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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

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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)