Question

Potassium helps the human body prevent muscle cramping. Researchers sampled 52 random professional wrestlers. The average potassium level was 3.8 millimoles per liter and the standard deviation was 1.4 millimoles per liter. Construct and interpret a 95% confidence interval to estimate the mean potassium level in the population. A. The 95% confidence interval is (3.7460, 3.8541). We are 95% confident that the true population mean potassium level for professional wrestlers will be between 3.7460 millimoles per liter and 3.8541 millimoles per liter.
B. The 95% confidence interval is (3.4102, 4.1898). Ninety-five percent of all samples of this size will yield a confidence interval of (3.4102, 4.1898).
C. The 95% confidence interval is (3.4102, 4.1898). There is a 95% chance that a randomly selected wrestler is one of the wrestlers whose potassium level lies between 3.4102 millimoles per liter and 4.1898 millimoles per liter.
D. The 95% confidence interval is (3.4102, 4.1898). We are 95% confident that the true population mean potassium level for professional wrestlers will be between 3.4102 millimoles per liter and 4.1898 millimoles per liter.
E. The 95% confidence interval is (3.7460, 3.8541). Ninety-five percent of all the samples of this size will yield a confidence interval of (3.7460, 3.8541).

Answer 1

Answer:

D. The 95% confidence interval is (3.4102, 4.1898). We are 95% confident that the true population mean potassium level for professional wrestlers will be between 3.4102 millimoles per liter and 4.1898 millimoles per liter.

Step-by-step explanation:

Hello!

The variable if interest is X: potassium level of a professional wrestler  (mmol/L)

A sample of n= 52 professional wrestlers was taken and a sample mean of X[bar]= 3.8 mmol/L and a sample standard deviation of S= 1.4 mmol/L

You have to estimate the population average potassium level using a 95% confidence interval. Assuming that the variable has a normal distribution, and since the population variance is unknown, I'll use a student t to construct the interval:

[X[bar] ± $t_{n-1;1-\alpha /2}$* $\frac{S}{\sqrt{n} }$]

$t_{n-1;1-\alpha /2}= t_{51;0.975}= 2.008$

[3.8±2.008*$\frac{1.4}{\sqrt{52} }$]

[3.4102; 4.1898]

With a 95% confidence level you'd expect that the interval [3.4102; 4.1898]mmol/L will contain the average potassium level of professional wrestlers.

I hope this helps!