The 2006 Statistical Abstract of the United States reports on a survey that asked a national sample

kolutastmr

kolutastmr

Answered question

2022-07-06

The 2006 Statistical Abstract of the United States reports on a survey that asked a national sample of 80,000 American households about pet ownership. Suppose that one-third of all American households own a pet cat. The survey discovered that 31.6% of all the households sampled owned a pet cat. What is the z-score of this?

From the standard deviation formula for a sample proportion, I found that standard deviation is 0.0016. From there, I plugged that into the z-score formula, and got (0.316-0.333)/0.0016 = -10.625. However, a z-score that high baffles me and I cannot imagine getting a z-score that high. Where did I go wrong?

Answer & Explanation

Keely Fernandez

Keely Fernandez

Beginner2022-07-07Added 14 answers

Your calculations are correct. The extreme z score you get indicates that if the percentage of households was really 33%, then this sample is highly unrepresentative. The conclusion you would therefore draw is that the actual percentage must in reality be lower than 33%, assuming that the sample is random and representative of the population as a whole.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?