Question

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).

91

90

81

107

99

111

84

91

The sample mean is x ≈ 94.3. 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?

A: H₀: μ = 85; H₁: μ < 85; left-tailed

B: H₀: μ = 85; H₁: μ > 85; right-tailed    

C: H₀: μ > 85; H₁: μ = 85; right-tailed

D: H₀: μ = 85; H₁: μ ≠ 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 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.    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.

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?

A: At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.

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

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

D: At the α = 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.

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

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

Answer 1