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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). 103 99 110 82 87 The sample mean is x* 92.8. 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 e = 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 Hg: - 85; H, * 85; two-tailed O Hoi H = 85; H,: u> 85; right-talled O Hoi H- 85; H,: H< 85; left-tailed O Hại > 85; H,: = 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 known a. O The Student's t, since we assume that x has a normal distribution with known a. O The standard normal, since we assume that x has a normal distribution with unknown a. O The Student's t, sincen is large with unknown e. Compute thez 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. n-3 -1 1 -2 -2 -1 -2 1 2

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). 103 99 110 82 87 The sample mean is x* 92.8. 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 e = 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 Hg: - 85; H, * 85; two-tailed O Hoi H = 85; H,: u> 85; right-talled O Hoi H- 85; H,: H< 85; left-tailed O Hại > 85; H,: = 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 known a. O The Student's t, since we assume that x has a normal distribution with known a. O The standard normal, since we assume that x has a normal distribution with unknown a. O The Student's t, sincen is large with unknown e. Compute thez 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. n-3 -1 1 -2 -2 -1 -2 1 2

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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### Gentle Ben's Glucose Levels Statistical Analysis #### Study Context Gentle Ben is a Morgan horse at a Colorado dude ranch. Over the past 8 weeks, a veterinarian recorded the following glucose readings (in mg/100 ml): - 95, 86, 89, 103, 99, 110, 82, 87 The sample mean is \( \bar{x} = 92.8 \). Assume that \( x \) is a normally distributed random variable, given that the standard deviation \( \sigma = 12.5 \) is known from past experience. The typical mean glucose level for horses should be \( \mu = 85 \) mg/100 ml. We want to determine if Gentle Ben has a higher average glucose level than 85, using \( \alpha = 0.05 \). #### (a) Level of Significance Identify the null and alternate hypotheses: - \( H_0 : \mu = 85 \); \( H_1 : \mu \neq 85 \); two-tailed - \( H_0 : \mu = 85 \); \( H_1 : \mu > 85 \); right-tailed - \( H_0 : \mu = 85 \); \( H_1 : \mu < 85 \); left-tailed #### (b) Sampling Distribution Selection Choose an appropriate sampling distribution and justify: - Standard normal: \( x \) has a normal distribution and \( \sigma \) is known. - Student’s t: \( x \) has a normal distribution, but \( \sigma \) is unknown. - Student's t: \( n \) is large with unknown \( \sigma \). Calculate the z-value of the sample test statistic and round to two decimal places. #### (c) P-value Estimation Estimate the p-value and round to four decimal places. **Graph Explanation:** The provided graphs illustrate a normal distribution curve with shaded areas representing the tail regions corresponding to the p-value. Each plot shows a curve on a standard normal axis ranging from -3 to 3. #### (d) Hypothesis Test Conclusion Based on your answers: - At \( \alpha = 0.05 \) level, we reject or fail to reject the null hypothesis and determine statistical significance: - Reject \( H_0 \) (data statistically significant) - Fail to reject \( H_
Transcribed Image Text:### Gentle Ben's Glucose Levels Statistical Analysis #### Study Context Gentle Ben is a Morgan horse at a Colorado dude ranch. Over the past 8 weeks, a veterinarian recorded the following glucose readings (in mg/100 ml): - 95, 86, 89, 103, 99, 110, 82, 87 The sample mean is \( \bar{x} = 92.8 \). Assume that \( x \) is a normally distributed random variable, given that the standard deviation \( \sigma = 12.5 \) is known from past experience. The typical mean glucose level for horses should be \( \mu = 85 \) mg/100 ml. We want to determine if Gentle Ben has a higher average glucose level than 85, using \( \alpha = 0.05 \). #### (a) Level of Significance Identify the null and alternate hypotheses: - \( H_0 : \mu = 85 \); \( H_1 : \mu \neq 85 \); two-tailed - \( H_0 : \mu = 85 \); \( H_1 : \mu > 85 \); right-tailed - \( H_0 : \mu = 85 \); \( H_1 : \mu < 85 \); left-tailed #### (b) Sampling Distribution Selection Choose an appropriate sampling distribution and justify: - Standard normal: \( x \) has a normal distribution and \( \sigma \) is known. - Student’s t: \( x \) has a normal distribution, but \( \sigma \) is unknown. - Student's t: \( n \) is large with unknown \( \sigma \). Calculate the z-value of the sample test statistic and round to two decimal places. #### (c) P-value Estimation Estimate the p-value and round to four decimal places. **Graph Explanation:** The provided graphs illustrate a normal distribution curve with shaded areas representing the tail regions corresponding to the p-value. Each plot shows a curve on a standard normal axis ranging from -3 to 3. #### (d) Hypothesis Test Conclusion Based on your answers: - At \( \alpha = 0.05 \) level, we reject or fail to reject the null hypothesis and determine statistical significance: - Reject \( H_0 \) (data statistically significant) - Fail to reject \( H_
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