 320 cm. The sample mean was recorded 250 cm with standard deviation of 150 cm. Which one of the following significance tests is correct for the selected samples ?
1. Z - test
2. X² - test
3. F - test
4. t - test

Answer 1

Correct Answer - Option 4 : t - test

Test of significance	Characteristics
Z - test	A z-test is used when the samples are large. The variable is the difference between the before and after measurements. Example: The average weight of subjects before and after following a diet for 6 weeks
X2 - test	Chi-Square Test for Independence use for an association of significance between two categorical variables in a population sample. Typically used with random sampling.
F - test	An F-test is used to compare 2 populations’ variances. The samples can be any size. It is the basis of ANOVA. Example: Comparing the variability of bolt diameters from two machines.
t-test	If a small sample of size less than 30 is drawn from a normally distributed universe with a given mean M and standard deviation as SD T-test use for a Student’s t-distribution i.e, in a normally distributed population where the standard deviation is unknown and the sample size is comparatively small. Paired t-tests compare two samples.

Hence, the correct answer is t - test