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)