Question

QUESTION 11

1. A sample of 5000 college students were asked if they support the legalization of marijuana and if they support the legalization of abortion (results are presented below). Using StatCrunch (you don't need to open a dataset from the textbook), calculate the confidence interval for percentage of people more likely to support legalizing marijuana than legalizing abortion. List the lower confidence interval below ____________- round to 2 decimal places.

   	Support the Legalization of Abortion
   Support the Legalization of Marijuana	Yes	No	Totals
   Yes	2000	2000	4000
   No	200	800	1000
   Totals	2200	2800	5000

1. List the upper confidence interval from question _______ - round to 2 decimal places.

2. Now perform a hypothesis test on the data presented in question 11. You are testing the null hypothesis that there is no difference in the proportion of those that believe in legalizing marijuana and the proportion of those that believe in legalizing abortion. Your alpha or p-level is set at .05. List the z statistic below - round to 2 decimal places.____________

What is the p-value in the test you just ran? _________ Round to 2 decimal places.

Assuming that the p-level or alpha level was set at .05, based on the p-value you calculated, would you reject or fail to reject the null hypothesis that there is no difference in the proportion of people who support the legalization of marijuana and the proportion that support the legalization of abortion?

		Reject
		Fail to reject

Answer 1

Solution:-

The confidence interval for percentage of people more likely to support legalizing marijuana than legalizing abortion is C.I = (0.34 , 0.38).

C.I = 0.36 + 0.019032

C.I = (0.341 , 0.379)

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: P₁ = P₂
Alternative hypothesis: P₁ P₂

Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the proportion from population 1 is too big or if it is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a two-proportion z-test.

Analyze sample data. Using sample data, we calculate the pooled sample proportion (p) and the standard error (SE). Using those measures, we compute the z-score test statistic (z).

p = (p₁ * n₁ + p₂ * n₂) / (n₁ + n₂)
p = 0.62
SE = sqrt{ p * ( 1 - p ) * [ (1/n₁) + (1/n₂) ] }
SE = 0.00971
z = (p₁ - p₂) / SE

z = 37.08

where p₁ is the sample proportion in sample 1, where p₂ is the sample proportion in sample 2, n₁ is the size of sample 1, and n₂ is the size of sample 2.

Since we have a two-tailed test, the P-value is the probability that the z-score is less than -37.08 or greater than 37.08.

Thus, the P-value = 0.00.

Interpret results. Since the P-value (0.00) is less than the significance level (0.05), we reject the null hypothesis.

Reject H₀, we reject the null hypothesis that there is no difference in the proportion of people who support the legalization of marijuana and the proportion that support the legalization of abortion.