Question

In: Statistics and Probability

A sample of size n = 16 is made from a normal distribution with mean μ....

A sample of size n = 16 is made from a normal distribution with mean μ. It
turns out that the sample mean is x = 23 and the sample standard deviation is s = 6.
Construct a 90% confidence interval for μ.

Expert Solution

Given that,

= 23

s =6

n = 16

Degrees of freedom = df = n - 1 =16 - 1 = 15

At 90% confidence level the t is ,

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

t /2,df = t0.05,15 =1.753 ( using student t table)

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

= 1.753 * (6 / $\sqrt$ 16) = 2.6295

The 90% confidence interval estimate of the population mean is,

- E < < + E

23- 2.6295< < 23+ 2.6295

20.3705 < < 25.6295

( 20.3705, 25.6295)

orchestra answered 1 year ago

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