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 99 112 86 B9 The sample mean is Q :2 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 a = 12.5. The mean glucose level for horses should be [4 = 85 Wig/100 m|.1' Do these data indicate that Gentle Ben has an overall average glucose level higher than 85? Use at = 0.05. (a) What is the level of signicance? : State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? 0 H0111 = 85; H1: p. 85; H1: [.1 = 85; right-tailed 0 H0111 = 85; H1: p. t 85; two-tailed O Ho: [1 = 85; H1: [4 > 85; right-tailed (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. 0 The standard normal, since we assume that x has a normal distribution with known 0'. O The Student's 1', since we assume that x has a normal distribution with known a. O The Student's t, since n is large with unknown 0. O The standard normal, since we assume that x has a normal distribution with unknown 0. Compute the 2 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. 0-3 -2 -1 0 l 2 3 O-3 -2 -1 0 1 2 3 0-3 -Z 1 0 1 2 3 -3 -2 _1 o 1 2 3 0 Q (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically signicant at level a? 0 At the a = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. 0 At the at : 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. 0 At the a = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. 0 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. 0 There is sufficient evidence at the 0.05 level to conclude that the horse's glucose is higher than 85 mg/100 ml. 0 There is insufficient evidence at the 0.05 level to conclude that the horse's glucose is higher than 85 mg/100 ml