Statistics 245 Homework Solutions: Problems and Calculations, Assignments of Data Analysis & Statistical Methods

Download Statistics 245 Homework Solutions: Problems and Calculations and more Assignments Data Analysis & Statistical Methods in PDF only on Docsity! Statistics 245 Homework #8 Solutions Problem #8.2 a) phat=15/84 » 0.1786, and SEphat=sqrt(phat(1-phat)/84) » 0.0418. b) phat ± 1.645 SEphat Þ (0.1098, 0.2473) Problem #8.6 a) phat=421/500 = 0.842, and SEphat = sqrt(phat(1-phat)/500) » 0.0163 b) 0.842 ± 1.96(0.0163) Þ (0.8100, 0.9280) Problem #8.12 a) We want to know if p (the proportion of urban respondents) is significantly different from 64%, so we test H0: p = 0.64 vs. Ha: p Þ 0.64 b) We have phat=0.62; under H0, Þ phat = sqrt(0.64(0.36)/500) » 0.0215, so z=(0.62-0.64)/0.0215)=0.9317. This is clearly not significant (in fact P-value » 0.35). c) The results are the same as the previous exercise; in general, performing a test on a proportion p will give the same results as the equivalent test on p’ = 1-p Problem #8.14 N=(1.96/0.03)2 (0.44)(0.56) » 1052.7. Use n=1052 Problem #8.16 We want to know if p (the proportion of respondents with no children) is significantly different from 48%, so we test H0: p = 0.48 vs. Ha: p Þ 0.48. We have phat = 0.44; under H0, Þphat=sqrt((0.48)(0.52)/500) » 0.0223, so z = (0.44-0.48)/0.0223 » -1.79. This has P-value » 2(0.0367) =0.0734; we don’t have quite enough evidence to conclude that the telephone survey reached households without children in a different proportion than such households are found in the population. Problem #7.2 Note: you need not use the computer, simply use the df in the table closest to the df you need to find. a) df=54, t* satisfies P(Tdf=54 Þ t*) = (1-CL)/2 » P(Tdf=50 Þ t*) = (1-CL)/2=0.005. Looking at table D (pg T-11) give t*=2.678 (exact value is 2.6700). b) df=34, t* satisfies P(Tdf=34 Þ t*) = (1-CL)/2 » P(Tdf=30 Þ t*) = (1-CL)/2=0.05. Looking at table D (pg T-11) give t*=1.697 (exact value is 1.6909). c) df=90, t* satisfies P(Tdf=90 Þ t*) = (1-CL)/2 » P(Tdf=80 Þ t*) = (1-CL)/2=0.025. Looking at table D (pg T-11) give t*=1.990 (exact value is 1.9870). 1