Question

In: Statistics and Probability

Assuming normality, construct the requested confidence interval. A sociologist is interested in the age at which...

Assuming normality, construct the requested confidence interval.

A sociologist is interested in the age at which a mother has her first child. A random sample of 20 recent births yielded an average maternal age to be 30 years with a standard deviation of 6.2 years.

Construct a 99% confidence interval for the mean age at which a mother has her first child.

Question 17 options:

	(27.10, 32.90)
	(26.43, 33.57)
	(27.28, 32.72)
	(27.60, 32.40)
	(26.03, 33.97)

Expert Solution

c )solution

Given that,

= 30

s =6.2

n = 20

Degrees of freedom = df = n - 1 = 20- 1 = 19

At 99% confidence level the t is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

t /2 df = t0.005,19 = 2.861 ( using student t table)

Margin of error = E = t/2,df * (s / $\sqrt$ n)

= 2.861* ( 6.2/ $\sqrt$ 20) = 3.97

The 99% confidence interval is,

- E < < + E

30 - 3.97< <30 + 3.97

(26.03, 33.97)

orchestra answered 2 years ago

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