Question

Based on the information from Harper's Index, 37 out of 100 adult Americans who did not attend college believe in extraterrestrials. However, out of a random sample of 100 adults who did attend college, 47 claim that they believe in extraterrestrials. Does this indicate the proportion of adult americans that attended college and believe in extraterrestrials is higher than the proportion that did not attend college? (a=0.01)

Answer 1

Answer: Yes, this indicate the  proportion of adult americans that attended college and believe in extraterrestrials is higher than the proportion that did not attend college.

Step-by-step explanation:

Since we have given that

Hypothesis:

$H_0:p_1=p_2\\\\H_a:p_1>p_2$

n₁ = 100

x₁ = 37

So, $p_1=\dfrac{x_1}{n_1}=\dfrac{37}{100}=0.37$

n₂ = 100

x₂ =47

So, $p_2=\dfrac{47}{100}=0.47$

At 0.01 level of significance, z = 2.33

So, test statistic value would be

$z=\dfrac{p_1-p_2}{\sqrt{\dfrac{p_1(1-p_1)}{n_1}+\dfrac{p_2(1-p_2)}{n_2}}}\\\\z=\dfrac{0.37-0.47}{\sqrt{\dfrac{0.37\times 0.63}{100}+\dfrac{0.47\times 0.53}{100}}}\\\\z=-1.44$

Since, 2.33>-1.44

Hence, we will reject the null hypothesis.

Therefore, Yes, this indicate the  proportion of adult americans that attended college and believe in extraterrestrials is higher than the proportion that did not attend college