Question

According to the Centers for Disease Control and Prevention, the proportion of U.S. adults age 25 or older who smoke is 0.22. A researcher suspects that the rate is lower among U.S. adults 25 or older who have a bachelor's degree. She took a random sample of 275 U.S. adults 25 or older who have a bachelor's degree, and the proportion of smokers in her sample is 0.18. What is the null hypothesis in this case? What is the alternative hypothesis in this case?

Answer 1

Answer: Null hypothesis :
`H_0:\ p=0.22`

Alternative hypothesis :
`H_a:\ p<0.22`

Explanation:

Given claim : The proportion of U.S. adults age 25 or older who smoke :
`p=0.22`

A researcher suspects that the rate is lower among U.S. adults 25 or older who have a bachelor's degree. i.e.
`p<0.22`

Since the null hypothesis is a fact checked by the researcher or the experimenter that always contains a equals to sign.

∴ Null hypothesis :
`H_0:\ p=0.22`

Alternative hypothesis :
`H_a:\ p<0.22`