For a data set obtained from a sample, n=75 and x¯=47.80. It is known that σ=3.8....

For a data set obtained from a sample, n=75 and x¯=47.80. It is known that σ=3.8.

a. What is the point estimate of μ?

The point estimate is .

b. Make a 90% confidence interval for μ.

Round your answers to two decimal places.

(,)

c. What is the margin of error of estimate for part b?

Round your answer to three decimal places.

E=

Solutions

Expert Solution

Solution :

Given that,

Point estimate = sample mean = = 47.80

Population standard deviation = = 3.8
Sample size = n =75

At 90% confidence level the z is

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

Z/2 = Z0.05 = 1.645 ( Using z table )

Margin of error = E = Z/2 * ( / $\sqrt$ n)

= 1.645* ( 3.8 / $\sqrt$ 75 )

=0.7
At 90% confidence interval estimate of the population mean
is,

- E < < + E

47.80 - 0.7 < < 47.80+ 0.7

47.1 < < 48.5

orchestra answered 11 months ago

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