Question

show all work for question 15a) only

15. A rare congenital disease, Everley's syndrome, generally causes a reduction in concentration of blood sodium. A doctor has measured the blood sodium concentration for 16 patients with the disease. Assuming that the concentrations are nor- mally distributed, a 95% confidence interval for the average blood sodium concentration was found to be [108.607, 121.393] (in mmol/l). (a) (2 points) Find the sample mean and the sample standard deviation . (b) (2 points) Construct a 90% confidence interval for the standard deviation of the blood sodium concentration. (c) (1 point) Interpret your answer from part (b).

Answer 1

Answer:

C=95%, n=16

Given confidence interval is

(108.607 , 121.393)

Formula to get sample mean is

108.607 + 121.393 T =

$\bar x$ =115

sample mean = 115

Now calculate margin of error

108.607 – 121.393 ME=

Margin of Error= 6.393

Now formula is

Margin of error = tc * ( s / $\sqrt{n}$ )

Where tc is the t critical value for c=95% with df=n-1= 15

Using t table we get

tc= 2.131

Now put all values in formula

6.393 = 2.131 * (s/V16)

S= 12

Sample standard deviation= 12