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# PRIN OF STATISTICS I STAT 211

Texas A&M

GPA 3.54

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This 5 page Class Notes was uploaded by Darien Kutch on Wednesday October 21, 2015. The Class Notes belongs to STAT 211 at Texas A&M University taught by Staff in Fall. Since its upload, it has received 51 views. For similar materials see /class/225762/stat-211-texas-a-m-university in Statistics at Texas A&M University.

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Date Created: 10/21/15

Stat 21 1 Spring03 The amount of radon released in showers was investigated Radonenriched water was used in the experiment and six different orifice diameters were tested in showerheads The data from the experiment are of the orifice affect the mean percentage of radon released We will use the notation Ll1 le Ll3 M4 Lls M6 for the true mean percentage of radon released for the sizes 037 051 071 102 140 199 respectively The true means being the same implies the size of the orifice does not affect the percentage of radon released The data are found to be normally distributed The following are the results of single factor ANOVA Tukey s pairwise comparisons equal variance testing obtained by MINTTAB Analysis of Variance Source DF SS MS F P Treatment 5 113338 22668 3085 0000 Error 18 13225 735 Total 23 126563 Level N Mean StDev 037 4 82750 2062 051 4 77000 2309 071 4 75000 1826 102 4 71750 3304 140 4 65000 3559 199 4 62750 2754 95 Tukey39s pairwise comparisons for l ji i 037 051 071 102 140 3 051 70335 11835 071 1665 74085 13835 8085 102 4915 70835 72835 17085 11335 9335 140 11665 5915 3915 0665 23835 18085 16085 12835 199 13915 8165 6165 2915 73835 26085 335 1833 1508 8335 those two numbers for each combination ij are the confidence interval limits on Tukey s intervals Test for Equal Variances Bartlett39s Test normal distribution Test Statistic 21 P7Value 0873 Use the int rmati n and the MTNTTAB outputs above to answer the f 11 inn 11 an ti n Use a005 when it is necessar Stat211 1 N 9 gt V 0 gt1 Spring03 Which of the following is the corresponding null hypothesis for observing if the size of the orifice affect the mean percentage of radon released a 1 2 3 b u u5 u6 0 01111 1u2 lLl3lLl4 1u5 1u6 CD11 1u2 lLl3lLl4 1u5 1u6 0 Do you have enough evidence based on the data to conclude that the size of the orifice affect the mean percentage of radon released a Yes We failed to reject H0 b Yes We rejected H0 c No We failed to reject H0 d No We rejected H0 Which of the following is the point estimate for H6 Ll1 a We do not have enough information to answer this question Do you have enough evidence based on the data to conclude that le and 3 being significantly different a No 0 falls in the corresponding Tukey s interval b No 0 does not fall in the corresponding Tukey s interval c Yes 0 falls in the corresponding Tukey s interval d Yes 0 does not fall in the corresponding Tukey s interval Which of the following is the test statistics to observe if the true mean percentage of radon released for the size 051 is 7238 Hint You are finding the test statistics for H0 2 le 7238 a 10004 b 20009 c 40017 d 80035 Which of the following is the error degree of freedom on the analysis of variance 5 b 6 c 18 d 23 e 24 Which of the following would be the test statistics if I asked you to test the sizes 051 and 071 having the same true variance a 11354 b 12645 c 13251 d 15989 Stat211 00 O H 0 1 1 N L Spring03 Do you have enough evidence based on the data to conclude that constant variance assumption is satisfied for single factor ANOVA a Yes We failed to rejectH0 constant variance b Yes We rejected H 0 constant variance c No We failed to reject H 0 constant variance d No We rejected H 0 constant variance I believe that there should not be any difference between true means of the sizes 140 and 199 When 1 look at the Tukey s 95 confidence intervals data also support this Which of the following 1 may have made a Typel error b Type 11 error c Correct decision Which of the following would be the test statistics if I asked you to test the true standard deviation for the size 071 being 22 Hint You are finding the test statistics for H0 2 03 22 where O3 is the true standard deviation for the size 071 b 249 c 276 d 332 1f 1 ask you to tell me the degrees of freedom to compute 95 confidence interval for any 1 Llj as we discussed in Chapter 9 what would you tell me a Too much work 1 need to specifically know which pair b 6 c 8 d 18 e 23 1f the test statistics is t715 and to 059 1833 for the lower tailed test with 10 observations which of the following would be your decision a Reject H 0 b Fail to reject H0 Which of the following is not a legitimate alternative hypothesis a p gt 04 b 02 lt 253 c u S 29 d Lu H2 0 e all of the above are legitimate alternative hypothesis 1f the test statistics and the critical value are F26 and t002523 2069 df23 and 0F005 for the two tailed test of H 0 I Ll1 le 0 which of the following would be the corresponding conclusion a We have enough evidence based on the data to conclude that the true means of two populations are the same b We have enough evidence based on the data to conclude that the true means of two populations are different Stat 21 1 Spring03 15 1f the Pvalue is 0023 and a005 would you reject H0 a 1 need to know if this is upper tailed lower tailed or two tailed test b Yes c No A statistician is claiming that majority of all MBA39s continue their formal education by taking courses within 10 years of graduation Using a sample of 200 people he found that 111 had taken coursework since receiving their MBA Let p be the true proportion of MBA39s continue their formal education by taking courses within 10 years of graduation The 98 twosided confidence interval for p is computed as 04731 06369 Answer the following 4 questions using this 39 f 39 16 Based on the 98 twosided confidence interval for the true proportion of MBA39s continue their formal education by taking courses within 10 years of graduation which of the following would be the conclusion a The majority more than 50 of all MBA39s continue their formal education by taking courses within 10 years of graduation b 50 of all MBA39s continue their formal education by taking courses within 10 years of graduation c Less than 50 of all MBA39s continue their formal education by taking courses within 10 years of graduation 17 The statisticians claim will be tested with H0 2 p S 05 versusHu I p gt 05 Which of the following is the corresponding test statistics a 14653 b 15556 c 15651 d 16784 18 If X is the number of MBA s continue their formal education by taking courses within 10 years of graduation which of the following is the possible rejection region for H a I p gt 05 a 195196197198199200 b 012345 c 01234196197198199200 d It is not possible to determine 19 To compute the Pvalue for Ha I p gt 05 which of the following you would do a 1 would look at the area above the test statistics on the corresponding table b 1 would look at the area below the test statistics on the corresponding table c 1 would look at the area above the absolute value of the test statistics on the corresponding table and multiply by two 20 1 was wondering if it is better to teach more theory or applications Let p1 and p2 be the true proportion of students who prefer more theory and more application respectively I collected the data to test H a 2 p1 lt p2 and obtained the test statistics z175 Using a005 which of the following conclusion is obtained by this data Z0 025 196 Z0 05 1645 Z0 10 128 a Students prefer more theory b Students prefer more application 21 Pairs of Pvalues and significance levels are given In which case H 0 would be rejected a P value0084 a005 Stat211 b P value0039 06001 c P value0023 0F010 Answer Key 1 c 2b 3b 421 5c 6c 7d 821 130 Mb 15b 16b 17b 1821 1921 20h 9c 21c 10a 11b Spring03 12b

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