Agriculture: Ground Water Unfortunately, arsenic occurs naturally in some ground water (Reference: Union Carbide Technical Report K/UR-1). A mean arsenic level of µ = 8.0 parts per billion (ppb) is considered safe for agricul- tural 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 37 tests gave a sample mean of x = 7.2 ppb arsenic, with s = 1.9 ppb. Does this information indicate that the mean level of arsenic in this well is less than 8 ppb? Use a = 0.01.
(a) What is the level of significance? State the null and alternate hypotheses.
(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. Compute the value of the sample test statistic.
(c) Find (or estimate) the P-value. Sketch the sampling distribution and show the area corresponding to the P-value.
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level a?
(e) Interpret your conclusion in the context of the application. Note: For degrees of freedom d.f. not given in the Student’s t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value by a small amount and therefore produce a slightly more “conser-vative” answer.
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