256 middle managers were randomly selected and their annual income noted. The sample mean is $35,420.00 and the sample standard deviation is $2050.00.  a) What is the estimated mean income of all...

256 middle managers were randomly selected and their annual income noted. The sample mean is $35,420.00 and the sample standard deviation is $2050.00. 

a) What is the estimated mean income of all middle managers?

b) What is the 89% confidence interval (rounded to the nearest $10)?

c)Interpret your answer for (b)?

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a) The sample mean of the data is `barx =` $35,420, so our estimated mean income for any middle manager in the population is exactly that, $35,420.

b) Assuming that the income of middle managers is Normally distributed, then the sampling distribution of the sample mean variable `barX` is such that

`bar X` ~ Normal(`mu`, `sigma^2/n` )

` `where `mu` is the mean income of a middle manager and `sigma^2` is the population variance. We are interested in a conifdence interval for the mean `mu`.

We estimate the mean of `bar X`...

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