Question

In: Statistics and Probability

Forma a 95% confidence interval on the mean pouring temperature for iron castings if a sample...

Forma a 95% confidence interval on the mean pouring temperature for iron castings if a sample of size 25 yielded a mean of 2560 and a standard deviation (s) of 20.

Expert Solution

Solution :

Given that,

= 2560

s = 20

n = 25

Degrees of freedom = df = n - 1 = 25 - 1 = 24

a ) At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t_/2,df = t_0.025,24 =2.064

Margin of error = E = t_/2,df * (s / $\sqrt$ n)

= 2.064* (20 / $\sqrt$ 25) = 8.256

The 95% confidence interval is,

- E < < + E

2560 - 8.256< < 2560 + 8.256

2551.744 < < 2568.256

(2551.744 , 2568.256)

orchestra answered 1 year ago

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