Question

4. Hypothesis testing for a Population proportion Write down the null and alternate hypotheses for part a) and b) first. a) points) According to a 2005 survey conducted by the Association for Dressings and Sauces, 85% of American adults cat salad at least once a week. A nutritionist suspects that the percentage is lower than this. He conducts a survey of 200 American adults and finds that 158 of them eat salad at least once a week. Using either the classical or the P-value approach with level of significance a = 0.05, determine if we have enough evidence to reject the null hypothesis that p=0.85. b) (3 points) According to the US Census Bureau, in 2009, 2.7% of Americans worked at home. An economist suspects that the percentage of Americans working at home has increased since then. He randomly selects 250 working Americans and finds that 8 of them work at home. Using either the classical or the P-value approach with level of significance_a=0.10, determine if we have enough evidence to reject the null hypothesis that p = 0.027. c) (4 points) Given H,: p = 0.4 versus H:p*0.4. Suppose n =1000, x = 420 and a = = 0.01 Using either the classical or the P-value approach, determine if we have enough evidence to reject the null hypothesis.

Answer 1

P=8570 20.85 n = 200 H=158 158 0.79 200 HiP 40185 Cleft tailed). a) Given e-P 7 - PCI-P) Hospro 85 0:79 -0.85 0.06 -2.37 0.02525 (6.85*(1-0:85) 200 P[a 2.-2.37 0.0089 (from 1 tabl) P=0.0089 < X -0.65 Reject Ho There is enough evidence to reject the, b) P=207% -6.07 n=250 Ho P 20.85 r = 8 P = 0.032 250 Hoop=0.027 H, :p0.027 toos 0.032-0.027 €14:88 0.0102515 ZA -P 01027X160.0021) 250 clo P[P3 4.68] = 1-Pf<4.88H-1 Reject Ho evidence to reject the pa d=011 There is enough null pso.627

c) Ho: P=0.4 d=0:0) Hio Proy n=1000 x=420 420 1000 = 0.42 0.42-004 2- 0.02 (1.29 0.0154919 oil Xo6 1000 X a.1020 = 0 2040 P-valee tailed 2xPſz<-197) -21 fail foreject Ho is not enough evidence to reject hypothesis Pexo.ol There is not the nell