Question

6.A random sample of 60 married couples who have been married 7 years was ask the number of children they have. You may assume requirements are satisfied.The results of the survey are as follow000333132231324033310233142313350230442232222343221432421232a.What is the shape of the distribution of the sample mean? Why?b.Compute a 95% confidence interval for the mean number of children of all couples who have been married for 7 years. Interpret the interval.c.Computer the 99% confidence interval for the mean number of childrenof all couples who have been married 7 years. Interpret the interval.

Answer 1

(1.962 ; 2.578) ;

There is a 95% chance that the true population mean of the number of children of all couples who have been married for 7 years lies within the interval (1.962 ; 2.578);

(1.865 ; 2.675);

There is a 99% chance that the true population mean of the number of children of all couples who have been married for 7 years lies within the interval (1.8646 ; 2.6754)

Explanation:

Given the data :

0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 5

Using calculator :

Mean, xbar = 2.27

Standard deviation, s = 1.219

Sample size = 60

Confidence interval :

Xbar ± Margin of error

Margin of Error = Zcritical * s/sqrt(n)

Zcritical at 95% = 1.96

Margin of Error = 1.96 * 1.219/ sqrt(60) = 0.3084

Lower boundary = (2.27 - 0.3084) = 1.962

Upper boundary = (2 27 + 0.3084) = 2.578

(1.962 ; 2.578)

There is a 95% chance that the true population mean of the number of children of all couples who have been married for 7 years lies within the interval (1.962 ; 2.578)

C.) 99% confidence interval :

Xbar ± Margin of error

Margin of Error = Zcritical * s/sqrt(n)

Zcritical at 99% = 2.576

Margin of Error = 2.576 * 1.219/ sqrt(60) = 0.4054

Lower boundary = (2.27 - 0.4054) = 1.8646

Upper boundary = (2.27 + 0.4054) = 2.6754

(1.865 ; 2.675)

There is a 99% chance that the true population mean of the number of children of all couples who have been married for 7 years lies within the interval (1.8646 ; 2.6754)