MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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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_
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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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