Question

Background: This activity is based on the results of a recent study on the safety of airplane drinking water that was conducted by the U.S. Environmental Protection Agency (EPA). A study found that out of a random sample of 316 airplanes tested, 40 had coliform bacteria in the drinking water drawn from restrooms and kitchens. As a benchmark comparison, in 2003 the EPA found that about 3.5% of the U.S. population have coliform bacteria-infected drinking water. The question of interest is whether, based on the results of this study, we can conclude that drinking water on airplanes is more contaminated than drinking water in general.

Question 1: (Remember write all answer in an MS Word doc and upload)

Let p be the proportion of contaminated drinking water in airplanes. Write down the appropriate null and alternative hypotheses.

Question 2:

Based on the collected data, is it safe to use the z-test for p in this scenario? Explain.

Use the following instructions to conduct the z-test for the population proportion:

Instructions - 2 Options

Option 1: Click on the following link to use the MS Excel hypothesis test template: hypothesis.xls
R | StatCrunch | Minitab | Excel 2007 | TI Calculator

Question 3:

Now that we have established that it is safe to use the Z-test for p for our problem, go ahead and carry out the test. Paste the output below.

Question 4:

What is the test statistic for this test? (Hint: Calculation already done by either technology option.) Interpret this value.

Question 5:

What is the P-Value? Interpret what that means, and draw your conclusions. Assume significance level of 0.05.

Answer 1

Question 1: (Remember write all answer in an MS Word doc and upload)

Let p be the proportion of contaminated drinking water in airplanes. Write down the appropriate null and alternative hypotheses.

The hypothesis being tested is:

H₀: p = 0.035

H_a: p > 0.035

Question 2:

Based on the collected data, is it safe to use the z-test for p in this scenario? Explain.

z-test because the One proportion Z-test is used to compare an observed proportion to a theoretical one, when there are only two categories.

Question 3:

The output is:

Observed	Hypothesized
0.1266	0.035	p (as decimal)
40/316	11/316	p (as fraction)
40.	11.06	X
316	316	n
	0.0103	std. error
	8.86	z
	0.00E+00	p-value (one-tailed, upper)

Question 4:

What is the test statistic for this test? (

The test statistic is 8.86

Question 5:

What is the P-Value?

The P-value is 0.0000.

Since the p-value (0.0000) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that drinking water on airplanes is more contaminated than drinking water in general.