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:
[tex]H_0:p_1=p_2\\\\H_a:p_1>p_2[/tex]
n₁ = 100
x₁ = 37
So, [tex]p_1=\dfrac{x_1}{n_1}=\dfrac{37}{100}=0.37[/tex]
n₂ = 100
x₂ =47
So, [tex]p_2=\dfrac{47}{100}=0.47[/tex]
At 0.01 level of significance, z = 2.33
So, test statistic value would be
[tex]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[/tex]
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
