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).94 87 83 104 98 108 8489The sample mean is x = 93.4. 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 u = 85 mg/100 ml.t 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: H = 85; H,: u + 85; two-tailedO Ho: H = 85; H: µ > 85; right-tailedO Ho: H > 85; H,: µ = 85; right-tailedO Ho: H = 85; H,: µ < 85; left-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 o.O The standard normal, since we assume that x has a normal distribution with known o.O The Student's t, since n is large with unknown o.O The standard normal, since we assume that x has a normal distribution with unknown o.What is the 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-3-2-13O-3-2-113-2-11o-3-2-1(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 hypothesis and conclude the data are statistically 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 Gentle Ben's glucose is higher than 85 mg/100 ml.O There is insufficient evidence at the 0.05 level to conclude that Gentle Ben's glucose is higher than 85 mg/100 ml.

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Gentie 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 mi). 94 7 3 104 100 4 9 The sample mean is93.4. 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 e- 12.5. The mean glucose level for horses should be 85 mg/100 ml. Do these data indicate that Gentle Ben has an overal average glucese level higher than 85? Use a-0.os. (a) What is the level of significance? State the null and alternate hypotheses. W you use a left-taled, right-taled, or two-tailed test? OH -85, H 5, two tailed O M:-85, H, 85; right-tailed O Mg > 85; H,- 85; right-taled O Mi - 85; M H «5, leh-tailed (a) what sampling distribution wil you use Explain the rationale for yoour choice of sampling distribution. O The Student's t, since we assume that x has a normal distribution with known e. O The standard normal, since we assume that x has a normal distribution with known e. O The Student's t, since n is larpe with unknown a. O The standard normal, since we assume that x has a nermal distribution with unknown e. what is the value of the sample test statistic? (kound your answer to two decimal places.) (O Find (er estimate) the Pvalue. (Round your answer to four decimal places. O Sketch the sampling distribution and show the area corresponding te the Pvalue. . -2 -2 1 o-3 1 2 3 -2 -2 -1 (4) Based en your answers in parts (a) te (e), will you reject or fall to reject the nul hypothesis? Are the data statistically significant at level a OAt the a- 0.OS level, we reject the null hypothesis and conclude the data are statistically significant. O At the a-0.OS 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 nul hypothesis and conclude the data are statistically significant. O Mthe a0.05 level, we fal to reject the nul ypothesis and conclude the data are not statistically significant. (e) State your concusion in the context of the application O There is sufficient evidence at the 0.05 level to conclude that Gentle Ben's glucose is higher than 85 mg/100 ml. O There is insufficient evidence at the 0.05 level to condude that Gentle Ben's glucose is Nigher than 85 mg/100 mi. .