Question

Suppose that based on a survey conducted in BC and Ontario, 62% in BC and 56% in Ontario support the idea of carbon pricing. Suppose also that the sample sizes in BC and Ontario are 523 and 446, respectively. You want to conduct a hypothesis test to investigate if the difference in proportion of people in BC and Ontario who support carbon pricing is not equal to 5% (i.e., HA: PBC - PON + 5%). Find the 2 test statistic for this test. Note: 1- Only round your final answer to 2 decimal places. Enter your final answer with 2 decimal places.

Answer 1

Solution:

We are given:

$\hat{p}_{BC}=0.62, \hat{p}_{ON}=0.56$

$\hat{p}_{p}=\frac{(0.62 \times 523)+(0.56 \times 446)}{523+446}=0.592383901$

The z-test statistic is:

\$\large z=\frac{\hat{p}_{BC}-\hat{p}_{ON}}{\sqrt{\hat{p}_{p}(1-\hat{p}_{p})}\sqrt{\frac{1}{n_{BC}}+\frac{1}{n_{ON}}}}$

  $\large =\frac{0.62-0.56}{\sqrt{0.592383901(1-0.592383901 )}\sqrt{\frac{1}{523}+\frac{1}{446}}}$

  $\large =\frac{0.06}{0.031671666}$

$\large \boldsymbol{=1.89 }$