Question

the real estate assessor for a company government wishes to study various characteristics concerning single- family house in the country. A random sample of 700 houses results in a mean heated area for the house of 1800 sq. ft. with a standard deviation of 400 sq ft. In addition, it was learned that 420 out of the 700 houses had central air conditioning. Suppose that, using this data, a statistical hypothesis test is conducted to determine if there is significant evidence that the proportion of all houses in the country with central air conditioning is different .50.

If $\pi$ represents the proportion of all houses in the country with central air conditioning the correct alternative hypothesis is.

a. $\Pi$ < .50

b. $\Pi \neq$ .50

c. $\Pi$ > .50

d. $\Pi$ = .50

Answer 1

Solution:

Given that , the statistical test is performed to determine if there is significance evidence that the proportion of all houses in the country with central air conditioning is different from 0.50

i.e. population proportion is not equal to 0.50

i.e $\pi$ $\neq$ 0.50

so,alternative hypothesis is $\pi$ $\neq$ 0.50

option b. is correct.