In: Statistics and Probability
A random sample of 24 chemical solutions is obtained, and their strengths are measured. The sample mean is 5437.2 and the sample standard deviation is 376.9.
(a) Construct a two-sided 98% confidence interval for the average strength.
(b) Estimate how many additional chemical solutions need to be measured in order to obtain a twosided 98% confidence interval for the average strength within a margin of error that is 150
Solution :
Given that,
Point estimate = sample mean = = 5437.2
sample standard deviation = s = 376.9
sample size = n = 24
Degrees of freedom = df = n - 1 = 24 - 1 = 23
a) At 98% confidence level
= 1 - 98%
=1 - 0.98 =0.02
/2
= 0.01
t/2,df
= t0.01,24 = 2.500
Margin of error = E = t/2,df * (s /n)
= 2.500 * (376.9 / 24 )
Margin of error = E = 192.34
The 98% confidence interval estimate of the population mean is,
± E
= 5437.2 ± 192.34
= ( 5244.86, 5629.54 )
b) margin of error = E = 150
sample size = n = [t/2,df* s / E]2
n = [2.500 * 376.9 / 150 ]2
n = 39.45
Sample size = n = 40