2. [-/4.08 Points] DETAILS BBUNDERSTAT12 8.1.020.MI. MY NOTES ASK YOUR TEACHER 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 80 107 97 110 84 91 The sample mean is x = 93.8. 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 o = 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 a = 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: M = 85; H1: M > 85; right-tailed O Ho: M = 85; H1: M # 85; two-tailed O Ho: M = 85; H1: M 85; H1: M = 85; right-tailed (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The standard normal, since we assume that x has a normal distribution with unknown o. The Student's t, since n is large with unknown o. The Student's t, since we assume that x has a normal distribution with known 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 3 0-3 -2 -1 0 3 0-3 -2 -1 0 2 O - 3 -2 2 (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 a = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. O At the a = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. O At the a = 0.05 level, we fail to reject the null hyp atistically significant. O At the a = 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. There is insufficient evidence at the 0.05 level to conclude that the horse's glucose is higher than 85 mg/100 ml