Question

In: Statistics and Probability

For a data set obtained from a sample, n=79 and x¯=46.55. It is known that σ=3.8....

For a data set obtained from a sample, n=79 and x¯=46.55. It is known that σ=3.8.

a. What is the point estimate of μ?

The point estimate is___ .

b. Make a 95% 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=___

Expert Solution

= Solution :

Given that,

(A)

Point estimate = sample mean = = 46.55

Population standard deviation = = 3.8

Sample size n =79

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96 ( Using z table )

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

= 1.96 * (3.8 / $\sqrt$ 79 )

=0.84
(b)

At 95% confidence interval =
is

- E < < + E

46.55- 0.84 < < 46.55+ 0.84

45.71< <47.39

(45.71 , 47.39)

c.

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

= 1.96 * (3.8 / $\sqrt$ 79 )

=0.84

orchestra answered 1 year ago

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