entle 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).

92 | 90 | 82 | 106 | 101 | 111 | 84 | 89 |

The sample mean is x ≈ 94.4. Let *x* be a random variable representing glucose readings taken from Gentle Ben. We may assume that *x* has a normal distribution, and we know from past experience that σ = 12.5. The mean glucose level for horses should be μ = 85 mg/100 ml.† Do these data indicate that Gentle Ben has an overall average glucose level higher than 85? Use α = 0.05.

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

*H*

_{0}: μ = 85;

*H*

_{1}: μ < 85; left-tailed

*H*

_{0}: μ = 85;

*H*

_{1}: μ ≠ 85; two-tailed

*H*

_{0}: μ = 85;

*H*

_{1}: μ > 85; right-tailed

*H*

_{0}: μ > 85;

*H*

_{1}: μ = 85; right-tailed

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

*x*has a normal distribution with known σ.

*t*, since

*n*is large with unknown σ.

*x*has a normal distribution with unknown σ.

*t*, since we assume that

*x*has a normal distribution with known σ.

Compute the

*z*value of the sample test statistic. (Round your answer to two decimal places.)

(c) Find (or estimate) the

*P*-value. (Round your answer to four decimal places.)

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 α?

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

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