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] ± [tex]t_{n-1;1-\alpha /2}[/tex]* [tex]\frac{S}{\sqrt{n} }[/tex]]
[tex]t_{n-1;1-\alpha /2}= t_{51;0.975}= 2.008[/tex]
[3.8±2.008*[tex]\frac{1.4}{\sqrt{52} }[/tex]]
[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!
