Gentle Ben is a Morgan horse at a Colorado dude ranch. Over the past 8 weeks, a veterinarian took the following glucose readings from this horse (in mg/100 ml).

959082107971088491

The sample mean isx94.3. Letxbe a random variable representing glucose readings taken from Gentle Ben. We may assume thatxhas a normal distribution, and we know from past experience that= 12.5.The mean glucose level for horses should be= 85 mg/100 ml.Do these data indicate that Gentle Ben has an overall average glucose level higher than 85? Use= 0.05.

(a)

What is the level of significance?

State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?

H₀:= 85;H₁:> 85; right-tailed

H₀:> 85;H₁:= 85; right-tailed

H₀:= 85;H₁:< 85; left-tailed

H₀:= 85;H₁:85; two-tailed

(b)

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

The standard normal, since we assume thatxhas a normal distribution with unknown.

The Student'st, sincenis large with unknown.

The Student'st, since we assume thatxhas a normal distribution with known.

The standard normal, since we assume thatxhas a normal distribution with known.

Compute thezvalue of the sample test statistic. (Round your answer to two decimal places.)

(c)

Find (or estimate) theP-value. (Round your answer to four decimal places.)

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

A plot of the normal probability curve has a horizontal axis with values from3 to 3. 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 between3 and2.09 is shaded.

A plot of the normal probability curve has a horizontal axis with values from3 to 3. 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 2.09 and 3 is shaded.

A plot of the normal probability curve has a horizontal axis with values from3 to 3. 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 between3 and2.09 as well as the area under the curve between 2.09 and 3 are both shaded.

A plot of the normal probability curve has a horizontal axis with values from3 to 3. 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 between3 and 2.09 is 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= 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.

At the= 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.

At the= 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

At the= 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e)

State your conclusion in the context of the application.

There is sufficient evidence at the 0.05 level to conclude that the horse's glucose is higher than 85 mg/100 ml.

There is insufficient evidence at the 0.05 level to conclude that the horse's glucose is higher than 85 mg/100 ml.