Gentle Ben is a Morgan horse at a Colorado dude ranch. Over the past 8 weeks, a veterinarian tock the following glucose readings from this horse (in ma/100 m). 94 89 81 106 98 110 6 91 The sample mean isx94.4. Let x be a random variable representing glucose readings taken from Gentie Ben. We may assume that x has a normal distribution, and we know from past experience that a- 12.5. The mean glucose level for horses should be - 85 mg/100 mi. De these data indicate that Gentle Ben has an overal average glucose level higher than 8S? Use a- 0.05. (a) What is the level of significance? State the null and alternate hypocheses. Will you use a left-taled, righe-talled, or bwo-taled best *Hai- 85; M.: > 85; right-taled O Hgi 85, M -85, right-tailed O Hg: -85; 85, left-taled Hg: 85; H 85; two-taled (b) What sampling distribution will yocu use? Explain the rationale for your cholce of samping distribution. O The standard normal, since we assume that x has a normal distribution with unknown e. O The Studene's, since a is large with unknown a. l O The Student's t, since we assume that x has a normal distribution with known e. 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 ansiwer to two decimal places.) 213 (c) Find for estimate) the Pvalue. (Round your answer to four desimal places.) Sketch the sampling distribution and show the area coresponding to the Pvalue. -3 -2 -1 3 -2 -1 1 -3 -2 -1 -2 -1 2 2 Based on your answers in parts (a) to (), will you reject or fail to reject the nul hypothesis? Are the data statistically significant at level a? At the a-0.05 level, we reject the nul hypothesis and conclude the data are statistically significant. A the a-0.05 level, we reject the nut hypothesis and conclude the data are not szatistically signircane At the a0.05 level, we fall to reject the null hypothesis and concude the data are statistically significant. At the a-0.05 level, we fall to reject the null hypothesis and conciude the data are not statistically significant. (e) State your conciusion in the context of the application. * There is suffcient evidence at the 0.05 level to condude that Gente Ben's gluccse is higher than 85 mg/100 ml. O There is insufficent evidence at the 0.05 level to conclude that Gentle Ben's glucose is higher than 85 mg/100 ml.