question archive Newborn weight
Newborn weight
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Newborn weight. A study takes a SRS from a population of full-term infants. The standard deviation of birth weights in this population is 2 pounds. Calculate 95% confidence intervals for μ for samples in which:
a) n = 81 and = 7.0 pounds
b) n = 9 and = 7.0 pounds
c) Which sample provides the most precise estimate of the mean birth weight?
d) Interpret the CI you computed in part a).
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Answer:
(a) The output is:
| 7.00 | mean Data |
| 2.00 | std. dev. |
| 0.22 | std. error |
| 81 | n |
| 80 | df |
| 6.56 | confidence interval 95.% lower |
| 7.44 | confidence interval 95.% upper |
| 0.44 | margin of error |
The 95% confidence interval for μ is between 6.56 and 7.44.
(b) The output is:
| 7.00 | mean Data |
| 2.00 | std. dev. |
| 0.67 | std. error |
| 9 | n |
| 8 | df |
| 5.46 | confidence interval 95.% lower |
| 8.54 | confidence interval 95.% upper |
| 1.54 | margin of error |
The 95% confidence interval for μ is between 5.46 and 8.54.
(c) Part (A) sample provides the most precise estimate of the mean birth weight because it has a low margin of error.
(d) The 95% confidence interval for μ from part (a) is between 6.56 and 7.44 which means that the birth weight will range from 6.56 to 7.44 for 95% of the time.
