Unfortunately, arsenic occurs naturally in some ground water†. Amean arsenic level of μ = 8.0 parts per billion (ppb) isconsidered safe for agricultural use. A well in Texas is used towater cotton crops. This well is tested on a regular basis forarsenic. A random sample of 36 tests gave a sample mean ofx = 6.8 ppb arsenic, with s = 2.9 ppb. Does thisinformation indicate that the mean level of arsenic in this well isless 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 ppbH₀:μ = 8 ppb; H₁: μ < 8ppb    H₀: μ = 8ppb; H₁: μ ≠ 8ppbH₀: μ = 8 ppb;H₁: μ > 8ppbH₀: μ > 8 ppb;H₁: μ = 8 ppb

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

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

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


(c) Estimate the P-value.

P-value > 0.2500.100 < P-value <0.250    0.050 < P-value <0.1000.010 < P-value < 0.050P-value <0.010

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