Question

For each of the following problem, you must:

a) Define the population and the parameter of interest;

b) Identify the given and unknown information and write them in correct notations,

c) Verify if the sampling distribution is approximately normal by checking the conditions np > 5 and nq > 5),

d) Compute the probability.

e) Interpret the answer.

1) Suppose 47% of all adult women think they do not get enough time to themselves. An opinion poll interviews 1025 randomly selected women and records the sample proportion who feels they don’t get enough time for themselves. If this sample were repeated numerous times, in what range would the middle 95% of the sample results fall? What is the probability the poll gets a sample in which fewer than 45% say they do not get enough time for themselves?

Answer 1

Answer:

Given,

sample n = 1025

p = 0.47

np = 1025*0.47

= 481.75

nq = 1025*(1-0.47)

= 543.25

Here the sampling distribution is approximately normal because np > 5 and nq > 5.

= 0.47

= sqrt(p(1 - p)/n)

substitute values

= sqrt(0.47*0.53/1025)

= 0.0156

P(p^ < 0.45) = P(z < (0.45 - 0.47)/0.0156)

= P(z < -1.28)

= 0.1002726 [since from z table]

= 0.1003