Statistics
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Statistics II Project Ch 10-14 Name______________________________ Dr. C. Monticelli Show all work as done on the Sample Project & Notes. 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 Project. Scan in the Project 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 project 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 project. 5) NO late projects will be accepted. 6) I will confirm receipt of all projects. If you did not receive an email confirmation or grade
posting within 24 hours, then I did not receive your project and you must contact me asap. 7) All work on the project must be your own; no joint efforts allowed. -------------------------------------------------------------------------------------------------------------------------------- 1. a) A physical education director claims by taking a special vitamin, a weight lifter
can increase his strength. Eight athletes are selected and given a test of strength, using the standard bench press. After two weeks of regular training, supplemented with the vitamin, they are tested again. Test the vitamin regimen is effective in increasing strength at the .05 level of significance. Each value in the data that follow represents the maximum number of pounds the athlete can bench press.
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 95% confidence interval for, . Interpret the interval in a sentence. Confidence Interval Name__________________________________ Interval___________________________________________ Interpret_____________________________________________
athlete 1 2 3 4 5 6 7 8 Before 210 230 182 205 262 253 219 216 after 219 236 179 204 270 250 222 216
µd
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2. An instructor hypothesizes that the variance of the final exam grades in her statistics
class is larger for male students than it is for female students. The data from the final exam for the last semester are as shown. Is there enough evidence to support her
claim, using a .01 level of significance?
claim ………………………………................ ________________________
null hypothesis…………………………………. ________________________
alternative hypothesis………………………….. ________________________
Calculator Screen Name……………………… ________________________
test statistic ………………………… ________________________
pvalue/alpha comparison………………………. ________________________
decision …………………………. ________________________
Conclusion …………………………. ________________________ 3. a) A survey found that the average hotel room rate in New Orleans is $88.42 and the
average room rate in Phoenix is $80.61 from data obtained from two samples of 50 hotels. The population standard deviations were $5.62 and $4.83 respectively. At the .05 level of significance, test the claim that there is no difference between the rates. Assume populations normal.
claim ………………………………................ ________________________
null hypothesis…………………………………. ________________________
alternative hypothesis………………………….. ________________________
Calculator Screen Name……………………… ________________________
test statistic ………………………… ________________________
pvalue/alpha comparison………………………. ________________________
decision …………………………. ________________________
Conclusion …………………………. ________________________
b) Construct a 95% confidence interval for . Interpret the interval. Confidence Interval Name__________________________________ Interval___________________________________________ Interpret ________________________________________
Males Females n1 =16 n2 =18
s1 = 4.2 s2 = 2.3
µ1 − µ2
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4. a) A researcher wishes to determine whether the salaries of professional nurses employed by private hospitals are higher than those of nurses employed by government- owned hospitals. She selects a sample of nurses from each type of hospital and calculates the means and standard deviations of their salaries. At the .01 level of significance, test the claim that private hospitals pay more than government owned hospitals. Assume both populations normal and the variances are equal.
claim ………………………………................ ________________________
null hypothesis…………………………………. ________________________
alternative hypothesis………………………….. ________________________
Calculator Screen Name……………………… ________________________
test statistic ………………………… ________________________
pvalue/alpha comparison………………………. ________________________
decision …………………………. ________________________
Conclusion …………………………. ________________________
b) Construct a 99% confidence interval for based on the sample data above. Interpret the interval in a complete sentence.
Confidence Interval Name__________________________________ Interval___________________________________________ Interpret_____________________________________________
Private Gov 't x1 = $26,800 x2 = $25,400
s1 = $600 s2 = $450 n1 =10 n2 =8
µ1 − µ2
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5 a) A sample of 50 randomly selected men with high triglyceride levels consumed 2 tablespoons of oat bran daily for 6 weeks. After 6 weeks, 60% of the men had lowered their triglyceride level. A sample of 80 men consumed 2 tablespoons of wheat bran for six weeks. After six weeks, 25% had lower triglyceride levels. Test the claim that there is a significant difference in the two proportions at the .01 level.
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) Use a .05 level of significance to test the claim that the mean amount of tar in filtered king-size cigarettes is less than the mean amount of tar for non-filtered king-size cigarettes. Assume the variances are different and populations normal.
claim ………………………………................ ________________________
null hypothesis…………………………………. ________________________
alternative hypothesis………………………….. ________________________
Calculator Screen Name……………………… ________________________
test statistic ………………………… ________________________
pvalue/alpha comparison………………………. ________________________
decision …………………………. ________________________
Conclusion …………………………. ________________________
b) Construct a 95% confidence interval for . Interpret the interval in a complete sentence.
Confidence Interval Name__________________________________ Interval___________________________________________ Interpret_____________________________________________
Tar(mg) Tar(mg) Filt nonFilt n1 = 31 n2 = 35 x1 =13.3 x2 = 24
s1 = 3.7 s2 =1.7
µ1 − µ2
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7.Listed below are results from two different tests designed to measure productivity and dexterity for randomly selected employees.
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. = .05
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 dexterity, given he got a 40 on productivity. g) What percentage of the total variation can be explained by the regression line?
Productivity(x) 23 25 28 21 21 25 26 30 34 36 Dexterity(y) 49 53 59 42 47 53 55 63 67 75
α
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8. Responses to a survey question are broken down according to gender and the sample results are given below. At the .05 level of significance, test the claim that the response and gender are independent.
claim ………………………………................ ________________________
null hypothesis…………………………………. ________________________
alternative hypothesis………………………….. ________________________
Calculator Screen Name……………………… ________________________
test statistic ………………………… ________________________
pvalue/alpha comparison………………………. ________________________
decision …………………………. ________________________
Conclusion …………………………. ________________________
9. In studying the responses to a multiple-choice test question, the following sample data were obtained. At the .05 significance level, test the claim that the responses occur with the same frequency.
claim ………………………………................ ________________________
null hypothesis…………………………………. ________________________
alternative hypothesis………………………….. ________________________
Calculator Screen Name……………………… ________________________
test statistic ………………………… ________________________
pvalue/alpha comparison………………………. ________________________
decision …………………………. ________________________
Conclusion …………………………. ________________________
Yes No Undecided Male 25 50 15 Female 20 30 10
Response A B C D E Frequency 12 15 16 18 19
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10. At the .025 significance level, test the claim that the four brands have the same mean 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 BrandD 15 20 21 15 25 17 22 15 21 22 20 14 23 23 19 23 22 18 22 20 28
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