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 80 107 99 108 86 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 ? = 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? b. (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The Student's t, since we assume that x has a normal distribution with known ?.The Student's t, since n is large with unknown ?. The standard normal, since we assume that x has a normal distribution with unknown ?.The standard normal, since we assume that x has a normal distribution with known ?. Compute the z value of the sample test statistic. (Round your answer to two decimal places.) 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.

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ISBN:9781119256830

Author:Amos Gilat

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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).

107

108

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 ? = 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?

(b)

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

The Student's t, since we assume that x has a normal distribution with known ?.The Student's t, since n is large with unknown ?. The standard normal, since we assume that x has a normal distribution with unknown ?.The standard normal, since we assume that x has a normal distribution with known ?.

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

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.

C. A random sample of n₁ = 16 communities in western Kansas gave the following information for people under 25 years of age.

x₁: Rate of hay fever per 1000 population for people under 25

97	92	122	127	94	123	112	93
125	95	125	117	97	122	127	88

A random sample of n₂ = 14 regions in western Kansas gave the following information for people over 50 years old.

x₂: Rate of hay fever per 1000 population for people over 50

94	109	100	99	110	88	110
79	115	100	89	114	85	96

(i) Use a calculator to calculate x₁, s₁, x₂, and s₂. (Round your answers to four decimal places.)

x₁	=
s₁	=
x₂	=
s₂	=

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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