1 You Are Interested In Whether People That Live Close To A Freeway Consider Their Neighborhood To Be Different In Spat 1 (311.54 KiB) Viewed 33 times
1. You are interested in whether people that live close to a freeway consider their neighborhood to be different in spatial scale. You have 2 samples. The first sample is from 250 randomly selected adults (a). The second sample is from 100 randomly selected adults who live close to a freeway (f). Assume data are distributed nearly normal. a. List the null and alternative hypotheses. b. In the sample of US adults (a) 125 reported their neighborhood to be small in spatial scale. In the sample of US adults living by a freeway (f) 65 reported their neighborhood to be small in spatial scale. Proportions for respondents selecting a small neighborhood are provided in the last row of the table below. Calculate the standard error for a confidence interval for the difference in proportions of respondents that consider their neighborhood to be a small. Response Adults (a) Adults by Freeway (f) Small neighborhood 125 65 Total sample size (n) 350 100 Proportion reporting small .5 65 Paltat Pro + na nf SEộa-ỘE =V c. We need to calculate a point estimate for the difference in these proportions. Calculate the point estimate for the difference in proportion of residents reporting a small neighborhood p(a)-p(f) d. Construct a 95% (z*=1.96) confidence interval for the difference in these proportions using the standard error and point estimate you calculated. CI = (fa - Pi+ z* se e. What information does this confidence interval provide in terms of the null and alternative hypotheses?
. Griver @ The null and Aldeginative hypothesis 0918 : Ho : Pa - Pf Hy : Papp 90 qgle : plopositions Po 99.0 = } 0.5 and na 250 Do nf = 100 Standgold 29191091 : S.Eopa-fe Pa (1-P) + P* (1-6) na ng E 0.5X0.5 + 0.65 0.35 100 250 0.05793 11 0.003275
Point - estimate : . = 0.5 -0.65 = -0.15 95% fall CI II Confidence in interval difference Propositiong - (A - Pc + z*se) (-0.15 + 1.96 x 0.05723) (-0.15 0.1128) ( (-0.2622, -0.0378 ) = The 95% confidence interval for pl-p2 is -0.2622<p1-p2<-0.0378. Rule : If the 95% confidence interval does not contain the hypothesize parameter, then a hypothesis test at the 0.05 level will almost always reject the null hypothesis. Since, the obtained confidence interval doesn't contain the hypothesized value 0, we reject the null hypothesis and conclude there is difference between two sample Proportion. #note: if you have any doubt regarding this question please comment. I'll answer. Comment >
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