Question

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).

94 | 88 | 81 | 104 | 97 | 111 | 82 | 88 |

The sample mean is *x* ≈ 93.1. 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?

*H*_{0}: *μ* = 85; *H*_{1}:
*μ* ≠ 85; two-tailed *H*_{0}: *μ* =
85; *H*_{1}: *μ* < 85;
left-tailed *H*_{0}:
*μ* > 85; *H*_{1}: *μ* = 85;
right-tailed *H*_{0}: *μ* = 85;
*H*_{1}: *μ* > 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 known *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 unknown *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.

(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 α?
At the (e) State your conclusion in the context of the application. There is sufficient evidence at the 0.05 level to conclude that Gentle Ben's glucose is higher than 85 mg/100 ml. There is insufficient evidence at the 0.05 level to conclude that Gentle Ben's glucose is higher than 85 mg/100 ml. |

Answer #1

a)

0.05 is level of significance

H0: μ = 85; H1: μ > 85; right-tailed

b)

The standard normal, since we assume that x has a normal distribution with known σ.

Test statistic,

z = (xbar - mu)/(sigma/sqrt(n))

z = (93.1 - 85)/(12.5/sqrt(8))

z = 1.83

c)

P-value Approach

P-value = 0.0336

As P-value < 0.05, reject the null hypothesis.

d)

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

e)

There is sufficient evidence at the 0.05 level to conclude that Gentle Ben'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
89
81
104
100
110
82
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...

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).
92
87
80
105
100
110
82
89
The sample mean is x ≈ 93.1. 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...

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). 94 87 80 103 101 111 85 87 The
sample mean is x ≈ 93.5. 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...

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 89 83 104 100 108 82 91
The sample mean is x ≈ 93.5. 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...

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
87
84
105
101
112
86
91
The sample mean is x ≈ 94.6. 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...

1.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).
93
89
80
103
98
109
84
91
The sample mean is x ≈ 93.4. 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...

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