Salaries of 32 college graduates who took a statistics course in college have a mean of...

Salaries of 32 college graduates who took a statistics course in college have a mean of $64,300. Assume a standard deviation of $16,200, construct a 95% confidence interval for estimating the population mean.

$ __ < u < $ __ (round to nearest integer as needed).

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Expert Solution

## Q ) Salaries of 32 college graduates who took a statistics course in college have a mean of $64,300. Assume a standard deviation of $16,200, construct a 95% confidence interval for estimating the population mean.

Answer : we have given :

n = sample size = 32

xbar = sample mean = 64300

σ = Assume a standard deviation of 16,200

95 % confidence interval for u :

= ( xbar ± ( critical value * σ / SQRT ( n) )

critical value = ± 1.96 ( from table)

se = standard error = σ / SQRT ( n) = 16200 / 5.6568

se = 2863.7824

lower limit = 64300 - ( 1.96 * 2863.7824) = 58686.98 ie 58687

upper limit = 64300 + ( 1.96 * 2863.7824) = 69913.0135 ie 69913

## we can say 95 % confident that population mean is lies within 58687 to 69913 . ie

$ 58687 < u < $ 69913

orchestra answered 1 year ago

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