Is there a difference in the gestation time for first and second births to the s
ID: 3224921 • Letter: I
Question
Is there a difference in the gestation time for first and second births to the same parent? The following table shows the gestation time (days) for a sample of four mothers with their first two children.Mother 1 2 3 4 First birth 245 267 249 263 Second birth 243 267 243 261
Assume that the changes in gestation (second time—first time) have an approximately Normal distribution. A 90% confidence interval for the mean difference in gestation times between the first and second births is a. –2.5 ± 4.00. b. –2.5 ± 2.96 c. –2.5 ± 5.92. d. –2.5 ± 2.07. Is there a difference in the gestation time for first and second births to the same parent? The following table shows the gestation time (days) for a sample of four mothers with their first two children.
Mother 1 2 3 4 First birth 245 267 249 263 Second birth 243 267 243 261
Assume that the changes in gestation (second time—first time) have an approximately Normal distribution. A 90% confidence interval for the mean difference in gestation times between the first and second births is a. –2.5 ± 4.00. b. –2.5 ± 2.96 c. –2.5 ± 5.92. d. –2.5 ± 2.07.
Explanation / Answer
X1
X2
245
243
267
267
249
243
263
261
Mean =
256
253.5
Standard deviation =
10.6458
12.3693
Confidence Interval formula:
(X1 bar – X2 bar ) (-/+) E
E = tc * SE (x1-x2)
tc is the critical value for 6 degrees of freedom at 10% level of significance.
From t-table we get the critical t as 1.943
SE(x1-x2) = ((n1-1)*s1^2+(n2-1)*s2^2)/(n1+n2-2) * (1/n1+1/n2)
= ((4-1)*10.6458^2+(4-1)*12.3693^2)/(4+4-2) * (1/4+1/4)
= 8.1599
E = 1.943 * 8.1599
= 15.8561
X1 bar – x2 bar = 2.5
2.5 (-/+) 15.8561
(2.5 – 15.8561) (2.5 + 15.8561)
-13.36 and 18.36
The 90% confidence interval for the mean different in the gestation times between the first and the second birth is (-13.36 to 18.36)
X1
X2
245
243
267
267
249
243
263
261
Mean =
256
253.5
Standard deviation =
10.6458
12.3693
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