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 31 tests gave a sample mean of x = 7.0 ppb arsenic, with s = 2.2 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 Student's t, since the sample size is large and σ is known.

The standard normal, since the sample size is large and σ is known.

The standard normal, since the sample size is large and σ is unknown.

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.)


(c) Estimate the P-value.

P-value > 0.250

0.100 < P-value < 0.250    

0.050 < P-value < 0.100

0.010 < P-value < 0.050

P-value < 0.010

Sketch the sampling distribution and show the area corresponding to the P-value.

Answer 1