Question

A research team wanted to compare the difference between serum uric acid levels in patients with and without Down syndrome. A sample of 12 individuals with Down syndrome yielded a mean of 4.5 mg/100 ml with standard deviation 1 mg/100 ml while a sample of 15 individuals without Down syndrome yielded a mean of 3.4 mg/100 ml with standard deviation 1.2 mg/100 ml. Let those with Down syndrome be group 1 and those without be group 2. Note: When doing calculations with the means and standard deviations, just use the main number. For example: “4.5 mg/100 ml” --> just use 4.5

A. What are the sample statistics (p̂₁ and p̂₂ or ȳ₁ and ȳ₂)? Please calculate/write their values and calculate their difference (p̂₁-p̂₂ or ȳ₁-ȳ₂).

B. Construct a 95% confidence interval for the true average difference in serum uric acid levels overall between those with Down syndrome and those without. Use t* = 2.06 if solving by hand. Provide the interval in (left endpoint, right endpoint) format.

C. Interpret the confidence interval in the context of the study.

Answer 1

Solution :

Given

n1 = 12 sample size of down syndrome

n 2 = 15 sample size of without down syndrome.

A) sample statistics are

sample mean of down syndrome

and. . Sample mean of without down syndrome.

s1 = 1 sample standard deviations of down syndrome

s2 = 1.2. Sample standard deviations of without down syndrome

The difference of sample statistics is

B ) The 95% confidence interval for the difference in mean is

Where

. Given

)

( 0.2092795, 1.9907205)

( 0.2093, 1.991)

This is the 95% confidence interval of difference in mean.

C ) Interpretation of confidence interval

If we take 100 different random sample then 95 times of the difference between serum uric acid with down syndrome and without down syndrome lies between this interval.