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 82 103 97 108 84 91 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

108

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?

H
₀: ? = 85;H
₁: ? > 85; right-tailed

H
₀: ? > 85;H
₁: ? = 85; right-tailed

H
₀: ? = 85;H
₁: ? ≠ 85; two-tailed

H
₀: ? = 85;H
₁: ? < 85;="">

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

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

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

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

The Student'st, 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.)

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 ??

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

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

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

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.

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.

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 88 82 103 97 108 84 91 The sample...

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