Question

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

(a)

n = 145, x = 0.88, s² = 0.084

to

(b)

n = 70, x = 25.6, s² = 3.49

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

Answer 1

Here we apply t test for finding Confidence Interval because population standard deviation is unknown.

a) 90% Confidence Interval

Degrees of freedom (df) = n-1 = 145-1 = 144

= (0.840, 0.920)

b) 90% Confidence Interval

Degrees of Freedom (df) = n-1 = 70-1 = 69

=( 25.228, 25.972)

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