Final answer:
To construct a confidence interval estimate of the mean weight of newborn girls, we can use the formula CI = x ± z * (s / sqrt(n)). Using the given sample mean, standard deviation, and sample size, we can calculate the confidence interval to be (30.624 hg, 32.776 hg) at a 98% confidence level. This confidence interval is not very different from the given confidence interval of (30.5 hg < u < 32.7 hg) with a smaller sample size and slightly different sample mean and standard deviation.
Step-by-step explanation:
In order to construct a confidence interval estimate of the mean, we will use the formula:
CI = x ± z * (s / sqrt(n))
where x is the sample mean, s is the sample standard deviation, n is the sample size, and z is the critical value from the standard normal distribution table.
Using the given information, we can calculate the confidence interval as follows:
Sample mean (x): 31.7 hg
Sample standard deviation (s): 6.3 hg
Sample size (n): 185
Critical value (z) at 98% confidence level: 2.326 (from the standard normal distribution table)
CI = 31.7 ± 2.326 * (6.3 / sqrt(185))
Calculating the confidence interval:
CI = 31.7 ± 2.326 * 0.463
CI = 31.7 ± 1.076
CI = (30.624, 32.776)
The 98% confidence interval estimate of the mean weight of newborn girls is (30.624 hg, 32.776 hg).
Comparing this confidence interval to the given confidence interval of (30.5 hg < u < 32.7 hg) with only 19 sample values, x=31.6 hg, and s=1.9 hg, we can see that these results are not very different. Both confidence intervals overlap, indicating that the means are likely to be similar.