Question

Suppose that 44% of all Americans approve of the job the President is doing. The most recent Gallup poll consisted of a random sample of 1,400 American adults.

a. What is the mean of the sampling distribution?

b. What is the standard deviation of the sampling distribution (don't forget to justify the use of the formula)?

c. Describe the normal approximation for this sampling distribution (don't forget to justify this) You can simply write as N (mean, standard deviation)

d. What is the probability that the Gallup poll will come up with a proportion within three percentage points of the true 44%

Answer 1

a) Mean = n × p, n is 1400 and p is 0.44, using what you know 0.44 (p)× 1400 (n) = 616

b) SD = √ (n×p×q) n 1400 p is 0.44 and q = 1-p=1-0.44=0.56