Question 1 1 pts Why is the Central Limit Theorem useful? Because we do not always know that we are sampling from a parent distribution that is normal O Because we do not always know the standard deviation of the parent population Because we do not always know the mean of the parent population O Because we often know that we are sampling from a parent distribution that is normal Question 2 1 pts Researchers wish to estimate the population prevalence of hepatitis C among men and women older than 50 years old. The method they use in calculating a 95% confidence interval is based on the formula p - 1.96 p(1 - P) -, p + 1.96, /P(1 - p) n+ 4 n+ 4 where n is the sample size and p-tilde is (2+number of individuals in the sample with hepatitis C)/(sample size + 4). Suppose the 95% confidence interval for the population prevalence p is (0.012, 0.047). Which of the statements below is correct? I. The probability that the population prevalence p lies between 1.2% and 4.7% is 95%. Il. In obtaining the 95% confidence interval (0.012, 0.047), a method was used that captures the unknown population prevalence p 95% of the time in the calculated confidence interval. O II only O I only O I and IIQuestion 3 1 pts To construct a confidence interval, we add the margin of error to and subtract the margin of error from the point estimate. Which of the following increases the margin of error? I. decrease the sample size, holding everything else constant Il. increase the confidence level, holding everything else constant O I and II O lI only O I only O neither I nor II Question 4 1 pts Suppose we obtain 1000 samples, each of a fixed size, from the same normal population. For each sample, we construct an 80% confidence interval for the unknown population mean. So we will have 1000 confidence intervals. How many of these 1000 intervals do you expect NOT to contain the population mean? O 200 O 800 O It depends on the sample size. O 20Question 5 1 pts The zeinterval procedure [which uses 1.96 x sigma .f sqrt{n} as the margin of error] works reasonably well even when we are sampling from a parent distribution that is not normally distributed and the sample size is moderate, provided that the parent distribution is not far from being normal. Thus, we sayr that the zinterval procedure is to moderate violations of the normality assumption. 0 sensitive O robust O vital O opposed Question 6 1 pts To construct a condence interval for the population mean, we subtract and add the product of a zscore and the standard error of the sample mean. This product of the zscore and the standard error of the sample mean is called the 0 standard deviation of the sample mean 0 degree of condence 0 width of the condence interval 0 margin of error Question 7 1 pts When the sample size is fixed, increasing the confidence level O decreases precision of the confidence interval estimate O improves precision of the confidence interval estimate O decreases the chance that the confidence interval contains the true mean O increases the standard error of the point estimate Question 8 1 pts Which of the following confidence levels results in a confidence interval with the shortest length? O 99% confidence 0 95% confidence O 80% confidence O 90% confidenceQuestion 9 1 pts Ep = Z p(1 - p) n Solving for n, 2 n = Z p(1 - p) The first equation gives the margin error when we construct the confidence interval for the population proportion. We can solve for the sample size n to derive the second equation, if the confidence level and the margin of error are provided. p is usually unknown. When we perform the sample size calculation, we typically replace p with O 0.5 O 0.25 O 1.0 O 0.01 Question 10 1 pts To calculate the margin of error, we need to decide the confidence level to use. Typically, a 95% confidence level is used. For a 95% confidence level, z=1.96. Suppose a 97% level of confidence is desired. Which statement is true? O z will be larger than 1.96 O z will be smaller than 1.96. O z will still be 1.96