Question

Q3. A study is run to estimate the mean total cholesterol level in children 2-6 years of age. A sample of 13 participants is selected and their total cholesterol levels are measured as follows.

170 185 225 240 196 175 180 194 147 223 240 220 210

a) Assume the mean total cholesterol level is 190 in children 2-6 years of age at national level. Test whether the cholesterol level in this sample is significantly different from national level.

b) Generate a 95% confidence interval for the true mean total cholesterol levels in children 2-6 years of age

Answer #1

a)

Below are the null and alternative Hypothesis,

Null Hypothesis, H0: μ = 190

Alternative Hypothesis, Ha: μ ≠ 190

Rejection Region

This is two tailed test, for α = 0.05 and df = 12

Critical value of t are -2.179 and 2.179.

Hence reject H0 if t < -2.179 or t > 2.179

Test statistic,

t = (xbar - mu)/(s/sqrt(n))

t = (200.3846 - 190)/(28.6692/sqrt(13))

t = 1.306

P-value Approach

P-value = 0.216

As P-value >= 0.05, fail to reject null hypothesis.

b)

sample mean, xbar = 200.3846

sample standard deviation, s = 28.6692

sample size, n = 13

degrees of freedom, df = n - 1 = 12

Given CI level is 95%, hence α = 1 - 0.95 = 0.05

α/2 = 0.05/2 = 0.025, tc = t(α/2, df) = 2.179

ME = tc * s/sqrt(n)

ME = 2.179 * 28.6692/sqrt(13)

ME = 17.326

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))

CI = (200.3846 - 2.179 * 28.6692/sqrt(13) , 200.3846 + 2.179 *
28.6692/sqrt(13))

CI = (183.06 , 217.71)

A study is run to estimate the mean total cholesterol level in
children 2 to 6 years of age. A sample of 9 participants is
selected and their total cholesterol levels are measured as
follows.
Subject
Chol
A
185
B
225
C
240
D
196
E
175
F
180
G
194
H
147
I
223
A. Calculate the deviation score for each observation
B. Calculate the sum of squares
C. Calculate the standard deviation

Data set 1: Blood Cholesterol (in mg/dL) Levels of 32
Participants at a Community Health Fair
180 185
200 198
211 203 199
195
210 190
210 200 180
197 188
198
187 240
189 168 185
220 188
200
188 259 195
221 200
196 194
196
For the previous data sets, do the following:
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6. It is known that the mean cholesterol level for all Americans
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Deviation is 15)

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125 135 160 146 135 140 154 170 110 140
Compute Quartiles 1 and 3
Q1=135 and Q2= 152
Q1=152 and Q2=135
Q1=125 and Q2=160
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A cholesterol level over 200 is considered high. The
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They randomly select ten people with high cholesterol to
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Pat.#
Before
After
1
195
125
To the left is 2 datasets measured for
a sample of 107 patients with the high cholesterol level before and
after taking medication. Obtain the following for both sets:
2
208
164
3
254
152
1- the mean, mode and median
4
226
144
5
290
212
2- the variance and standard
deviation
6
239
171
7
216
164
3- First, second and third
quartiles
8
286
200
9
243
190
10
217
130...

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X
XXn
NOTE: The standard error is another name for the standard
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X
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Is there an association between patient BMI and cholesterol
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Patient ID
Drug
Sex
Age
Height
BMI
Weight
Cholesterol
1
B
F
22
67.13
21.52787
138
197
2
B
M
22
63
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115
181
3
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F
22
72
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190
190
4
A
M
22
69
16.98068
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