STA 6166 Exam 1 Fall 2006 PRINT Name _______________1. You want to ask a sample of professors at your school how they feel about the tenure system for faculty. You realize that opinions may differ depending on the rank of the professor, especially because assistant professors do not have tenure. You take separate simple random samples of assistant, associate, and full professors and combine them to form your data. You have used aa. simple random sample.b. stratified random sample.c. systematic sampled. completely randomized design experiment.e. randomized complete block design experiment.Suppose a student is randomly selected from this population.STA 6166 Exam 1 Fall 2006 PRINT Name _______________1. You want to ask a sample of professors at your school how they feel about the tenure system for faculty. You realize that opinions may differ depending on the rank of the professor, especially because assistant professors do not have tenure. You take separate simple randomsamples of assistant, associate, and full professors and combine them toform your data. You have used a a. simple random sample.b. stratified random sample.c. systematic sampled. completely randomized design experiment.e. randomized complete block design experiment.2. True or False? Bar graphs and pie charts are used for quantitative data; histograms are used for qualitative data.3. Complete the following statement by placing the correct words in the blanks. A parameter is a descriptive measure of a __________, a statistic is a descriptive measure of a __________.4. Egg quality (Grade AA, Grade A, Grade B) is measured on a a) nominal scale.b) ordinal scale.c) interval/ratio scale.d) random scale.5. A study of the effect of parents' smoking habits on the smoking habits of students in a high school produced the following table of proportions.Supposea studentisrandomly selected from this population.a. What is the probability the student smokes and at least one parent of the student smokes?b. Given the student smokes, what is the probability neither parent smokes?Parents Student smokesStudent does not smokeTotalBoth parents smoke 0.07 0.26 0.33One smokes 0.08 0.34 0.42Neither smokes 0.03 0.22 0.25Total 0.18 0.82 1.0016. The weight of tomato juice in mechanically filled cans varies from can to can according to a normal distribution with = 454 grams and = 8 grams. A sample of 25 cans is selected.What is the distribution of the sample mean, Y?7. In tests of hypotheses what is a Type I error?a) rejecting Ho when it is trueb) failing to reject Ho when it is false8. A measure of how unusual the observed outcome is, if Ho were true, is calleda) the p-valueb) the test statisticc) the rejection region9. Consider a test of Ho: mean = 50 versus Ha: > 50 using a sample of n= 25 and a significance level of 5%. Is the power of the test increased, decreased, or unchanged ifa. the sample size is increased to 50? ______________________b. the significance level is changed to 10%? __________________c. the true value of the mean is 65 rather than 75? ________________10. For each of the following situations, is the p-value above or below 0.05 for the value of the test statistic (TS) shown?a. Ho: = 35, Ha: > 35, n = 26, TS = 2.781 > 0.05 or < 0.05b. Ho: = 45, Ha: ≠ 45, n = 12, TS = -1.749 > 0.05 or < 0.0511. The significance level for a hypothesis test isi. the probability of not rejecting Ho when Ho is false.ii. the probability of rejecting Ho when Ho is false.iii. the probability of not rejecting Ho when Ho is true.iv. the probability of rejecting Ho when Ho is true.12. For a particular sample, the 95% confidence interval for the population mean is [23, 37]. Which of the following statements is true?i. 95% of the population is in the interval [23, 37].ii. 95% of the samples from this population have means in the interval [23, 37].iii. This interval was calculated using a procedure that gives correct intervals 95% of the time.213. A consumer advocate selects sample cans of two brands of canned gravy.She analyzes each can for fat content (in grams). Output from a statistical software package for the data is shown below.________________________________________________Group N Mean Std. Dev. Std. Error M 7 33.386 1.2536 (A) R 12 32.433 0.7152 xxxxxxxVariances T df Pr>|T|Unequal xx xx 0.1012Equal xx (B) 0.0483For Ho: variances are equal, Fobs = (C) DF = (D) Prob>F' = 0.1021a. The printer was having problems. Provide the correct values for (set up calculations with numbers, not letters): (A) Std Error of Mean for Group M = ______________ (B) df = ____________(C) Fobs = ______________(D) Numerator df = _________ Denominator df = ___________b. Is there significant evidence the mean fat content for the two brands of gravy differ at the =0.05 significance level? (NOTE: You do not need to calculate the value of a test statistic.) Choosethe best response from the analysis. i. Yes, the appropriate P-value is .1012ii. No, the appropriate P-value is .1012iii. Yes, the appropriate P-value is .0483iv. No, the appropriate P-value is .048314. A study was conducted to illustrate the effect of alcohol on an individual's ability to perform a physical task. Each of twenty subjectsperformed a test of dexterity, the time to perform the task is (WITHOUT).Each subject was then given two drinks containing 1.5 oz. Of alcohol, andthe time to perform the task is (WITH). Output is shown below, where DIFFis the value of WITH minus WITHOUT. Set-up a 95% confidence interval forthe mean increase in performance time after drinking alcohol (using numbers, not symbols).Variable N Mean Std. Dev. 95% CIWITH 20 13.20 1.856WITHOUT 20 8.60 1.693 DIFF 20 4.60 1.985 15. Find the appropriate 2 quantiles for confidence intervals for withthe stated level of confidence.3n = 15, 95% confidence 2L = _________ 2U = ______________16. Find the appropriate F quantiles for confidence intervals for 1/2 with the stated level of confidence. n1 = 9, n2 = 9, 95% confidence FL = ________ FU = _________17. An experiment was conducted with four treatment groups. The table below gives the number of observations for each treatment and the treatment means. A partial ANOVA table is also furnished. Use this information to answer the questions.Treatment A B C DSa. Size 5 4 3 4Mean 56.900 55.775 53.233 51.125Source DF Mean Sq.Treatment ______ 28.559Error ______
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