A test of hypothesis is performed to determine whether the proportion of Montrealers (population 1) who want the decriminalization of marijuana is greater than the proportion of Torontonians (population 2) who want decriminalization of marijuana. A random sample of 120 Montrealers had 90 who favor while a random sample 150 Torontonians also had 90 who favor. The level of significance of the test is 1%. Then the classical action limit for the appropriate test of hypothesis is:

Question

A test of hypothesis is performed to determine whether the proportion of Montrealers (population 1) who want the decriminalization of marijuana is greater than the proportion of Torontonians (population 2) who want decriminalization of marijuana. A random sample of 120 Montrealers had 90 who favor while a random sample 150 Torontonians also had 90 who favor. The level of significance of the test is 1%. Then the classical action limit for the appropriate test of hypothesis is:

-.1343 ?
.1487 ?
-.1487 ?
.1343 ?

Answer 1

To find the classical action limit for this hypothesis test, we first need to define the null and alternative hypotheses.

Null Hypothesis (H0): The proportion of Montrealers who favor the decriminalization of marijuana is equal to or less than the proportion of Torontonians who favor it.
Alternative Hypothesis (H1): The proportion of Montrealers who favor the decriminalization of marijuana is greater than the proportion of Torontonians who favor it.

Since we are comparing two proportions, we can use the z-test for proportions. The formula for calculating the test statistic is:

z = (p̂1 - p̂2) / √(p̂(1-p̂) * (1/n1 + 1/n2))

Where:
p̂1 = proportion of Montrealers who favor decriminalization
p̂2 = proportion of Torontonians who favor decriminalization
p̂ = (x1 + x2) / (n1 + n2) (combined proportion)
n1 = sample size of Montrealers
n2 = sample size of Torontonians

Given the information provided:
n1 = 120
n2 = 150
x1 = 90
x2 = 90

Calculating the proportions:
p̂1 = 90/120 = 0.75
p̂2 = 90/150 = 0.6
p̂ = (90 + 90) / (120 + 150) = 0.675

Now we can calculate the test statistic:
z = (0.75 - 0.6) / √(0.675 * (1-0.675) * (1/120 + 1/150))
z = 0.15 / √(0.2275 * 0.3225 * 0.0128)
z ≈ 0.15 / √(0.011352)
z ≈ 0.15 / 0.106555
z ≈ 1.4077

Looking up the critical value for a one-tailed test with a 1% significance level, we find that it is approximately 2.33.

The classical action limit is calculated as the critical value multiplied by the standard error (in this case, z * standard deviation):

action limit = 2.33 * (0.106555)
action limit ≈ 0.2482

Therefore, none of the given options exactly match the classical action limit.