Question 1 1 pts Suppose we are given a random sample of n=64 observations from a population with finite variance. This sample produced a sample mean of 16 and a sample standard deviation s=3. Find a 95% confidence interval for the population mean. O (13.53 , 18.47) O (15.265 , 16.735) O (12.72 , 19.28) Question 2 1 pts Suppose Y is distributed according to t-distribution with 11 degrees of freedom. find the value c such that P(Y c) = .01. O 2.718 O 3.106 O -2.718 O -3.106Question 3 1 pts The following data represent the age (in weeks) at which 10 randomly selected babies crawled for the first time. 43, 44, 42, 31, 38, 45, 36, 39, 50, 52 Suppose that the data is a random sample from a population with a normal distribution. Construct a 90 confidence interval for the average age at which babies first crawl. O (38.33, 45.67) O (39.23, 44.77) O (40.84, 43.16) O (41.13, 42.87) Question 4 1 pts In a study, researchers wanted to estimate the true mean skidding distance along a new road in a European forest. The skidding distance (in meters) were measured at 20 randomly selected road sites. The 95% confidence interval constructed based on the data collected was (303.3, 413.6). A logger working on the road claims that the mean skidding distance is at least 425 meters. Does the confidence interval supports the loggers claim? O No, it does not support the claim. O Yes, it supports the claim.Question 5 1 pts In estimating a population mean with a confidence interval based on a random sample X1,.,Xn from a Normal distribution with an unknown mean and a known variance, how the length of the confidence interval changes if we increase the sample size? O Will decrease O Remains the same Will increase Question 6 1 pts In estimating a population mean with a confidence interval based on a random sample X1,.,Xn from a Normal distribution with an unknown mean and a known variance, Compare the length of the 95% and 90% confidence intervals for the unknown mean based on X1..,Xn. O The 90% confidence interval is wider than the 95% confidence interval O Both 95% and 90% confidence intervals have the same length O The 95% confidence interval is wider than the 90% confidence intervalQuestion 7 1 pts In a recent study, a random sample of 1200 Americans were tested for magnesium level. In total, 540 were found to have deficient magnesium levels. American Medical Association claims that 50% of Americans are magnesium deficient. Find a 95% confidence interval for the true proportion of Americans who have deficient magnesium levels and determine if there is any evidence to suggest that the percentage of Americans who have deficient magnesium levels is different from this value? Let p be "true proportion of Americans who have deficient magnesium levels". 95% C.I. is (.4129, .5351). Since 0.5 lies in this C.I., there is evidence to suggest that p is not different from 0.5. 95% C.I. is (.4129. .5351). Since 0.5 lies in this C.I., there is evidence to suggest that p is different from 0.5. 95% C.I. is (.4219. .4781). Since 0.5 does not lie in this C.I., there is evidence to suggest that p is not different from 0.5. 95% C.I. is (.4219. .4781). Since 0.5 does not lie in this C.I., there is evidence to suggest that p is different from 0.5.Question 3 1 pts A University of Florida economist conducted a study of Virginia elementary school lunch menus. During the state-mandated testing period. school lunches average 863 calories. The economist claimed that after the testing period end, the average calories content of Virginia school lunches dropped signicantly. Set up the null and alternative hypothesis to test the economists claim. Let m be the average calories content of Virginia school lunches. C} HID: m = 8:53, Ha: m s 363 {j HID: m = 8:53, Ha: m is not equal to 8:53 C} HID: m = 8:53, Ha: m =- 363 Question 9 1 pts According to a researcher, the average level of mercury uptake in wading birds in Everglades has declined over the past several years. Ten years ago, the average level was 15 parts per million {ppm}. Suppose we are interested in testing whether the average level todayr is less than 15 ppm. Describe the type I error for the test of hypothesis. {j The mean mercury level is less than 15 ppm when in fact the mean is equal to 15 ppm. C} The mean mercury level is equal to 15 ppm when in fact the mean is less than 15 ppm. C} The mean mercury level is greater than 15 ppm when in fact the mean is equal to 15 ppm. Question 10 1 pts Suppose you are interested in conducting the statistical test of HO: mu = 320 against Ha: mu > 320, where mu is the mean of the population. Suppose you have decided to use the following decision rule: Reject HO if the sample mean of a random sample of 100 items is more than 336. Assume that the standard deviation of the population is 80. Find the probability of making a Type I error, by using this decision rule. O 0.4772 O 0.0228 O 0.0301 O 0.4699 Question 11 1 pts Consider the test of hypothesis HO: mu=1200 against the alternative Ha: mu 2.24 O T 1.96