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 | 81 | 106 | 97 | 110 | 83 | 89 |
The sample mean is x ≈ 93.0. 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?
H0: μ = 85; H1: μ ≠ 85; two-tailedH0: μ = 85; H1: μ < 85; left-tailed H0: μ = 85; H1: μ > 85; right-tailedH0: μ > 85; H1: 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.
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(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 α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
The statistic software output for this problem is:
(a)
level of significance = 0.05
Two tailed test
H0 : μ = 85
HA : μ ≠ 85
(b)
The standard normal, since we assume that x has a normal distribution with known σ
z = 1.81
(c)
P-value = 0.0703
Graph II
(d)
At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
Gentle Ben is a Morgan horse at a Colorado dude ranch. Over the past 8 weeks,...
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
87
82
106
99
108
84
90
The sample mean is x ≈ 93.6. 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...
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 82 103 101 109 82 90 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...
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 81 104 97 111 85 88 The sample mean is93.5. 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 μ-85 mg/100 ml. t Do these data indicate that Gentle...
Gentle Ben is a Morgan horse at aColorado dude ranch. Over the past 8 weeks, a veterinarian took the following glucose readings from this horse (in mg/100 ml) 92 87 82 107 97 110 86 88 The sample mean is x-93.6. Let x be a rando variable representing glucose readings taken from Gentle Ben. we may assume that x has a normal dstribution, and we know from past experience that σ·125. The mean glucose level for horses should be μ-85...
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 87 83 107 101 110 83 89 The sample mean is x ≈ 94.1. 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...
Bill Alther is a zoologist who studies Anna's hummingbird (Calypte anna).† Suppose that in a remote part of the Grand Canyon, a random sample of six of these birds was caught, weighed, and released. The weights (in grams) were as follows. 3.7 2.9 3.8 4.2 4.8 3.1 The sample mean is x = 3.75 grams. Let x be a random variable representing weights of hummingbirds in this part of the Grand Canyon. We assume that x has a normal distribution...
The price to earnings ratio (P/E) is an important tool in
financial work. A random sample of 14 large U.S. banks (J. P.
Morgan, Bank of America, and others) gave the following P/E
ratios.†
24
16
22
14
12
13
17
22
15
19
23
13
11
18
The sample mean is
x ≈ 17.1.
Generally speaking, a low P/E ratio indicates a "value" or
bargain stock. Suppose a recent copy of a magazine indicated that
the P/E ratio of...
Total blood volume (in ml) per body weight (in kg) is important
in medical research. For healthy adults, the red blood cell volume
mean is about μ = 28 ml/kg.† Red blood cell volume that is
too low or too high can indicate a medical problem. Suppose that
Roger has had seven blood tests, and the red blood cell volumes
were as follows.
34
26
42
35
28
37
31
The sample mean is x ≈ 33.3 ml/kg. Let x...
Total blood volume (in ml) per body weight (in kg) is important in medical research. For healthy adults, the red blood cell volume mean is about μ = 28 ml/kg.† Red blood cell volume that is too low or too high can indicate a medical problem. Suppose that Roger has had seven blood tests, and the red blood cell volumes were as follows. 33 26 39 36 29 37 30 The sample mean is x ≈ 32.9 ml/kg. Let x...
The average annual miles driven per vehicle in the United States
is 11.1 thousand miles, with σ ≈ 600 miles. Suppose that a
random sample of 31 vehicles owned by residents of Chicago showed
that the average mileage driven last year was 10.8 thousand miles.
Does this indicate that the average miles driven per vehicle in
Chicago is different from (higher or lower than) the national
average? Use a 0.05 level of significance.
What are we testing in this problem?...