Question

a). A car company is investigating whether or not to issue a recall of a model of car that has shown signs of having a defective emissions system. If not preliminary study is made to estimate p, the probability the part is defective, how large a sample should the investigator use to obtain a 98% confidence level that the point estimate for p will be in error either way by less than 0.03?

b). Aerodynamic engineers want to know the mean shear force on the wings of an FC5000 fighter jet as the jet comes out of a 3,000 vertical dive. A random sample of FX5000 jets flown by Air Force fighter pilots was used for 37 test flights. The sample standard deviation of wing shear force was 948 foot pounds. The engineers want to have 95% confidence that the sample mean is within 250 foot pounds of the population mean. How many more test flights should be made?

Answer 1

Solution,

a) Given that,

=  1 - = 0.5

margin of error = E = 0.03

At 98% confidence level

= 1 - 98%

= 1 - 0.98 =0.02

/2 = 0.01

Z/2 = Z_0.01 = 2.33

sample size = n = (Z _{/ 2} / E )² * * (1 - )

= (2.33 / 0.03)² * 0.5 * 0.5

= 1508.02

sample size = n = 1509

b) Given that,

sample standard deviation = s = 948

sample size = n = 37

Degrees of freedom = df = n - 1 = 37 - 1 = 36

At 95% confidence level

= 1 - 95%

=1 - 0.95 =0.05

/2 = 0.025

t/2,df = t_0.025,36 = 2.028

margin of error = E = 250

sample size = n = [t/2,df* s / E]²

n = [2.028 * 948 / 250 ]²

n = 59.13

Sample size = n = 60