Statistics
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Statistics II Midterm Ch 10-14 Name______________________ Dr. C. Monticelli Show all work as done on the Practice Midterm Assume all populations normal. 1) You must use the TI83/84 (or plus calculator); failure to do so will result in grade of 0. *Conclusions must have ‘support’ or ‘reject’ and the word ‘claim’ as done on my materials. *Interpret confidence intervals must be as done on my materials. PROBLEMS MUST BE DONE AS SHOWN ON MY MATERIALS FOR CREDIT! 2) Please handwrite the solutions in blue or black pen on the Midterm. Scan in the Midterm
Solutions with a scanner from home, an office store like Staples, or with a free phone app such as CamScanner, Genius Scan etc.; these apps allow you to save pages into a single, multi-page pdf, which is preferred.
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) Click on SUBMIT ASSIGNMENT, choose file, type phone number in comments box, SUBMIT. 4) Please do NOT email me your Midterm. 5) NO late Midterms will be accepted. 6) I will confirm receipt of all Midterms. If you did not receive an email confirmation or grade
posting within 24 hours, then I did not receive your Midterm and you must contact me asap. 7) All work on the Midterm must be your own; no joint efforts allowed. ---------------------------------------------------------------------------------------------------------------------------- 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.
Did you subtract before – after or after – before? _______________________
claim ………………………………................ ________________________
null hypothesis…………………………………. ________________________
alternative hypothesis………………………….. ________________________
Calculator Screen Name……………………… ________________________
test statistic ………………………… ________________________
pvalue/alpha comparison………………………. ________________________
decision …………………………. ________________________
Conclusion …………………………. ________________________
b) Construct a 99% confidence interval for, . Interpret interval in a 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
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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. Assume populations normal.
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
σ1 =1.5 σ2 = .9
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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
BrandZ BrandW n1 =15 n2 = 25 x1 = 67.3 x2 = 61.8 s1 = 4.4 s2 =11.9
µ1 − µ2
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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
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6 a) Test the claim that Brand Z and Brand W have the different means. Use the .04 level. Assume the variances are different and the populations normal.
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_____________________________________________
BrandZ BrandW n1 = 25 n2 = 50 x1 = 87.3 x2 = 81.8 s1 = 7.4 s2 =11.9
µ1 − µ2
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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
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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
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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.
claim ………………………………................ ________________________
null hypothesis…………………………………. ________________________
alternative hypothesis………………………….. ________________________
Calculator Screen Name……………………… ________________________
test statistic ………………………… ________________________
pvalue/alpha comparison………………………. ________________________
decision …………………………. ________________________
Conclusion …………………………. ________________________
BrandA BrandB BrandC 32 27 22 34 24 25 37 33 32 33 30 22 36 21 39