Question

For a recent report on sleep deprivation, the Centers for Disease Control and Prevention interviewed 11600 residents of California and 4750 residents of Oregon. In California, 940 respondents reported getting insufficient rest or sleep during each of the preceding 30 days, while 442 of the respondents from Oregon reported the same.

Required:
Using California as population 1 and Oregon as population 2, what are the correct hypotheses for conducting a hypothesis test to determine if these data provide strong evidence the rate of sleep deprivation is different for the two states?

Answer 1

H0: p1-p2=0

Ha: p1-p2≠0

This hypotheses can be written as

H0: p1=p2

Ha: p1 ≠p2

Explanation:

Here the claim is if these data provide strong evidence the rate of sleep deprivation is different for the two states which will be formulated as alternate hypothesis .

Ha: p1-p2≠0

The null hypothesis is

H0: p1-p2=0 i.e these data do not provide strong evidence the rate of sleep deprivation is different for the two states.

where p1 = as population 1 of California

p2= as population 2 of Oregon

This hypotheses can be written as

H0: p1=p2

Ha: p1 ≠p2

which will also give the same results as above and a two tailed test will be performed for both hypotheses.