Question

According to a Gallup survey conducted in July 2011, 20% of Americans favor reducing the U.S. budget deficit by using spending cuts only, with no tax increases. An economics professor believes that fewer college students would favor deficit reduction through spending cuts only. The professor surveys 500 college students and finds that 75 of them favor reducing the deficit using only spending cuts. What is the test statistic?

A. Z=-2.80
B. Z=2.80
C. Z=-3.13
D. Z=3.13

Answer 1

Option C is correct.

The test statistic for this question is -3.13

Explanation:

To compute the z-test statistic, the formula is given as

z = (x - μ₀)/σₓ

x = p = sample proportion of the 500 college students sampled, that favor reducing the deficit using only spending cuts with no tax increase = (75/500) = 0.15

μ₀ = p₀ = the proportion to be compared against, that is, the proportion of Americans that favor reducing the U.S. budget deficit by using spending cuts only, with no tax increases = 20% = 0.20

σₓ = standard error of the sample proportion = √[p(1-p)/n]

p = 0.15

n = Sample size = 500

σₓ = √[0.15×0.85/500] = 0.01597

z = (0.15 - 0.20) ÷ 0.01597

z = -3.13

Hope this Helps!!!