Assume that we want to construct a

Answered question

2022-03-28

Assume that we want to construct a confidence interval. Do one of the​ following, as​ appropriate: (a) find the critical value

tα/2​,

​(b) find the critical value

zα/2​,

or​ (c) state that neither the normal distribution nor the t distribution applies.

Here are summary statistics for randomly selected weights of newborn​ girls:

n=162​,

x=30.1

​hg,

s=6.1

hg. The confidence level is

99​%.

Answer & Explanation

nick1337

nick1337

Expert2023-04-26Added 777 answers

To construct a confidence interval, we need to determine whether to use a t-distribution or a normal distribution, and then find the appropriate critical value.
In this problem, we have a sample size of n = 162, and we want to construct a 99% confidence interval for the mean weight of newborn girls. Since the sample size is large, we can use a normal distribution to construct the confidence interval.
The formula for a confidence interval for the population mean is:
x¯±zα/2sn
where x¯ is the sample mean, s is the sample standard deviation, n is the sample size, and zα/2 is the critical value of the standard normal distribution that corresponds to the level of confidence α.
Substituting the given values, we have:
x¯±zα/2sn=30.1±z0.0056.1162
To find the critical value z0.005, we can look up the value in a standard normal distribution table, or use a calculator or software. The value is approximately 2.576.
Therefore, the 99% confidence interval for the mean weight of newborn girls is:
30.1±2.576·6.1162
Simplifying and rounding to one decimal place, we get:
(28.9,31.3)
In conclusion, we can use a normal distribution to construct a 99% confidence interval for the mean weight of newborn girls, and the interval is (28.9, 31.3) with a margin of error of approximately 1.2.

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