Family Size : A random sample of 60 married couples who have been married 7 year
ID: 2933603 • Letter: F
Question
Family Size: A random sample of 60 married couples who have been married 7 years was asked the number of children they have. The results of the survey are as follows:
0
0
0
3
3
3
1
3
2
2
3
1
3
2
4
0
3
3
3
1
0
2
3
3
1
4
2
3
1
3
3
5
0
2
3
0
4
4
2
2
3
2
2
2
2
3
4
3
2
2
1
4
3
2
4
2
1
2
3
2
a) Compute a 95% confidence interval for the mean number of children of all couples who have been married 7 years. (Hint: T-interval) Round 2 decimals.
Interpret the interval.
(b) Compute a 99% confidence interval for the mean number of children of all couples who have been married 7 years. (Hint: T-interval) Round 2 decimals.
Interpret the interval.
0
0
0
3
3
3
1
3
2
2
3
1
3
2
4
0
3
3
3
1
0
2
3
3
1
4
2
3
1
3
3
5
0
2
3
0
4
4
2
2
3
2
2
2
2
3
4
3
2
2
1
4
3
2
4
2
1
2
3
2
Explanation / Answer
From the given data we have
mean = 2.2667
std. dev. = 1.2092
n = 60
SE = 1.2092/sqrt(60) = 0.1561
(a)
95% CI, t-value = 1.6711
ME = t*SE = 1.6711*0.1561 = 0.2609
Confidence interval = (mean - ME, mean + ME)
= (2.2667 - 0.2609, 2.2667 + 0.2609)
= (2.0058, 2.5276)
Interpretation:
If an another sample of 60 couples who have been married 7 years is taken, there is 95% chance that its mean will lie within the interval (2.0058, 2.5276)
(b)
99% CI, t-value = 2.3912
ME = t*SE = 2.3912*0.1561 = 0.3733
Confidence interval = (mean - ME, mean + ME)
= (2.2667 - 0.3733, 2.2667 + 0.3733)
= (1.8934, 2.64)
Interpretation:
If an another sample of 60 couples who have been married 7 years is taken, there is 99% chance that its mean will lie within the interval (1.8934, 2.64)
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