Question

Efficiency experts study the processes used to manufacture items in order to make them as efficient as possible. One of the steps used to manufacture a metal clamp involves the drilling of 3 holes. In a sample of 74 clamps the mean to complete this step was 53.6 seconds. Assume that the population standard deviation is 6 seconds. What is the lower bound of the 98% confidence interval. Round your answer to one decimal place

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 53.6

Population standard deviation =    = 6

Sample size = n =74

At 98% confidence level the z is ,

= 1 - 98% = 1 - 0.98 = 0.02

= 0.02

Z= Z_0.02 = 2.05 ( Using z table    )

Margin of error = E = Z * ( /n)

= 2.05 * ( 6 /  74 )

E= 1.43
At 98% confidence interval estimate of the population mean
is,

- E
53.6 - 1.43
52..2

lower bound =52.2