Question

# A nationwide sample of influential Liberals and Conservatives was asked as a part of a comprehensive...

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  (is more or 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: (Reject or 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: _________

a)

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

H0 is rejected if z is less than -2.326

b)

 pooled prop p̂ =(x1+x2)/(n1+n2)=(24+55)/(372+745)= 0.0707

c)

 Liberals Conservatives x= 24 55 n = 372 745 p̂=x/n= 0.0645 0.0738 estimated prop. diff =p̂1-p̂2    = -0.0093
 std error Se=√(p̂1*(1-p̂1)*(1/n1+1/n2) = 0.0163 test stat z=(p̂1-p̂2)/Se = -0.57

d)

Do not reject

e)

 P value   = 0.2843 (from excel:1*normsdist(-0.57)

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