A random sample of size 15 is taken from a population assumed to be normal, with...

A random sample of size 15 is taken from a population assumed to be normal, with sample mean = 1.2 and sample variance = 0.6. Calculate a 95 percent confidence interval for population mean.

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Expert Solution

Point estimate = sample mean = = 1.2

sample standard deviation = s = 0.7746

sample size = n = 15

Degrees of freedom = df = n - 1 = 15 - 1 = 14

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t_/2,df = t_0.025,14 = 2.145

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

= 2.145 * (0.7746 / $\sqrt$ 15)

= 0.4

The 95% confidence interval estimate of the population mean is,

- E < < + E

1.2 - 0.4 < < 1.2 + 0.4

0.8 < < 1.6

A 95% confidence interval for population mean.(0.8 , 1.6)

orchestra answered 1 year ago

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