Question

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

(a)

n = 130, x = 0.85, s² = 0.084

to

(b)

n = 40, x = 20.1, s² = 3.86

to

(c)

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

There is a 10% chance that an individual sample proportion will fall within the interval.In repeated sampling, 10% of all intervals constructed in this manner will enclose the population proportion.    In repeated sampling, 90% of all intervals constructed in this manner will enclose the population mean.90% of all values will fall within the interval.There is a 90% chance that an individual sample proportion will fall within the interval.

Answer 1

a) At 90% confidence interval the critical value is t^* = 1.657

The 90% confidence interval for population mean is

+/- t^* * sqrt(s²/n)

= 0.85 +/- 1.657 * sqrt(0.084/130)

= 0.85 +/- 0.042

= 0.808, 0.892

b) At 90% confidence interval the critical value is t^* = 1.685

The 90% confidence interval for population mean is

+/- t^* * sqrt(s²/n)

= 20.1 +/- 1.685 * sqrt(3.86/40)

= 20.1 +/- 0.523

= 19.577, 20.623

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