Question

(4 pts.) Couples' therapists performed a study to determine factors that would predict divorce. A random sample of 180 committed couples produced a sample mean of the time that they knew each other of 52.28 months. Assume a population standard deviation of 41.40 months. Construct a 95% confidence interval for the mean time that spouses have known each other among all married couples.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 52.28

Population standard deviation =    = 41.40

Sample size = n =180

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

Margin of error = E = Z/2 * ( /n)

= 1.96 * (41.40 /  180 )

= 6.0481
At 95% confidence interval estimate of the population mean
is,

- E < < + E

52.28 -6.0481 <   <52.28 + 6.0481

46.2319 <   < 58.3281

(46.2319 , 58.3281)