Question

5. (a) Suppose a national polling agency conducted 1000 polls in a year, using proper random sampling, and reported a 98% confidence interval for each poll. About how many of those confidence intervals would we expect to NOT cover the true population value?

(b) In each part, identify whether the sample is a simple random sample, stratified random sample,
cluster sample, or systematic sample. Explain why in each case using a complete sentence.

1) A class of 200 students is seated in 10 rows of 20 students per row. Two students from each row are
selected at random.

2) Alaska Airlines randomly chooses all passengers on one of its roughly 15 weekday, non-stop flights
between Seattle and Boston to fill out a survey on meal satisfaction.

3) In a factory producing tablets, every 50th tablet is inspected.

Answer 1

5)

a)

The proportion of confidence intervals reported that would not cover the true proportion value is 100-98 = 2%.

Required number of confidence intervals = 0.02(1000) = 20

b)

1)

In this case, 2 students are selected from each stratum. So this is the case of stratified sampling.

2)

Alaska Airlines chose all passengers on one of its roughly 15 weekday, non-stop flights i.e. all the members of a cluster.

So this is the case of cluster sampling.

3)

Since every 50th tablet is inspected, so this is the case of systematic sampling.