Question

O CONFIDENCE INTERVALS AND HYPOTHESIS TESTING Hypothesis test for a population proportion Lau A decade-old study found that the proportion, p, of high school seniors who beleved that "getting rich" was an important personal goal was 70%. A researcher decides to test whether or not that percentage still stands. He finds that, among the 220 high school seniors in his random sample, 135 beleve that "getting rich" is an important goal. Can he conclude, at the 0.1 level of significance, that the proportion has indeed changed? Perform a two-tailed test. Then fill in the table below. Carry your intermediate computations to at least three decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.) The nu hypothesis: The alternatie.hvaothesis Osa The type of test atatistic (Choose one) The value of the test statistic: (Round to at least three decimal places.) LYnnten.cntical.co.ne.at.thn Explanation Check ALRgne Reserved Tems of Use Pvacy A II

Answer 1

(null) Ho :   p =    0.7
(alternate) H1 :   p ╪   0.7

type of test statistic = Z test

Number of Items of Interest,   x =   135                  
Sample Size,   n =    220                  
                          
Sample Proportion ,    p̂ = x/n =    0.6136                  
                          
Standard Error ,    SE = √( p(1-p)/n ) =    0.0309                  
Z Test Statistic = ( p̂-p)/SE = (   0.6136   -   0.7   ) /   0.0309   =   -2.795

critical z value =    -1.645 , 1.645 [excel formula =NORMSINV(0.10/2)]

since, z stat <-1.645, so, we reject the null hypothesis

answer: YES