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 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 88 84 105 101 110 84 87
The sample mean is x≈ 93.8. 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 o = 12.5. The mean glucose level for horses should be μ 85 mg/100 ml. 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?
OH₁: μ = 85; H₁: μ< 85; left-tailed
O Ho: >85; H₁: μ = 85; right-tailed
O Ho: μ = 85; H₁: μ #85; two-tailed
OH₁: μ = 85; H₁: μ>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 unknown o.
O The standard normal, since we assume that x has a normal distribution with known σ.
O The Student's t, since we assume that x has a normal distribution with known o.
O The Student's t, since n is large with unknown o.
Compute the z 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.
4
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Transcribed Image Text: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 88 84 105 101 110 84 87 The sample mean is x≈ 93.8. 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 o = 12.5. The mean glucose level for horses should be μ 85 mg/100 ml. 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? OH₁: μ = 85; H₁: μ< 85; left-tailed O Ho: >85; H₁: μ = 85; right-tailed O Ho: μ = 85; H₁: μ #85; two-tailed OH₁: μ = 85; H₁: μ>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 unknown o. O The standard normal, since we assume that x has a normal distribution with known σ. O The Student's t, since we assume that x has a normal distribution with known o. O The Student's t, since n is large with unknown o. Compute the z 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. 4
Sketch the sampling distribution and snow the area corresponding to the P-value.
0-3
0-3
-2 -1 0
-2 -1 0
1 2
3
1 2 3
i
0-3
-2
-1
0
1
2
3
(i)
4
(e) State your conclusion in the context of the application.
O There is sufficient evidence at the 0.05 level to conclude that the horse's glucose is higher than 85 mg/100 ml.
O There is insufficient evidence at the 0.05 level to conclude that the horse's glucose is higher than 85 mg/100 ml.
0-3
-2
(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.
-1
0
1
2
3
i
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Transcribed Image Text:Sketch the sampling distribution and snow the area corresponding to the P-value. 0-3 0-3 -2 -1 0 -2 -1 0 1 2 3 1 2 3 i 0-3 -2 -1 0 1 2 3 (i) 4 (e) State your conclusion in the context of the application. O There is sufficient evidence at the 0.05 level to conclude that the horse's glucose is higher than 85 mg/100 ml. O There is insufficient evidence at the 0.05 level to conclude that the horse's glucose is higher than 85 mg/100 ml. 0-3 -2 (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. -1 0 1 2 3 i
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