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, *s*^{2} =
0.084

to

(b)

*n* = 70, *x* = 25.6, *s*^{2} =
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

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