A marketing study was conducted to compare the mean age of male
and female purchasers of a certain product. Random and independent
samples were selected for both male and female purchasers of the
product. It was desired to test to determine if the mean age of all
female purchasers exceeds the mean age of all male purchasers. The
sample data is shown here:
Female: n = 10, sample mean = 50.30, sample standard deviation =
13.215
Male: n = 10, sample mean = 39.80, sample standard deviation =
10.040
Which of the following assumptions must be true in order for the
pooled test of hypothesis to be valid?
I. Both the male and female populations of ages must possess
approximately normal probability distributions.
II. Both the male and female populations of ages must possess
population variances that are equal.
III. Both samples of ages must have been randomly and independently
selected from their respective populations.
Question 1 options:
I, II, and III 

I only 

II only 

III only 
Solution :
The assumptions that must be true in order for the pooled test of hypothesis to be valid are as follows :
I. Both the male and female populations of ages must possess
approximately normal probability distributions.
II. Both the male and female populations of ages must possess
population variances that are equal.
III. Both samples of ages must have been randomly and independently
selected from their respective populations.
Hence, option containing I, II and III is correct.
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