Microsoft Word - 112Midterm_ONLINE.doc 1 Statistics II Midterm Name______________________ Chapter 8 -10 XXXXXXXXXXShow all work as done on the Practice Midterm...

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Microsoft Word - 112Midterm_ONLINE.doc 1 Statistics II Midterm Name______________________ Chapter 8 -10 Show all work as done on the Practice Midterm Inordertoreceivecredit,pleasefollowthedirectionsbelow: 1) You must use the TI83/84 (or plus calculator; failure to do so will result in grade of 0. 2) PleasehandwritethesolutionsinblueorbackpenontheMidterm.ScanintheMidterm Solutions. OR Type the answers in MS Word copying and pasting from the Symbols link. Save your midterm as a .pdf file. Please do NOT attach photos as they are hard to see and grade. 3) ClickonSUBMITASSIGNMENT,choosefile,typephonenumberincommentsbox,SUBMIT. 4) PleasedoNOTemailmeyourmidterm. 4)NOlatemidtermswillbeaccepted. 5)Iwillconfirmthereceiptofallmidtermsviaemail.Ifyoudidnotreceiveanemailconfirmation frommewithin24hours,thenIdidnotreceiveyourmidtermandyoumustcontactmeasap. 6)Allworkonthemidtermmustbeyourown;nojointeffortsallowed. ---------------------------------------------------------------------------------------------------------------------------- 1. a) Two different schools create their own versions of the same aptitude test, and a Department Chair administers both versions to the same randomly selected subjects with the results given below. At the .01 level of significance, test the claim that both versions produce the same mean. Assume both populations are normal. claim ………………………………................ ________________________ null hypothesis…………………………………. ________________________ alternative hypothesis………………………….. ________________________ Calculator Screen Name……………………… ________________________ test statistic ………………………… ________________________ pvalue/alpha comparison………………………. ________________________ decision …………………………. ________________________ Conclusion …………………………. ________________________ b) Construct a 99% confidence interval for, , the mean difference of the before minus the after times. Interpret the interval in a complete sentence. Confidence Interval Name__________________________________ Interval___________________________________________ Interpret_____________________________________________ TestB(before) 109 118 104 127 126 99 104 108 113 TestC(after) 102 115 107 116 104 91 113 112 112 µd 2 2. Test the claim that the variances are the same. Use a .05 level of significance. claim ………………………………................ ________________________ null hypothesis…………………………………. ________________________ alternative hypothesis………………………….. ________________________ Calculator Screen Name……………………… ________________________ test statistic ………………………… ________________________ pvalue/alpha comparison………………………. ________________________ decision …………………………. ________________________ Conclusion …………………………. ________________________ 3. a) Two types of flares are tested for their burning times (in min) and sample results are given below. a) Test the claim that Brand Z has a mean greater than Brand W. Use a .03 significance level. claim ………………………………................ ________________________ null hypothesis…………………………………. ________________________ alternative hypothesis………………………….. ________________________ Calculator Screen Name……………………… ________________________ test statistic ………………………… ________________________ pvalue/alpha comparison………………………. ________________________ decision …………………………. ________________________ Conclusion …………………………. ________________________ BrandZ BrandW n1 = 30 n2 = 20 x1 = 61.8 x2 == 67.3 s1 = 11.9 s2 = 6.4 BrandZ BrandW n1 = 25 n2 = 30 x1 = 20.4 x2 == 16.1 σ 1 = 1.5 σ 2 = .9 3 b) Construct a 97% confidence interval for . Interpret the interval. Confidence Interval Name__________________________________ Interval___________________________________________ Interpret ________________________________________ 4. a) Test the claim that the mean for Brand Z is greater than Brand W at the .04 significance level. Assume both populations are normal and the variances are equal. claim ………………………………................ ________________________ null hypothesis…………………………………. ________________________ alternative hypothesis………………………….. ________________________ Calculator Screen Name……………………… ________________________ test statistic ………………………… ________________________ pvalue/alpha comparison………………………. ________________________ decision …………………………. ________________________ Conclusion …………………………. ________________________ b) Construct a 96% confidence interval for based on the sample data above. Interpret the interval in a complete sentence. Confidence Interval Name__________________________________ Interval___________________________________________ Interpret_____________________________________________ µ1 − µ2 Brand Z BrandW n1 = 15 n2 = 25 x1 = 67.3 x2 = 61.8 s1 = 4.4 s2 = 11.9 µ1 − µ2 4 5 a) A study is made of the defect rates of two machines used in manufacturing. Of 300 randomly selected items produced by the first machine, 7 are defective. Of 350 randomly selected items produced by the second machine, 20 are defective. At the .01 level of significance, test the claim that the two machines have the different rate of defects. claim ………………………………................ ________________________ null hypothesis…………………………………. ________________________ alternative hypothesis………………………….. ________________________ Calculator Screen Name……………………… ________________________ test statistic ………………………… ________________________ pvalue/alpha comparison………………………. ________________________ decision …………………………. ________________________ Conclusion …………………………. ________________________ b) Construct a 99% confidence interval for . Interpret the interval in a complete sentence. Confidence Interval Name__________________________________ Interval___________________________________________ Interpret_____________________________________________ p1 − p2 5 6 a) Test the claim that Brand Z and Brand W have the different means. Use the .04 level. Assume the variances are different. claim ………………………………................ ________________________ null hypothesis…………………………………. ________________________ alternative hypothesis………………………….. ________________________ Calculator Screen Name……………………… ________________________ test statistic ………………………… ________________________ pvalue/alpha comparison………………………. ________________________ decision …………………………. ________________________ Conclusion …………………………. ________________________ b) Construct a 96% confidence interval for . Interpret the interval in a complete sentence. Confidence Interval Name__________________________________ Interval___________________________________________ Interpret_____________________________________________ Brand Z BrandW n1 = 25 n2 = 50 x1 = 87.3 x2 = 81.8 s1 = 7.4 s2 = 11.9 µ1 − µ2 6 7. Listed below are results from two different tests designed to measure achievement. (x)TestB 64 48 51 59 60 43 41 42 35 50 45 (y) testC 91 68 80 92 91 67 65 67 56 78 71 a. Plot the scatter diagram below. Label x and y axes. Do a rough sketch. b. Find the value of the linear correlation coefficient r by the TI83 shortcut- state calculator screen name c) Test the claim of no linear relation by the TI83 p-value method. = .01 claim ………………………………................ ________________________ null hypothesis…………………………………. ________________________ alternative hypothesis………………………….. ________________________ Calculator Screen Name……………………… ________________________ test statistic ………………………… ________________________ pvalue/alpha comparison………………………. ________________________ decision …………………………. ________________________ Conclusion …………………………. ________________________ d) Find the estimated equation of the regression line by TI83 shortcut e) Plot the regression line on the scatter diagram in part a). f) Assuming a significant linear correlation, predict the score a student would get on Test C, given he got a 37 on test B. g) What percentage of the total variation can be explained by the regression line? α 7 8. Responses to a survey question are broken down according to employment and the sample results are given below. At the .05 significance level, test the claim that the response and employment status are independent. Yes No Undecided Employed 40 25 5 Unemployed 30 15 7 claim ………………………………................ ________________________ null hypothesis…………………………………. ________________________ alternative hypothesis………………………….. ________________________ Calculator Screen Name……………………… ________________________ test statistic ………………………… ________________________ pvalue/alpha comparison………………………. ________________________ decision …………………………. ________________________ Conclusion …………………………. ________________________ 9. In studying the occurrence f genetic characteristics, the following sample data were obtained. At the .04 significance level, test the claim that the characteristics occur with the same frequency claim ………………………………................ ________________________ null hypothesis…………………………………. ________________________ alternative hypothesis………………………….. ________________________ Calculator Screen Name……………………… ________________________ test statistic ………………………… ________________________ pvalue/alpha comparison………………………. ________________________ decision …………………………. ________________________ Conclusion …………………………. ________________________ Characteristic B C D E F G frequency 38 40 55 45 35 49 8 10. At the .02 significance level, test the claim that the three brands have the same mean level if the following sample results have been obtained. Use ANOVA. claim ……………………………….......