Question

A Gallup poll reports that 26% of Americans believe big business is the biggest threat to the nation. (Gallup.com website article, in U.S., Fear of Big Government at Near-Record Level, December 12, 2011). Let’s assume this value represents the true population proportion. Suppose we randomly sample 200 Americans and ask them their beliefs about big business. We will assume the population proportion, p = .26, sample size n = 200

A) What are the values of np, and n(1-p)?

B) Find the mean and the standard error of the sampling distribution of sample proportions. Use the assumed population proportion p = .26 and sample size n = 200

C) Now suppose you survey a random sample of 80 Americans and the sample proportion of p = .40 is observed.

(i) What are the values of n and p?

(ii) Find the mean and the standard error of the sampling distribution of sample proportions from samples of the size 80. Compare them to part (B)

(iii) Draw the normal curve and label Mp and p on the x-axis.

(iv) Find the Z-score of p?

(v) Shade the area under the normal curve where the sample proportions in the sampling distribution are greater than or equal to p.              

(vi) Find the percent of sample proportions that are greater than or equal to p.

(vii) Based on the sampling distribution, is it unusual to have a random sample of 80 Americans in which 40% or more believe big business is the greatest threat to the nation?

Please answer all the sub-questions (Thank you very much)

Answer 1

A)
np = 200 * 0.26 = 52
n(1-p) = 200*0.74 = 148

B)
mu(p) = 0.26
se(p) = sqrt(0.26 * 0.74/200) = 0.0310

C)
i)
n = 80, p = 0.4

ii)
mu(pcap) = 0.4
se(pcap) = sqrt(0.26*0.74/80) = 0.0490

iv)
z-score = (0.4 - 0.26)/0.0490 = 2.86

vi)
P(z > 2.86) = 0.0021

vii) Yes it is unusual.

iii) & v)

o3m 0360.309 0358040 0.113 0.162 0.211 0.358 0.407