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Inference for the Population Proportion: For this same data set, in column C2 the students were asked to state if the right distance from home

  1. Inference for the Population Proportion:

For this same data set, in column C2 the students were asked to state "if the right distance from home is the reason they joined this school or not." Answers were "Yes" or "No." In Minitab 1 represent the answer yes and 0 represent the answer no.

We will now investigate the proportion of students who choose this school because it is close to home. Find the mean of variable C2 "Distance." This will be p, the proportion of our population. Normally, we don't know p. But in this case, we do to illustrate a Confidence Interval for p.

  • What is the proportion of our population (p)?
  • We will now take a random sample of size n=200 from column C2 (our population of size N=1,800). To get a random sample, open Calc>Random Data> Sample from Columns in Minitab. Sample 200 rows from Column C2. Store the sample in a new column. Don't click on the sample with replacement box.
  • Construct a 95% Confidence Interval for the population proportion using our sample data from the previous part. Put your 95% CI. Did your Confidence Interval include p?
  • Use the Confidence Interval from the previous part to answer the following: The majority (50% or more) of students attend this school because it is close to home? Explain.
  1. In a random sample of 300 college students, 60 said they prefer late classes. Put a 95% Confidence Interval for the proportion of all college students who prefer late classes. Interpret the Confidence Interval.
  2. A sociologist wishes to estimate the percentage of U.S. citizens living in poverty. What sample size should be obtained if she wishes the estimate to be within 2% points (the error) with 99% Confidence if she uses the year 2000 estimate of 11.8% poverty obtained from the census?

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