Question

μ = the population mean speed (mph) of trucks in a specific region in Greeley, CO. A random sample of 8 trucks has a sample mean speed of 25.4 mph and the population standard deviation is known to be 3.2 mph. Find the 95% confidence interval for μ.

a.) (23.18, 27.62)

b.) (12.68, 18.70)

c.) (24.08, 30.05)

d.) (18.80, 24.56)

What is the required sample size if you want an error margin for the 95% confidence interval for μ to equal 0.8 mph?

a.) 62

b.) 60

c.) 58

d.) 64

Answer 1

Solution :

Given that,

Point estimate = sample mean =     = 25.4

Population standard deviation =    =3.2

Sample size n =8

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96   ( Using z table )

Margin of error = E =   Z/2    * ( /n)
= 1.96 * (3.2 / 8 )

= 2.22
At 95% confidence interval estimate of the population mean
is,

- E < < + E

25.4 - 2.22 <   <25.4 + 2.22

23.18 <   < 27.62
( 23.18 , 27.62 )

(B)

Solution

standard deviation ==3.2

Margin of error = E = 0.8

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96

sample size = n = [Z/2* / E] 2

n = ( 1.96* 3.2/0.8 )2

n =61.4656 ( rounded)

Sample size = n =62