Question

In: Statistics and Probability

For a data set obtained from a sample, n=77 and x⎯⎯=46.30. It is known that σ=3.8....

For a data set obtained from a sample, n=77 and x⎯⎯=46.30. It is known that σ=3.8.

a. What is the point estimate of μμ?

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.

Expert Solution

Solution :

Given that,

a

Point estimate = sample mean = = 46.30

Population standard deviation = = 3.8

Sample size n =77

(c)

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 / $\sqrt$ 77 $\sqrt$ )

= 0.85
b.

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

- E < < + E

46.30 - 0.85 < < 46.30+ 0.85

45.45 < < 47.15

orchestra answered 2 years ago

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