Question

During a period of 11 years 1392 of the people selected for grand jury duty were sampled, and 37% of them were immigrants. Use the sample data to construct a 99% confidence interval estimate of the proportion of grand jury members who were immigrants. Given that among the people eligible for jury duty, 52.4% of them were immigrants, does it appear the the jury selection process was somehow biased against immigrants?

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Answer 1

Here we want to find confidence interval for population proportion.

Let' write given information.

n = sample size = 1392

x = n * p = 1392 * 0.524 = 729.408 = 729

Let's use minitab :Using minitab.

The command for one sample proportion z interval in minitab is

Stat>>>Basic statistics>>>1-proportion...

Then click on summarized data

number of events = x = 729

Number of trials = n = 1392

then click on option

Level of confidence= 0.99

so put "Confidence level " = 99.0

Alternative = not equal

then click on "Use test and interval based on normal approximation"

Then click on OK and again click on OK

So we get the following output

From the above output the 99% confidence interval is (0.489, 0.558)

The correct option is

"Yes the confidence interval does not include the true percentage of immigrants."