Question

The Basic Steps to Calculating a Hypothesis Test

You want to start by determining whether you are interested in working with a mean or a proportion. Then identify each of the parts listed below.

1. In order to use the formulas for a hypothesis test we first need to confirm that the sample size requirements for the central limit theorem are satisfied. See the notes for more information. If the sample size is not met acknowledge that you need to proceed with caution.
2. Identify the null and alternative hypotheses. The null hypothesis will be listed first. When working with a proportion the hypothesis will include that symbol for the population proportion, p. When working with a mean the hypothesis will include that symbol for the population mean, µ.
3. Calculate the appropriate test statistic. When working with proportions you will calculate a z-statistic. When working with means you will calculate a t-statistic.
4. Compare your test statistic to the appropriate distribution to find the p-value.
5. Conclude the test in context of the problem.

For each of the four problems below provide all of the steps listed above. Complete all of the work by hand and show your work. You may use the applications listed in the notes to check your work.

2. Unfortunately, arsenic occurs naturally in some ground water (Reference: Union Carbide Technical Report K/UR-1). A mean arsenic level of 8.0 parts per billion (ppb) is considered safe for agricultural use. A well in Texas is used to water cotton crops. This well is tested on a regular basis for arsenic. A random sample of 35 tests gave a mean of 7.2 ppb arsenic, with standard deviation of 1.9 ppb. Does this information indicate that the mean level of arsenic in this well is less than 8ppb? Use α = 0.01.

Answer 1

2.

We will test for the mean.

Since n > 30, we can use t-test as population std. deviation is not known.

H0: = 8

H1: < 8

t = (-)/s/

= (7.2-8)/1.9/

= -2.491

df = n-1

= 34

p-value = 0.009 < 0.01 i.e. we can reject H0 and hence we can say that the mean level of arsenic in this well is less than 8ppb.

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