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

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