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

P-value =0.0047

Answer 2

that isn't one of the choices :/

Answer 3

The answer is .1343

Answer 4

e) Suppose your conclusion in part (c) is wrong, i.e., you failed to reject the null hypothesis when the mean gas mileage is actually different for the three types of mufflers. What type of error would you have made?

Answer 5

To find the classical action limit for the appropriate test of hypothesis, we need to perform a hypothesis test using the given sample data.

First, let's state the null and alternative hypotheses:

Null hypothesis (H0): The proportion of Montrealers who want the decriminalization of marijuana (population 1) is equal to the proportion of Torontonians who want the decriminalization of marijuana (population 2).
Alternative hypothesis (Ha): The proportion of Montrealers who want the decriminalization of marijuana (population 1) is greater than the proportion of Torontonians who want the decriminalization of marijuana (population 2).

Next, we need to calculate the test statistic. In this case, we will use the proportion difference test statistic formula:

test statistic (Z) = (p1 - p2) / sqrt(p*(1-p)*(1/n1 + 1/n2))

where:
p1 = proportion of Montrealers who favor decriminalization of marijuana
p2 = proportion of Torontonians who favor decriminalization of marijuana
p = (x1 + x2) / (n1 + n2) (common proportion)
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, we have:
p1 = 90/120 = 0.75
p2 = 90/150 = 0.6
n1 = 120
n2 = 150

Let's calculate p:
p = (90 + 90) / (120 + 150) = 0.125

Now let's calculate the test statistic:
Z = (0.75 - 0.6) / sqrt(0.125*(1-0.125)*(1/120 + 1/150)) = 2.041

The next step is to find the critical value of the test statistic at a 1% level of significance. Since the alternative hypothesis is one-tailed (greater than), we need to find the critical value from the standard normal distribution for a one-tailed test at a significance level of 1%.

Using a standard normal distribution table or software, we can find that the critical value for a one-tailed test at a significance level of 1% is approximately 2.326.

Finally, we compare the test statistic to the critical value. Since the test statistic (2.041) is less than the critical value (2.326), we fail to reject the null hypothesis. This means that there is not enough evidence to conclude that the proportion of Montrealers who want the decriminalization of marijuana is greater than the proportion of Torontonians who want decriminalization.

Therefore, the classical action limit for the appropriate test of hypothesis is 0.