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 86 84 103 101 108 84 89 The sample mean is x = 93.3. 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 σ = 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 α = 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? 85; H₁ < 85; left-tailed Ho: Ho=85; H₁: 85; two-tailed Ho H 85; H₁: > 85; right-tailed : Ho>85; H₁ = 85; right-tailed (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The standard normal, since we assume that x has a normal distribution with unknown σ. The Student's t, since we assume that x has a normal distribution with known σ. The Student's t, since n is large with unknown σ. The standard normal, since we assume that x has a normal distribution with known σ. 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. -2 -1 0 1 2 -2 -1 0 1 2 2 -1 0 1 2 -2 -1 1 2 3 (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? At the a = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. At the x = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. At the a 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. 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. There is sufficient evidence at the 0.05 level to conclude that the horse's glucose is higher than 85 mg/100 ml. There is insufficient evidence at the 0.05 level to conclude that the horse's glucose is higher than 85 mg/100 ml.

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 86 84 103 101 108 84 89 The sample mean is x = 93.3. 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 σ = 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 α = 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? 85; H₁ < 85; left-tailed Ho: Ho=85; H₁: 85; two-tailed Ho H 85; H₁: > 85; right-tailed : Ho>85; H₁ = 85; right-tailed (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The standard normal, since we assume that x has a normal distribution with unknown σ. The Student's t, since we assume that x has a normal distribution with known σ. The Student's t, since n is large with unknown σ. The standard normal, since we assume that x has a normal distribution with known σ. 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. -2 -1 0 1 2 -2 -1 0 1 2 2 -1 0 1 2 -2 -1 1 2 3 (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? At the a = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. At the x = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. At the a 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. 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. There is sufficient evidence at the 0.05 level to conclude that the horse's glucose is higher than 85 mg/100 ml. There is insufficient evidence at the 0.05 level to conclude that the horse's glucose is higher than 85 mg/100 ml.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter4: Equations Of Linear Functions

Section4.5: Correlation And Causation

Problem 23PFA

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Question

The sample mean is x ~ 93.3. 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 o = 12.5. The mean glucose level for horses should be M = 85 mg/100 ml.+ Do these data indicate that Gentle Ben has an overall average glucose level higher than 85? Use a = 0.05.

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 86 84 103 101 108 84 89
The sample mean is x = 93.3. 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 σ = 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 α = 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?
85; H₁ < 85; left-tailed
Ho:
Ho=85; H₁:
85; two-tailed
Ho H 85; H₁:
> 85; right-tailed
:
Ho>85; H₁ = 85; right-tailed
(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.
The standard normal, since we assume that x has a normal distribution with unknown σ.
The Student's t, since we assume that x has a normal distribution with known σ.
The Student's t, since n is large with unknown σ.
The standard normal, since we assume that x has a normal distribution with known σ.
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.
-2
-1
0
1
2
-2
-1
0
1
2
2
-1
0
1
2
-2
-1
1
2
3
(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?
At the a = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.
At the x = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.
At the a 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.
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.
There is sufficient evidence at the 0.05 level to conclude that the horse's glucose is higher than 85 mg/100 ml.
There is insufficient evidence at the 0.05 level to conclude that the horse's glucose is higher than 85 mg/100 ml.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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