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 97 112 84 87 The sample...

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

112

The sample mean is x ≈ 93.0. Letx be a random variable representing glucose readings taken from Gentle Ben. We may assume thatx has a normal distribution, and we know from past experience that ? = 12.5. The mean glucose level for horses should be ? = 85 mg/100 ml.† Do these data indicate that Gentle Ben has an overall average glucose level higher than 85? Use ? = 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?

A-H
₀: ? = 85;H
₁: ? < 85;="">

B-H
₀: ? = 85;H
₁: ? > 85; right-tailed

C-H
₀: ? > 85;H
₁: ? = 85; right-tailed

D-H
₀: ? = 85;H
₁: ? ≠ 85; two-tailed

(b)What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

A-The standard normal, since we assume thatx has a normal distribution with unknown ?.

B-The Student'st, since we assume thatx has a normal distribution with known ?.

C-The Student'st, sincen is large with unknown ?.

D-The standard normal, since we assume thatx has a normal distribution with known ?.

Compute thez value of the sample test statistic. (Round your answer to two decimal places.)

=___

(c)Find (or estimate) theP-value. (Round your answer to four decimal places.)

=__

Sketch the sampling distribution and show the area corresponding to theP-value.

(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 ? = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.

B-At the ? = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.

C-At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

D-At the ? = 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.

A-There is sufficient evidence at the 0.05 level to conclude that the horse's glucose is higher than 85 mg/100 ml.

B-There is insufficient evidence at the 0.05 level to conclude that the horse's glucose is higher than 85 mg/100 ml.

Jun 09, 2022

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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 86 84 103 97 112 84 87 The sample...

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