9. Breastfeeding Rates of Infants in Low Income Countries We want to test if infant breast-feeding rates are higher in low income countries than in high income countries. In the United States 25% of infants are breast fed. In Tajikistan, considered a low-income country by the World Bank, researchers found in a random sample of 500 new mothers that 147 were breast feeding their infant. The sample size is large enough to use the normal distribution. The standard error from a randomization distribution under the null hypothesis is SE : 0.024. Using a one population hypothesis test at the 5% significance level, determine if there is significant evidence to show that the breastfeeding rates in low income countries is larger than 25% and show all details of the test. 1. Define the parameters. (3 points) 2. Setup your hypotheses. (3 points) 3. State your sample statistic. Round your answer to three decimal places. (2 points) 4. Find the standardized test statistic and p-value (Use your TI calculator to find this. Write down the calculator commands.) (4 points) Standardized Test Statistic: p-value: 5. State your conclusion (Fail to reject or reject the null). (2 points) 6. State the conclusion in the context of the problem. (3 points) Short Answer/Multiple Choice: (each one is worth 1 point except number 1 which is 3 points) 1.Normal Distribution and the Empirical Rule: Fill in the blanks. (3 points) The Empirical Rule says that ifa distribution ofa sample of data is unimodal and roughly symmetric, then about % of the observations are within 1 standard deviation from the mean, and about 95% of the observations are within i standard deviations of the mean and nearly all of the observations are within _ standard deviations from the mean. 2.Suppose the p-value for a one-sided test for a proportion was 0.08. The p-value for the corresponding two-sided test would be: a. 0.04 b. 0.16 c. 0.12 d. It depends on if the one-sided test was less than or greater than. 3. A 95% confidence interval estimate for the true proportion of people who prefer chocolate over ice cream is (0.2, 0.4). Which of the following is a reasonable conclusion? 95% of the population prefers chocolate over ice cream. We are 95% confident that people prefer chocolate over ice cream. We are 95% confident that the true proportion of people who prefer chocolate over ice cream is 0.3. We are 95% confident that the true proportion of people who prefer chocolate over ice cream is between 0.2 and 0.4. ape-m 4. A 98% confidence interval for the proportion of hotel reservations that are canceled on the intended arrival day is (0.042, 0.112). What is the sample statistic proportion of hotel reservations that are canceled on the intended arrival day from which this interval was constructed? a. 0.032 b. 0.064 c. 0.080 d. 0.077 e. We cannot get the sample statistic from the CI because we don't know the true proportion. 5. Using a significance level of 5%, the appropriate conclusion for a test with a p-value of 0.0621 is a. Reject ['10 b. Accept H\" c. Fail to Reject Hu 6. The critical value ( z') for a 92% confidence interval is: a. 1.645 b. 1.751 c. 1.96 d. 2.326 e. 2.576 7. In a confidence interval, if we increase the confidence level and keep the sample the same (Le. from 95% to 99%), the margin of error will (Hint: Think about 2' and how it is used to calculate the margin of error) a. Increase b. Decrease c. Staythe same d. We need the SE to know 8. In a randomization distribution, the larger number of samples we use (i.e. 10000 samples), the distribution will a. Be nearly normal b. Be a mess, no shape c. Be Skewed left 9. The center of a randomization distribution with a lot of samples (La. 10000 samples) will have the a. Sample statistic b. Population parameter of interest