A 2010 survey asked 827 randomly sampled registered voters In California \"Do yo

Question

A 2010 survey asked 827 randomly sampled registered voters In California "Do you support or do you oppose drilling for oil and natural gas off the Coast of California? Or do you not know enough to say?" Below is the distribution of responses, separated based on whether or not the respondent graduated from college. Suppose that we wanted to test the hypothesis {H_0: p_college grad - p_not college grad = 0, H_A: p_college grad - p_not college grad notequalto 0} regarding the proportion of college graduates vs. non-college graduates who support off-shore drilling. What are the relevant sample proportions for the hypothesis test? Select one: a. p_college grad = 0.352, p_not college grad = 0.324. b. p_college grad = 0.463, p_not college grad = 0.324 c. p_college grad = 0.352, p_not college grad = 0.339 d. p_college grad = 0.267, p_not college grad = 0.339 e.p_college grad = 0.267, p_not college grad = 0.337 Continuing with the question above, what would the Z-score be for the hypothesis test? Continuing with the previous question, what would the p-value be for for the hypothesis test?

Explanation / Answer

Relative sample proportions

^pcollege graduates = 154/ 438 = 0.3516

^pnot college graduates = 132/389 = 0.3393

Option C is correct.

Test Statistic :

Pooled estimate p* = (154 + 132)/ ( 438 +389) = 0.346

Standard Error of estimate

Z = ( ^pcollege graduates - ^pnot college graduates)/ sqrt [p* (1-p*) (1/ n1 + 1/n2 )]

Z = (0.352 -0.339)/ sqrt [ 0.346 * 0.654 * ( 1/438 + 1/389)]

Z = 0.013 / 0.03314 = 0.3923

p - value for hyothesis test = 0.695

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