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). 95 88 82 103 100 108 84 87   The sample mean is x ≈ 93.4. 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. (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: μ = 85; H1: μ > 85; right-tailedH0: μ > 85; H1: μ = 85; right-tailed    H0: μ = 85; H1: μ ≠ 85; two-tailedH0: μ = 85; H1: μ < 85; left-tailed (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The Student's t, since n is large with unknown σ.The standard normal, since we assume that x has a normal distribution with unknown σ.    The standard normal, since we assume that x has a normal distribution with known σ.The Student's 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.)

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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).

95 88 82 103 100 108 84 87  

The sample mean is x ≈ 93.4. 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.

(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: μ = 85; H1: μ > 85; right-tailedH0: μ > 85; H1: μ = 85; right-tailed    H0: μ = 85; H1: μ ≠ 85; two-tailedH0: μ = 85; H1: μ < 85; left-tailed

(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.
The Student's t, since n is large with unknown σ.The standard normal, since we assume that x has a normal distribution with unknown σ.    The standard normal, since we assume that x has a normal distribution with known σ.The Student's 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.)

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