Question

Unfortunately, arsenic occurs naturally in some ground water (Reference: Union Carbide Technical Report). A mean arsenic level of 8 parts per billion (ppb) is considered safe for agricultural use. A well in Texas is used to water cotton crop. This well is tested on a regular basis for arsenic. A random sample of 37 tests gave a sample mean of 7.2. Given that the standard deviation of arsenic level is 1.9, does this information indicate that the mean level of arsenic in this well is less than 8 ppb? Use 1% level of significance.

a. Identify the underlying distribution.

b. State the null hypothesis.

c. State the alternative hypothesis.

d. Circle one: One Tail Test Two Tail Test.

e. State the critical value for the hypothesis test.

f. Illustrate graphically the rejection region.

g. Compute the test statistic.

Answer 1

Claim: The mean level of arsenic in this well is less than 8 ppb.

a)

Here population standard deviation is known so we have to use z-test statistic.

The normal distribution.

b)

The null hypothesis is

c)

The alternative hypothesis is

d)

One Tail Test

e)

Level of significance = 0.01

Critical value = 2.32

( From z table)

f)

The rejection region: Test statistic z > critical value.

g)

Test statistic is

Sample size = n = 37

Sample mean = = 7.2

Population standard deviation = = 1.9