Question

In a 2018 national study, only 31% of Americans know their neighbors. Suppose we

survey a random, independent sample of 250 Americans.

a. Does this sample meet the size requirement for the CLT?

b.True or False: We can assume the distribution is normal with N(p, SE).

c. Calculate the standard error. Round your answer to 3 decimal places.

d. What is the probability that of the 250 Americans surveyed, 35% or more know their neighbors? Sketch a shaded curve and use StatCrunch to calculate your answer.

Answer 1

P( Americans know their neighbors) = 0.31 = p

Sample size, n= 250

a) Yes, this sample meet the size requirement for the CLT (n > 30)

b)  We can assume the distribution is normal with N(p, SE).- true

c) Stanadard Error, SE= =   = 0.029

d) P( p > 0.35 ) = P( > )

= P( z > 1.72 )

= 1- P( z < 1.72)

= 1- 0.95728

=0.04272