Final answer:
To find the Z test statistic for this hypothesis test, calculate the pooled proportion and the standard error. Subtract the null hypothesis proportion from the sample proportion difference and divide by the standard error. The resulting Z test statistic is 2.711.
Step-by-step explanation:
To find the Z test statistic for this hypothesis test, we first need to calculate the pooled proportion and then the standard error.
The pooled proportion (pooled p) is found by taking the weighted average of the sample proportions from BC and Ontario:
pooled p = (BC proportion * BC sample size + Ontario proportion * Ontario sample size) / (BC sample size + Ontario sample size)
Using the given proportions and sample sizes, the pooled proportion is calculated as:
pooled p = (0.61 * 550 + 0.54 * 407) / (550 + 407) = 0.576
The standard error can be calculated using the formula:
standard error = sqrt((pooled p * (1 - pooled p) / BC sample size) + (pooled p * (1 - pooled p) / Ontario sample size))
Using the given values, the standard error is calculated as:
standard error = sqrt((0.576 * (1 - 0.576) / 550) + (0.576 * (1 - 0.576) / 407)) = 0.0256
Finally, the Z test statistic is calculated by subtracting the null hypothesis proportion (0) from the sample proportion difference (BC proportion - Ontario proportion) and dividing by the standard error:
Z test statistic = (BC proportion - Ontario proportion - 0) / standard error
Using the given values, the Z test statistic is calculated as:
Z test statistic = (0.61 - 0.54 - 0) / 0.0256 = 2.711