Question

Question 1 1 pts An experimenter is interested in determining the mean thickness in millimeters of the cortex of the sea urchin egg. The mean thickness for n = 10 sea urchin eggs is found to be 4.26 mm with a standard deviation of 0.9991 mm. Construct the 95% confidence interval for the true mean thickness of sea urchin eggs. (Adapted from Mendenhall, Beaver, & Beaver, 15e, page 440) 2.6371 < p <5.0829 3.9572 < p < 5.3628 3.5453< p < 4.9747 1.9864 < t < 7.0136

Answer 1

Solution :

Given that,

$\bar x$ = 4.26

s =0.9991

n =10

Degrees of freedom = df = n - 1 = 10 - 1 = 9

At 95% confidence level the t is ,

$\alpha$ = 1 - 95% = 1 - 0.95 = 0.05

  $\alpha$/ 2= 0.05 / 2 = 0.025

t$\alpha$ /2,df = t0.025,9 = 2.262 ( using student t table)

Margin of error = E = t$\alpha$/2,df * (s /$\sqrt$n)

=2.262 * ( 0.9991/ $\sqrt$ 10)

= 0.7147

The 95% confidence interval estimate of the population mean is,

$\bar x$ - E < $\mu$ < $\bar x$ + E

4.26 -0.7147 < $\mu$ < 4.26+ 0.7147

3.5453 < $\mu$ < 4.9747