Question

Provides data on sleep deprivation rates of Californians and Oregonians. The proportion of California residents who reported insucient rest or sleep during each of the preceding 30 days is 8.0%, while this proportion is 8.8% for Oregon residents. These data are based on simple random samples of 11,545 California and 4,691 Oregon residents.

Conduct a hypothesis test to determine if these data provide strong evidence the rate of sleep deprivation is different for the two states. Use Oreson as Group A and California as Group B. Test statistic (Round to 2 decimal places): p-value (round to two decimal places): Conclusion:

A. We accept the nutt hypothesis.
B. We fail to reject the null hypothesis.
C. We reject the null hypothesis.

Answer 1

To conduct a hypothesis test to determine if the rate of sleep deprivation is different for Californians and Oregonians, we set up the null and alternative hypotheses, calculate the test statistic using the sample proportions and sizes, and compare the p-value to the significance level.

Step-by-step explanation:

To conduct a hypothesis test to determine if the data provides evidence that the rate of sleep deprivation is different for Californians and Oregonians, we need to compare the proportions of those who reported insufficient sleep in the two states. We can set up the null and alternative hypotheses as follows:

1. Null hypothesis (H0): The rate of sleep deprivation is the same for Californians and Oregonians. (p1 = p2)
2. Alternative hypothesis (Ha): The rate of sleep deprivation is different for Californians and Oregonians. (p1 ≠ p2)

Next, we can calculate the test statistic using the formula:

Test statistic = (p1 - p2) / sqrt((p * (1 - p)) * ((1 / n1) + (1 / n2)))

where p1 and p2 are the sample proportions (8.0% and 8.8%), n1 and n2 are the sample sizes (11,545 and 4,691), and p is the pooled proportion ((x1 + x2) / (n1 + n2)).

Finally, we can calculate the p-value using the test statistic and compare it to the significance level (e.g., α = 0.05) to make a conclusion.