Question

Under ordinary circumstances: For all babies born in the entire global population, the proportion of male births tends to be consistently a bit higher, than the proportion of female births (Source: WHO - World Health Organization).

In fact: For a randomly sampled individual birth from the global population, the probability that the baby's sex will be male is approximately 51.2%.

Imagine that we will randomly record the sex outcome at birth for 1000 future individual babies from the global population.

We will let random variable X stand for the total number of male births in our sample.

[Note: This problem takes place within the Binomial Setting, and thus we model it using a Binomial Distribution.]

A.) What is the approximate value of P(X≥542) ?

Write your answer as a percentage value, and round to two digits after the decimal point. Include a percent symbol after your answer (no spaces).

B.) A famous mathematical theorem states that the Binomial Distribution in this problem, will be well-approximated by a ___________Distribution.

What single-word, formal distribution name correctly fills-in the blank in this last sentence?

A researcher wonders if the currently-believed global male-births proportion value of approximately p = 51.2% is still correct.

The researcher decides to perform a two-sided significance test, and in advance, chooses a significance-level of 1%.

The researcher then randomly samples the reported birth-sex information for 1000 recent global births, and finds that exactly 551 of these babies were reported to be males.

A.) In percentage form, and rounded to three digits past the decimal point: What is the approximate P-value of this test?

Include a percentage symbol at the end of your numerical answer (with no spaces).

Recall from the previous problems:

In order to study the global proportion of male baby births, a researcher randomly sampled the reported birth-sex information for 1000 recent global births. The researcher found that exactly 551 of these babies were reported to be males.

Using this same sample data, the researcher now decides to build a 99%-level confidence interval for estimating the current true global proportion of male baby births.

In percentage form, and rounded to two digits past the decimal point: What is the approximate value of the Lower Limit of this confidence interval?

A.) Include a percentage symbol at the end of your numerical answer (with no spaces).

B.) In percentage form, and rounded to two digits past the decimal point: What is the approximate value of the Upper Limit of this confidence interval?

Include a percentage symbol at the end of your numerical answer (with no spaces).

C.) In percentage form, and rounded to two digits past the decimal point: What is the approximate value of the Margin of Error for this confidence interval?

Include a percentage symbol at the end of your numerical answer (with no spaces).

C.) Suppose the researcher now wishes that they had instead built a confidence interval still having this same 99% confidence level, but with a margin of error no greater than 1%.

To achieve these new specifications: The researcher intends in the future, to draw a completely new random sample of reported birth-sex information for recent global births.

D.) What minimum sample size will the researcher need to draw, in order to achieve these new confidence interval specifications?

(Note: Your answer should be a whole number here. Do not include any commas in the number.)

Answer 1