Question

In: Statistics and Probability

Efficiency experts study the processes used to manufacture items in order to make them as efficient...

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 three holes. In a sample of 70 clamps, the mean time to complete this step was

57.8 seconds. Assume that the population standard deviation is =σ 10

seconds. Round the critical value to no less than three decimal places

Construct a 90% confidence interval for the mean time needed to complete this step.

Expert Solution

Solution :

Given that,

Point estimate = sample mean = = 57.8

Population standard deviation = = 10
Sample size = n =70

At 90% confidence level the z is

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

Z/2 = Z0.05 = 1.645 ( Using z table )

Margin of error = E = Z/2 * ( / $\sqrt$ n)

= 1.645 * (10 / $\sqrt$ 70 )

= 1.97
At 90% confidence interval mean
is,

- E < < + E

57.8 - 1.97 < < 57.8 + 1.97

55.83 < < 59.77

orchestra answered 1 year ago

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