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	131	236
NUMBER IN FAVOUR	30	83

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.

1. 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 ________ 2.33, 63.66 Incorrect

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

p-value is: _________ 0.0072, 0.101 Incorrect

Answer 1

1)

Ho:   p1 - p2 =   0          
Ha:   p1 - p2 <   0          
                  
sample #1   ----->   liberals          
first sample size,     n1=   131          
number of successes, sample 1 =     x1=   30          
proportion success of sample 1 , p̂1=   x1/n1=   0.2290          
                  
sample #2   ----->   conservative          
second sample size,     n2 =    236          
number of successes, sample 2 =     x2 =    83          
proportion success of sample 1 , p̂ 2=   x2/n2 =    0.3517          
                  
difference in sample proportions, p̂1 - p̂2 =     0.2290   -   0.3517   =   -0.123
                  
pooled proportion , p =   (x1+x2)/(n1+n2)=   0.3079          
                  
std error ,SE =    =SQRT(p*(1-p)*(1/n1+ 1/n2)=   0.0503          
Z-statistic = (p̂1 - p̂2)/SE = (   -0.123   /   0.0503   ) =   -2.44

2)

p-value =        0.0074   [Excel function =NORMSDIST(z)