Question

According to a report on sleep deprivation by the Centers for Disease Control and Prevention the proportion of California residents who reported insufficient rest or sleep during the on each of the preceding 30 days is 8.0% while this proportion is 8.8% for Oregon residents. A random sample of 11,545 California and 4,691 Oregon residents were surveyed. We are interested in finding out if there is evidence to suggest that the rate of sleep deprivation is different for the two states. What statistical method is appropriate for testing if the rate of sleep deprivation is different for the two states? Select one: a. paired t-test b. two proportion z-test c. two sample t-test d. one proportion z-test e. one sample t-test.

Answer 1

Given that, we are interested in finding out if there is evidence to suggest that the rate of sleep deprivation is different for the two states.

Therefore, the null and alternative hypotheses are,

H0 : p1 = p2

Ha : p1 ≠ p2

Where, p1 is the population proportion of California residents who reported insufficient rest or sleep during the on each of the preceding 30 days. And p2 is the population proportion of Oregon residents who reported insufficient rest or sleep during the on each of the preceding 30 days.

Therefore, this test is a two-proportion z-test.