1Part I. True/False questions. Read each statement and circle “true” if it is correct and “false” if incorrect (2points each).1. A t-distribution with 1000 degrees of freedom is wider than a normal distribution.True False2. Other factors equal, a confidence interval will be wider if the standard deviation is known than if itis estimated from a sample.True False3. The regression model is appropriate when the means of y conditional on x fall in roughly a straightlineTrue False4. When we know s instead of F, we should use the t-distribution in place of the normal distribution toconduct hypothesis tests for a mean.True False5. Holding other factors constant, a prediction interval calculated for an individual prediction from aregression equation will usually be wider than a confidence interval for a mean response predicted fromthe same regression equation.True FalsePart IIMultiple choice: For the problems below, circle the answer. There is only one correct answer to eachquestion.6. A radio talk show host with a large audience is interested in the proportion p of adults in hislistening area who think the drinking age should be lowered to eighteen. To find this out he poses thefollowing question to his listeners. "Do you think that the drinking age should be reduced to eighteen inlight of the fact that eighteen-year-olds are eligible for military service?" He asks listeners to phone inand vote "yes" if they agree the drinking age should be lowered and "no" if not. Of the 100 people whophoned in 70 answered "yes." Which of the following assumptions for inference about a proportionusing a confidence interval are violated? A) The data are an SRS from the population of interest. B) The population is not highly skewed. C) n is so large that both the count of successes n p and the count of failures n(1 – p) are ten ormore.D) A and BE) A and CF) There appears to be no violations.27. In forming a hypothesis for a statistical test of significance, the null hypothesis is oftenA) The statement of “no effect” or “no difference”B) The probability of observing the data you actually obtained.C) The statement that the data are all 0.D) .05E) A and BF) None of the above8. I draw an SRS of size 15 from a population that has a normal distribution with mean µ and standarddeviation σ. The one-sample t statistic has how many degrees of freedom? A) 15B) 14C) D) We cannot determine the degrees of freedom without knowing the value of s. E) We do not need to calculate degrees of freedom here.9. An SRS of 100 postal employees found that the average time these employees had worked for thepostal service was 7 years with standard deviation 2 years. Suppose we are not sure if the populationdistribution is normal. Which of the following situations would violate the conditions for using tprocedures?"A) A histogram of the data shows mild skewness B) A stemplot of the data has a small outlier C) The sample standard deviation is large D) A and BE) B and CF) A and CG) A, B, and CH) None of the above.310. Which of the following is an example of a matched pairs design?A) A teacher compares the pre-test and post-test scores of students. B) A teacher compares the scores of students using a computer based method of instruction with thescores of other students using a traditional method of instruction. C) A teacher compares the scores of students in her class on a standardized test with the nationalaverage score. D) A teacher calculates the average of scores of students on a pair of tests and wishes to see if thisaverage is larger than 80%. E) A and BF) B and CG) C and DH) A and DI) None of the above11. Eighty rats whose mothers were exposed to high levels of tobacco smoke during pregnancy wereput through a simple maze. The maze required the rats to make a choice between going left or goingright at the outset. Sixty of the rats went right when running the maze for the first time. Assume that theeighty rats can be considered an SRS from the population of all rats born to mothers exposed to highlevels of tobacco smoke during pregnancy. (Note that this assumption may or may not be reasonable,but researchers often assume lab rats are representative of such larger populations because lab rats areoften bred to have very uniform characteristics.) The standard error for the proportion p of those whowent right the first time when running the maze is A) 0.0023. B) 0.0484. C) 0.0548. D) 0.0559. 12. The weights of three adult males are (in pounds) 160, 215, and 195. The standard error of the meanof these three weights is A) 190.00. B) 27.84. C) 22.73. D) 16.07. Use the following text to answer questions 13 to 15: In 1989 two researchers surveyed a group ofninety-four third and fourth grade children asking them to rate their level of fearfulness about a varietyof situations. Two years later, the children again completed the same survey. The researchers computedthe mean fear rating for each child in both years and were interested in the relation between theseratings. They then assumed that the true regression line wasµ1991 Mean Rating = α + β(1989 Mean Rating)Suppose we wish to predict the 1991 mean fear rating for all children who had a 1989 mean fear ratingof 1.5. We use statistical software to do the prediction and obtain the following output.1989 Mean Fear Rating Fit StDev Fit 95% C.I. 95% P.I.1.5 1.4748 0.0284 (1.418, 1.531) (1.000, 1.950)413. The explanatory variable in this study is A) 1989 mean fear ratings. B) 1991 mean fear ratings. C) the difference in the mean fear ratings for the two years. D) the particular group of ninety-four children used in the study. 14. A 95% confidence interval for the 1991 mean fear rating for all children who had a 1989 mean fearrating of 1.5 isA) 1.418 to 1.531. B) 1.000 to 1.950. C) 1.4748 ± 0.0284. D) 1.5 ± 0.0284. 15. Suppose we wish to predict the 1991 mean fear rating for a child who had a 1989 mean fear ratingof 1.5. A 95% interval for this prediction is A) 1.418 to 1.531. B) 1.000 to 1.950. C) 1.4748 ± 0.0284. D) 1.5 ± 0.0284. Part III: Numerical and short answer questions. Please answer the questions below. If you hope to getpartial credit please show your work.1. For each case below, find the critical value (t* or z*) you would use for the significance test orconfidence interval (your answer should be a number). State whether you would use z or t, and give