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 115 Montrealers had 92 who favor while a random sample 145 Torontonians had 98 who favor. The level of significance of the test is 1%. Then the classical action limit for the appropriate test of hypothesis is:
Question 14 options:
.1538
.1487
.1288
.1343
To find the classical action limit for the appropriate test of hypothesis, we need to perform a hypothesis test for comparing proportions.
Step 1: State the null hypothesis (H0) and alternate hypothesis (H1):
The null hypothesis (H0) states that the proportion of Montrealers who want the decriminalization of marijuana is equal to the proportion of Torontonians who want the decriminalization of marijuana.
The alternate hypothesis (H1) states that the proportion of Montrealers who want the decriminalization of marijuana is greater than the proportion of Torontonians who want the decriminalization of marijuana.
Step 2: Define the significance level (α):
The significance level (α) is given as 1%, which means there is a 1% chance of rejecting the null hypothesis when it is actually true. This is also known as the level of significance.
Step 3: Calculate the test statistic:
To compare the proportions, we use the z-test formula:
z = (p1 - p2) / √(p(1-p) / n1 + p(1-p) / n2)
Where:
p1 = proportion in population 1 (Montrealers) who favor decriminalization
p2 = proportion in population 2 (Torontonians) who favor decriminalization
p = combined proportion of both populations (p = ( x1 + x2) / (n1 + n2))
x1 = number of Montrealers who favor decriminalization
x2 = number of Torontonians who favor decriminalization
n1 = sample size of Montrealers
n2 = sample size of Torontonians
In this case:
p1 = 92/115 ≈ 0.8
p2 = 98/145 ≈ 0.676
p = (92 + 98) / (115 + 145) ≈ (190/260) ≈ 0.7308
n1 = 115
n2 = 145
Calculating the test statistic:
z = (0.8 - 0.676) / √(0.7308 * (1 - 0.7308) / 115 + 0.7308 * (1 - 0.7308) / 145)
Step 4: Find the critical value:
Since the alternative hypothesis is one-tailed (greater than), we find the critical value corresponding to the significance level α = 1% (0.01) using the Z-table or a statistical software. The critical value for a one-tailed test at α = 0.01 is approximately 2.33.
Step 5: Compare the test statistic with the critical value:
If the test statistic is greater than the critical value, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.
Step 6: Draw the conclusion:
Comparing the test statistic with the critical value, if the test statistic is greater than 2.33, we reject the null hypothesis. This implies that the proportion of Montrealers who want the decriminalization of marijuana is greater than the proportion of Torontonians who want the decriminalization of marijuana.
Therefore, the classical action limit for the appropriate test of hypothesis is 2.33.