Question

A nationwide sample of influential Liberals and Conservatives was asked as a part of a comprehensive survey whether they favoured lowering environmental standards so that high-sulphur coal could be burned in coal-fired power plants. The results were:

	Liberals	Conservatives
Number sampled	372	745
Number in favour	24	55

At the 0.01 level of significance, can we conclude that there is a larger proportion of Conservatives in favour of lowering the standards? Calculate and interpret the p-value.

a. State the decision rule. (Round the final answer to 3 decimal places.)

H₀ is rejected if z  (Click to select)  is more  is less  than   .

b. Compute the pooled proportion. (Round the final answer to 4 decimal places.)

Pooled proportion            

c. Compute the value of the test statistic. (Negative answer should be indicated by a minus sign. Round the final answer to 2 decimal places.)

Value of test statistic            

d. What is your decision regarding the null hypothesis?

Decision             (Click to select)  Reject  Do not reject

e. Calculate the p-value. (Round the z-value to 2 decimal places. Round the final answer to 4 decimal places.)

p-value is:

Answer 1

a)

for 0.01 level with left tailed test , critical value of z=			-2.326	(from excel:normsinv(0.01)
Decision rule : reject Ho if test statistic z < -2.326

b)

pooled prop p̂ =(x1+x2)/(n1+n2)=(24+55)/(372+745)=

0.0707

c)

x=	24	55
p̂=x/n=	0.0645	0.0738
n =	372	745

std error Se=√(p̂1*(1-p̂1)*(1/n1+1/n2) =		0.0163
test stat z=(p̂1-p̂2)/Se =		-0.57

d) Do not reject Ho (since test statistic is not in rejection region)

e)

P value   =

0.2843

(from excel:1*normsdist(-0.57)