Question

In a representative sample of 1000 adult Americans, only 460 could name at least one justice who is currently serving on the U.S. Supreme Court. Using a significance level of 0.01, carry out a hypothesis test to determine if there is convincing evidence to support the claim that fewer than half of adult Americans can name at least one justice currently serving on the Supreme Court. (For z give the answer to two decimal places. For P give the answer to three decimal places.)z=p=

Answer 1

P=2.326

Explanation:

Raw Score (X):=1000

Population Mean (μ):=460

Standard Deviation (σ): =Sqrt(npq)

Where n=1000, p=460/1000=0.46 and q=1-0.46=0.54

Sqrt(npq)=sqrt(460X0.54)=15.7607

Z = (X - μ) / σ

Z = (1000 - 460) / 15.7607

Z = 34.26244

For p-value 0.01

P(x=0.01) = 2.32635

Hence, P=2.326 t 3 decimal places.