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 of31tests gave a sample mean ofx=7.1ppb arsenic, withs=2.0ppb. Does this information indicate that the mean level of arsenic in this well is less than8 ppb?Use= 0.01.

(a)

What is the level of significance?

State the null and alternate hypotheses.

H₀:< 8 ppb;H₁:= 8 ppb

H₀:= 8 ppb;H₁:8 ppb

H₀:> 8 ppb;H₁:= 8 ppb

H₀:= 8 ppb;H₁:< 8 ppb

H₀:= 8 ppb;H₁:> 8 ppb

(b)

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

The Student'st, since the sample size is large andis unknown.

The Student'st, since the sample size is large andis known.

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

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

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

(c)

Estimate theP-value.

P-value > 0.100

0.050 <P-value < 0.100

0.010 <P-value < 0.050

0.005 <P-value < 0.010

P-value < 0.005

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

A plot of the Student's t-probability curve has a horizontal axis with values from4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between4 and2.51 is shaded.

A plot of the Student's t-probability curve has a horizontal axis with values from4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between 2.51 and 4 is shaded.

A plot of the Student's t-probability curve has a horizontal axis with values from4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between2.51 and 4 is shaded.

A plot of the Student's t-probability curve has a horizontal axis with values from4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between4 and2.51 as well as the area under the curve between 2.51 and 4 are both shaded.

(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?

At the= 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.

At the= 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.

At the= 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

At the= 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e)

Interpret your conclusion in the context of the application.

There is sufficient evidence at the 0.01 level to conclude that the mean level of arsenic in the well is less than8 ppb.

There is insufficient evidence at the 0.01 level to conclude that the mean level of arsenic in the well is less than8 ppb.