The following problems are copied from the chapter 17 exercises from Introduction to Modern Statistics First Edition by Mine Çetinkaya-Rundel and Johanna Hardin (https://openintro-ims.netlify.app/inference-one-prop.html)

The following problem is a modified version of the problem that appears in your book.

  1. A CDC report on sleep deprivation rates shows that the proportion of California residents who reported insufficient 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.
  1. What type of numerical display could you use to display the number of residents within each state that did and did not experience insufficient rest of sleep?

ANSWER: Frequency Table

  1. Is it appropriate to use the normal approximation to calculate the p-value for the proposed investigation? Explain your answer.

ANSWER: Yes as both the success and failures for both were larger than 10 and the observations are independent.

  1. Conduct a hypothesis test to determine if these data provide strong evidence that the rate of sleep deprivation is different for the two states. Calculate the p-value for the test.

\(H_0 \space p_C = p_O\)

\(H_a \space p_C \ne p_O\)

prop.test(x=c (412.8, 923.6), n=c(4691, 11545), correct=FALSE, alternative = "two.sided")
## 
##  2-sample test for equality of proportions without continuity
##  correction
## 
## data:  c(412.8, 923.6) out of c(4691, 11545)
## X-squared = 2.825, df = 1, p-value = 0.09281
## alternative hypothesis: two.sided
## 95 percent confidence interval:
##  -0.001499599  0.017496188
## sample estimates:
##     prop 1     prop 2 
## 0.08799829 0.08000000
  1. State your findings in the context of the problem.

ANSWER: P-value= .0928. We fail to reject the null hypothesis and therefore conclude that the rate of sleep deprivation between the two states is roughly equal.

  1. Suppose you were to conduct the hypothesis test using the randomization distribution. Would you expect your conclusion to be the same as the conclusion you reached using the normal approximation method? Explain your answer.

ANSWER: It should be the same, since we were allowed to use the normal approximation method due to all of the prerequisites being present in terms of independence and numbers of successes and failures.

Date and time completed: Thu Nov 3 21:26:50 2022