Question

For each of the following problems, 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.

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1) The Gallup Poll asked a random sample of 1785 adults whether they attended church or synagogue during the past week. Of the respondents, 44% said they did attend. Suppose that 40% of the adult population actually went to church or synagogue last week. Let be the proportion of people in the sample who attended church or synagogue. Find the probability of obtaining a sample of 1785 adults in which 44% or more say they attended church or synagogue last week. Do you have any doubts about the result of this poll?

2) 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

Question 1:

The population of interest is the true adult population actually went to church or synagogue last week.

The sample is 1785 adult population actually went to church or synagogue last week.

n.p = 0.40*1785 10

n.(1 - p) = (1 - 0.40)*1785 10

p̂ ~ N(0.40, 0.0116)

p̂ = 0.44

p = 0.40

n = 1785

The test statistic, z = (p̂ - p)/√p(1-p)/n = (0.44 - 0.40)/√0.40(1-0.40)/1785 = 3.45

P(z > 3.45) = 0.0003

Since the probability is less than 0.05, we have doubts about the result of this poll.

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