Based on information from Harper's Index, 37 out of a random sample of 100 adult Americans who did not attend college believe in extraterrestrials. However, out of a random sample of 100 Americans who did attend college, 41 claim that they believe in extraterrestrials. At the 1% significance level, does this indicate that the proportion of people who attended college who believe in extraterrestrials is higher than the proportion who did not attend college?

Try a z-test for proportions (two samples).

Here is one such formula:

z = (p1 - p2)/(√pq)[√(1/n1 + 1/n2)]

p1 = 41/100 = .41
p2 = 37/100 = .37
p = (x1 + x2)/(n1 + n2) = (41 + 37)/(100 + 100) = 78/200 = .39
q = 1 - p = 1 - .39 = .61

Substitute into the formula:

z = (.41 - .37)/[√(.39)(.61)][√(1/100 + 1/100) = .58 (rounded)

Testing at the 1% significance level for a one-tailed test, you will fail to reject the null. You cannot conclude a difference.

Double check these calculations.
I hope this helps.

To determine if the proportion of people who attended college who believe in extraterrestrials is higher than the proportion who did not attend college, we need to conduct a hypothesis test.

Let's define the following hypotheses:

Null hypothesis (H0): The proportion of people who attended college who believe in extraterrestrials is equal to the proportion who did not attend college.
Alternative hypothesis (H1): The proportion of people who attended college who believe in extraterrestrials is higher than the proportion who did not attend college.

To determine if we reject or fail to reject the null hypothesis, we will compare the test statistic with the critical value based on the 1% significance level.

Now, let's calculate the test statistic and critical value using the given information:

For the sample of adults who did not attend college:
- Sample size (n1) = 100
- Number of "believers" (x1) = 37

For the sample of adults who attended college:
- Sample size (n2) = 100
- Number of "believers" (x2) = 41

First, calculate the sample proportions:

- Sample proportion for those who did not attend college (p̂1) = x1/n1 = 37/100 = 0.37
- Sample proportion for those who attended college (p̂2) = x2/n2 = 41/100 = 0.41

Next, calculate the pooled sample proportion:

- Pooled sample proportion (p̂) = (x1 + x2) / (n1 + n2) = (37 + 41) / (100 + 100) = 0.39

Now, we can calculate the test statistic, z:

- z = (p̂1 - p̂2) / √(p̂(1-p̂)(1/n1 + 1/n2))
- z = (0.37 - 0.41) / √(0.39 * (1 - 0.39) * (1/100 + 1/100))
- z ≈ -0.04 / √(0.39 * 0.61 * 0.02)
- z ≈ -0.04 / √(0.04758)
- z ≈ -0.04 / 0.2182
- z ≈ -0.1833

Using a standard normal distribution table or calculator, we find that the critical value for a one-tailed z-test with a 1% significance level is approximately 2.326.

Since the test statistic (z = -0.1833) is not greater 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 people who attended college who believe in extraterrestrials is higher than the proportion who did not attend college at the 1% significance level.

To determine if the proportion of people who attended college and believe in extraterrestrials is significantly higher than those who did not attend college, we will conduct a hypothesis test using the 1% significance level.

Firstly, let's establish our null and alternative hypotheses:

Null Hypothesis (H0): The proportion of people who attended college and believe in extraterrestrials is not higher than the proportion who did not attend college.
Alternative Hypothesis (H1): The proportion of people who attended college and believe in extraterrestrials is higher than the proportion who did not attend college.

To proceed with the hypothesis test, we will use a z-test for comparing proportions.

We can calculate the test statistic using the following formula:

z = (p1 - p2) / √(p (1-p) (1/n1 + 1/n2))

Where:
- p1 is the proportion of college attendees who believe in extraterrestrials
- p2 is the proportion of non-college attendees who believe in extraterrestrials
- p is the pooled proportion ((x1 + x2) / (n1 + n2))
- n1 is the sample size of college attendees
- n2 is the sample size of non-college attendees

Now, let's calculate the test statistic and check if it falls within the critical region.

p1 = 41/100 = 0.41
p2 = 37/100 = 0.37
p = (41 + 37) / (100 + 100) = 0.39
n1 = 100
n2 = 100

z = (0.41 - 0.37) / √(0.39 * (1 - 0.39) * (1/100 + 1/100))
z = 0.04 / √(0.39 * 0.61 * 0.02)
z ≈ 0.04 / 0.0785
z ≈ 0.51

Next, we need to determine the critical value for a one-tailed test at the 1% significance level. Looking up the z-table, the critical z-value for a one-tailed test at the 1% significance level is approximately 2.33.

Since our calculated test statistic of 0.51 is smaller than 2.33, it falls within the non-critical region. Therefore, we fail to reject the null hypothesis.

In conclusion, at the 1% significance level, there is not enough evidence to suggest that the proportion of people who attended college and believe in extraterrestrials is higher than the proportion who did not attend college.