Unfortunately, arsenic occurs naturally in some ground water. A mean arsenic level of= 8.0parts 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 of36tests gave a sample mean ofx=6.8ppb arsenic, withs=2.9ppb. Does this information indicate that the mean level of arsenic in this well is less than 8 ppb? Use= 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.

What is the value of the sample test statistic?

(c) Estimate theP-value.

Sketch the sampling distribution and show the area corresponding to theP-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?

(e) Interpret your conclusion in the context of the application.