Question

A survey of a random sample of U.S. adults by The Pew Research Center for the People and the Press conducted in early January 2010 recorded each participant’s highest level of education completed and whether they knew that responding to the Census was required by law. Of the 973 participants who had some college or less, 27.9% (271/973) knew that responding to the Census was required by law. Of the 526 participants who had a college degree or more, 37.1% (195/526) knew that responding to the Census was required by law. Is there an association between a person’s level of education and her/his Census awareness?

1. Use an appropriate randomization-based applet to find a p-value. Round your answer to two decimal places.
2. Based on this p-value, how much evidence do you have against the null hypothesis?
A. We have no evidence against the null hypothesis.
B. We have very weak evidence against the null hypothesis.
C. We have very strong evidence against the null hypothesis.

Answer 1

Multiple sub-parts. Solving first four

Proportion for who had degress or more, p1 = 271/973 = 0.28

Proportion for who had degress or less, p2 = 195 /526 = 0.37

Now, we use hypothesis testing proportion difference:

p = (271 +195) / (973+526) = 466/1499 = 0.31

SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] }

= V0.31 * 0.69 * 0.003

= 0.025

z = (p1 - p2) / SE

= (0.28- 0.37)/0.025 = -3.6

For this z, p-value is 0.0001

Hence we can reject null hypothesis by 99.99% surety

So, C. We have very strong evidence against the null hypothesis.

The appropriate standardized statistic in the context of the study is z = -3.6

The p-value and standardized statistic both lead you to the same conclusion. A. True