Answer Happy

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 82 103 99 110 86 89 The sample mean is x 93.8. Let x be a random variable representing glucose readings taken from Gentle Ben. We may assume that. 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? O Ho: μ = 85; H₁: >85; right-tailed Ho: M = 85; H₁: μ< 85; left-tailed O Ho: μ>85; H₁: μ = 85; right-tailed Ho: M = 85; H₁: μ = 85; two-tailed
(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The Student's t, since we assume that x has a normal distribution with known σ. O The standard normal, since we assume that x has a normal distribution with unknown σ. O The Student's t, since n is large with unknown σ. O The standard normal, since we assume that x has a normal distribution with known o. 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. O-3 -2 -1 0 1 2 O- 2 1 0 1 2 3 0-3 -2 -1 0 1 2 3 O-3 -2 -1 0 1 2 3 Ⓡ
(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 a? O At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. O At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. O At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. O 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. O There is sufficient evidence at the 0.05 level to conclude that the horse's glucose is higher than 85 mg/100 ml. O There is insufficient evidence at the 0.05 level to conclude that the horse's glucose is higher than 85 mg/100 ml.