Question

6) The board ofreal estate developers claims that 55% ofall voters will vote for a bond issue to construct a massive new water project. A random sample of 215 voters was take and 96 said that they would vote for the new water project. Test to see if this data indicates that less than 55% ofall voters favor the project. Use a 1% significance level. You will get eredit only if you will show your work 15 points b. Compute sample test statistics c. Find or estimate P value d. Conclude the test by rejecting or do not rejecting the null hypothesis e. State your conclusion in the context of application in English language

Answer 1

a. Here claim is that p<0.55

Here claim is that p < 0.55 H_0: p = 0.55 vs H_1: p < 0.55 p^^= 96/215 = 0.45 And SE = squareroot pq/n = 0.0339 Test Statistics is z = p^^- p/Sep = 0.45 - 0.55/0.0339 = -2.95 Pvalue is P(z < -2.95) = 0.0016 As P value is less than alpha hence we reject the null hypothesis Hence we have sufficient evidence to support the claim that less than 55% of voters favor the project.
vs

And SE=

Test Statistics is

b. P value is $P(z<-2.95)=0.0016$

c. As P value is less than alpha hence we reject the null hypothesis

d. Hence we have sufficient evidence to support the claim that less than 55% of voters favor the project.