Question

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

Answer 1

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