Question

15 patients have been tested for Uric Acid level, their average value of 10 mg/dL with a standard deviation of 2.2 mg/dL. the normal uric acid value is 5 mg/dL.

Is the value of uric acid is significantly more than the normal expected value at 99% confidence?

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 5
Alternative Hypothesis, Ha: μ > 5

Rejection Region
This is right tailed test, for α = 0.01 and df = 14
Critical value of t is 2.624.
Hence reject H0 if t > 2.624

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (10 - 5)/(2.2/sqrt(15))
t = 8.802

P-value Approach
P-value = 0
As P-value < 0.01, reject the null hypothesis.