Question

Unfortunately, arsenic occurs naturally in some ground water†. A mean arsenic level of μ = 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 41 tests gave a sample mean of x = 6.9 ppb arsenic, with s = 2.7 ppb. Does this information indicate that the mean level of arsenic in this well is less than 8 ppb? Use α = 0.01.

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: μ > 8 ppb; H₁: μ = 8 ppb H₀: μ < 8 ppb; H₁: μ = 8 ppb     H₀: μ = 8 ppb; H₁: μ ≠ 8 ppb H₀: μ = 8 ppb; H₁: μ < 8 ppb H₀: μ = 8 ppb; H₁: μ > 8 ppb

(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

The standard normal, since the sample size is large and σ is unknown. The standard normal, since the sample size is large and σ is known.     The Student's t, since the sample size is large and σ is known. The Student's t, since the sample size is large and σ is unknown.

What is the value of the sample test statistic? (Round your answer to three decimal places.)

Answer 1

The statistical software output for this problem is:

Hence,

a) Level of significance = 0.01

Hypotheses: H₀: μ = 8 ppb; H₁: μ < 8 ppb

b) The Student's t, since the sample size is large and σ is unknown.

Test statistic = -2.609