Statistics II Project Chapter 8 -10 Name______________________ Please put your phone number in the body of the email. Show all work as done on the Sample Project. (I will call if I have trouble downloading it.) Please also use the Sample Calculator Solutions as a guide. In order to receive credit, please follow the directions below: 1) Please handwrite the solutions in blue or back pen on the Project. Scan in the Project Solutions either with a home scanner; or you may have Staples scan and save your document to a memory stick. You must bring your own memory stick and will be charged approximately .50 cents per page to scan and save. Some students have also attached a photo of each page using the .jpg extension. OR Type the answers in a MS Word Document copying and pasting from the Symbols link on the on the Timeline. Save your file with a .pdf extension. 2) Please email me your document as an attachment via the WebStudy email. 3) NO late projects will be accepted. 4) I will confirm the receipt of all projects via email. If you did not receive an email confirmation from me within 24 hours, then I did not receive your project and you must contact me immediately. 5) 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. Assume both populations normal. 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 claim .................................................... ________________________ null hypothesis........................................ ________________________ alternative hypothesis................................ ________________________ Calculator Screen Name........................... ________________________ test statistic ________________________ .............................. pvalue/alpha comparison............................ ________________________ decision ............................... ________________________ Conclusion ............................... ________________________ b) Construct a 95% confidence interval for, d , the mean difference of the before minus the after times. Interpret the interval in a complete sentence. Confidence Interval Name__________________________________ Interval___________________________________________ Interpret_____________________________________________ 1 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 Males claim, using a .01 level of significance? n1 = 16 Females n2 = 18 s1 = 4.2 s2 = 2.3 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. claim .................................................... ________________________ null hypothesis........................................ ________________________ alternative hypothesis................................ ________________________ Calculator Screen Name........................... ________________________ test statistic ________________________ .............................. pvalue/alpha comparison............................ ________________________ decision ............................... ________________________ Conclusion ............................... ________________________ b) Construct a 95% confidence interval for 1 2 . Interpret the interval. Confidence Interval Name__________________________________ Interval___________________________________________ Interpret ________________________________________ 2 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 governmentowned 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. Pr ivate Gov 't x1 = $26,800 x2 = $25,400 s1 = $600 s2 = $450 n1 = 10 n2 = 8 claim .................................................... ________________________ null hypothesis........................................ ________________________ alternative hypothesis................................ ________________________ Calculator Screen Name........................... ________________________ test statistic ________________________ .............................. pvalue/alpha comparison............................ ________________________ decision ............................... ________________________ Conclusion ............................... ________________________ b) Construct a 99% confidence interval for 1 2 based on the sample data above. Interpret the interval in a complete sentence. Confidence Interval Name__________________________________ Interval___________________________________________ Interpret_____________________________________________ 3 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 p1 p2 . Interpret the interval in a complete sentence. Confidence Interval Name__________________________________ Interval___________________________________________ Interpret_____________________________________________ 4 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 kin-size cigarettes. Assume the variances are different. Tar(mg) Tar(mg) Filt n1 = 31 nonFilt n2 = 35 x1 = 13.3 x2 = 24 s1 = 3.7 s2 = 1.7 claim .................................................... ________________________ null hypothesis........................................ ________________________ alternative hypothesis................................ ________________________ Calculator Screen Name........................... ________________________ test statistic ________________________ .............................. pvalue/alpha comparison............................ ________________________ decision ............................... ________________________ Conclusion ............................... ________________________ b) Construct a 95% confidence interval for 1 2 . Interpret the interval in a complete sentence. Confidence Interval Name__________________________________ Interval___________________________________________ Interpret_____________________________________________ 5 7.Listed below are results from two different tests designed to measure productivity and dexterity for randomly selected employees. Pr oductivity 23 25 28 21 21 25 26 30 34 36 Dexterity 49 53 59 42 47 53 55 63 67 75 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? 6 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. Yes Male 25 Female 20 No Undecided 50 15 30 10 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. SHOW WORK for test statistic & p. Re sponse A B C D E Frequency 12 15 16 18 19 claim .................................................... ________________________ null hypothesis........................................ ________________________ alternative hypothesis................................ ________________________ Calculator Screen Name........................... ________________________ test statistic ________________________ .............................. pvalue/alpha comparison............................ ________________________ decision ............................... ________________________ Conclusion ............................... ________________________ 7 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. Use ANOVA. BrandA BrandB 15 20 25 21 23 22 20 17 22 23 BrandC 21 BrandD 15 22 20 19 15 14 23 18 22 28 28 claim .................................................... ________________________ null hypothesis........................................ ________________________ alternative hypothesis................................ ________________________ Calculator Screen Name........................... ________________________ test statistic ________________________ .............................. pvalue/alpha comparison............................ ________________________ decision ............................... ________________________ Conclusion ............................... ________________________ 8