Find a 90% confidence interval for a population mean ? for these values. (Round

ID: 2907845 • Letter: F

Question

Find a 90% confidence interval for a population mean ? for these values. (Round your answers to three decimal places.)

(a)

n = 150, x = 0.86, s2 = 0.084

= to =

(b)

n = 70, x = 29.4, s2 = 3.76

= to =

(c)

Interpret the intervals found in part (a) and part (b).

A. 90% of all values will fall within the interval.

B. There is a 10% chance that an individual sample proportion will fall within the interval.

C. There is a 90% chance that an individual sample proportion will fall within the interval.

D.In repeated sampling, 90% of all intervals constructed in this manner will enclose the population mean.

E. In repeated sampling, 10% of all intervals constructed in this manner will enclose the population proportion.

Solution:-
(a) n = 150, x = 0.86, s2 = 0.084

90% confidence interval for a population mean = X +/- Z*sqrt(s^2/n)
= 0.86 +/- 1.645*sqrt(0.084/150)
= 0.821 , 0.899
(b) n = 70, x = 29.4, s2 = 3.76

90% confidence interval for a population mean = X +/- Z*sqrt(s^2/n)
= 29.4 +/- 1.645*sqrt(3.76/70)
= 29.019 , 29.781

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