Question

 

As part of a study of natural variation in blood chemistry, serum potassium concentrations were measured in 84 randomly selected healthy women. The sample mean concentration was 4.36 mEq/l, and the sample standard deviation was 0.42 mEq/l.

(a) Find the lower bound for the 95% confidence interval for the true serum potassium concentrate in healthy women.

(b) Find the upper bound for the 95% confidence interval for the true serum potassium concentrate in healthy women.

(c) Interpret your confidence interval found in (a,b) in terms of the problem.

(d) Does your interval support the claim that normal serum potassium concentrations are above 2.3? (e) If we were to build a 99% confidence interval instead, would it widen or narrow?

Answer 1

Let denotes the true serum potassium concentrate in healthy women.

a) The lower bound for the 95% confidence interval for the true serum potassium concentrate in healthy women is 4.27

b) The upper bound for the 95% confidence interval for the true serum potassium concentrate in healthy women is 4.45

c) Interpretation : Out of 100 samples drawn, sample mean will lie between (4.27, 4.45) for 95 samples.

d) Since lower bound of the confidence interval > 2.3, so at 95% level of confidence or at 5% level of significance, we can conclude that normal serum potassium concentrations are above 2.3.

e) At 99% level of confidence,

Since critical value at 99% level of confidence > critical value at 95% level of confidence, so we can conclude that the confidence interval will be wider.