For the follow questions please record your answers to at least three decimal places. The scores of students on the SAT college entrance examinations at a certain high school had a normal distribution with mean u = 539.3 and standard deviation or = 25.2. (a) What is the probability that a single student randomly chosen from all those taking the test scores 544 or higher? ANSWER: For parts (b) through (d), consider a simple random sample (SR8) of 25 students who took the test. (b) What are the mean and standard deviation of the sample mean score 5:, of 25 students? The mean of the sampling distribution for :E is: The standard deviation of the sampling distribution for :E is: (c) What z-score corresponds to the mean score T of 544? ANSWER: (d) What is the probability that the mean score :5 of these students is 544 or higher? ANSWER: In a very large population, the distribution of annual income is skewed, with a long right tail. We take a simple random sample of 71 people from this population and record the n incomes. We expect a histogram of the n incomes in the sample 0 A. will resemble a Uniform distribution for all values of n. O B. will not resemble a Normal distribution whatever the value of n. O C. will resemble a Uniform distribution provided 11 is large. (9) D. will resemble a Normal distribution for all values of n. O E. will resemble a Normal distribution provided 11, is large. A confidence interval for a population mean has length 22. a) Determine the margin of error. b) If the sample mean is 58.5, obtain the confidence interval. Confidence interval: (Using the confidence interval when conducting a two-tail test for the population mean /, we do not reject the null hypothesis if the hypothesized value for M: A. falls between the lower confidence limit (LCL) and the upper confidence limit (UCL) O B. is to the left of the lower confidence limit (LCL) O C. is to the right of the upper confidence limit (UCL) Suppose that we reject a null hypothesis at the 0.05 level of significance. Then for which of the following a-values do we also reject the null hypothesis? O A. 0.06 O B. 0.02 O C. 0.04 O D. 0.03A random sample of 64 observations has a mean of 30. The population standard deviation is assumed to be 3. The 85.3% condence interval estimate for the population mean (to the third decimal place) is O A. (28.369, 31.631) 0 B. (28.560, 31.440) 0 c. (29.456, 30.544) 0 0. (29.383, 30.617) In developing an interval estimate for a population mean, the interval estimate was 62.84 to 69.46. The population standard deviation was assumed to be 6.50, and a sample of 100 observations was used. The mean of the sample was 0 A. 62.96 0 B. 56.34 0 C. 13.24 0 D. 66.15 A random sample of 80 observations produced a mean of} = 25.3 from a population with a normal distribution and a standard deviation or = 2.59. (For each of the following, rounded to 2 decimals} (a) Find a 95% confidence interval for ,u Slug (b) Find a 99% confidence interval for ,u S M S (c) Find a 90% confidence interval for ,u, S .U S A random sample of 11 measurements was selected from a population with standard deviation 0' : 17.4 and unknown mean u. Calculate a 95 % confidence interval for ,u, for each of the following situations: (rounded to 2 decimals) (a) n = 40, E = 77.9 S in S (b) n = 65, E = 77.9 S u S (0)11 = 85, E = 77.9 S u S (d) In general, we can say that for the same confidence level, increasing the sample size the margin of error (width) of the confidence interval. (Enter: "DECREASES", "DOES NOT CHANGE" or "INCREASES\For each problem, select the best response. (a) In testing hypotheses, which of the following would be strong evidence against the null hypothesis? 0 A. Using a small level of significance. 0 B. Using a large level of significance. 0 C. Obtaining data with a large P -va|ue_ O D. Obtaining data with a small P-value. (b) The P-value of a test of a null hypothesis is Q A. the probability the null hypothesis is true. 0 B. the probability, assuming the null hypothesis is true, that the test statistic will take a value at least as extreme as that actually observed. 0 C. the probability the null hypothesis is false. 0 D. the probability, assuming the null hypothesis is false, that the test statistic will take a value at least as extreme as that actually observed. (0) In formulating hypotheses for a statistical test of significance, the null hypothesis is often O A. 0.05 O B. a statement that the data are all 0. Q C. a statement of \"no effec " or "no difference". 0 D. the probability of observing the data you actually obtained For each statement, select the correct null hypothesis, Ho, and alternative hypothesis, Ha, in symbolic form. (a) The mean height of all adult Canadian males is 69 inches (5 ft 9 in). A researcher wonders if young Canadian males between the ages of 18 and 21 tend to be taller than 69 inches. A random sample of 100 young Canadian males ages 18 to 21 yielded a sample mean of 71 inches. OA. Ho : M > 69, Ha : A 69 OC. Ho : 1 = 71, Ha : 69 OF. Ho : A = 69, Ha : u # 69 (b) According to the Merck Veterinary Manual, the average resting heart rate for a certain type of sheep dog is 115 beats per minute (bpm). An Ontario farmer notices his aging sheep dog has been acting more lethargic than usual and wonders if her heart rate is slowing. He measures her heart rate on 15 occasions and finds a sample mean heart rate of 118.2 bpm. OA. Ho : u = 115, Ha : p > 115 OB. Ho : & = 118.2, Ha : x # 118.2 OC. Ho : u = 118.2, Ha : p 115 (c) A certain type of hummingbird is known to have an average weight of 4.55 grams. A researcher wonders if hummingbirds (of this same type) living in the Grand Canyon differ in weight from the population as a whole. The researcher finds a sample of 30 such hummingbirds from the Grand Canyon and calculates their average weight to be 3.75 grams. OA. Ho : M = 4.55, Ha : p 3.75 OE. Ho : /