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.)
H_{0} 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 |
H_{0} is rejected if z is less than -2.326
b)
pooled prop p̂ =(x_{1}+x_{2})/(n_{1}+n_{2})=(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 =p̂_{1}-p̂_{2} = | -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) |
Get Answers For Free
Most questions answered within 1 hours.