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 511 679

Number in favour 41 85

At the 0.02 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.

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.)

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

Answer 1

## it is two sample proportion test : z

To test :

Ho : p1 = p2 VS H1 : p1 < p2

where p1 : population proportion for liberals and p2 population proportion for conservatives

test statistics :

z = -2.57

p value = 0.0050 ( use statistical table )

decision : we reject Ho if p value is less than α value using p value approach here p value < α value we reject Ho

Conclusion : There is sufficient evidence to conclude that there is a larger proportion of conservatives in favour of lowering standards .