Question
A random sample of 838 births included 425 boys. Use a 0.01 significance level to test the claim that
of newborn babies are boys. Do the results
support the belief that
of newborn babies are boys?
Identify the null and alternative hypotheses for this test. Choose the correct answer below.
A.
D.
Identify the test statistic for this hypothesis test.
The test statistic for this hypothesis test is
(Round to two decimal places as needed.)
support the belief that
Identify the null and alternative hypotheses for this test. Choose the correct answer below.
A.
D.
Identify the test statistic for this hypothesis test.
The test statistic for this hypothesis test is
(Round to two decimal places as needed.)
Ask by Potter Matthews. in the United States
Mar 14,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Hypotheses:
Test Statistic:
Solution
Step 1. Identify the Claim and Determine the Hypotheses
The claim is that
of newborn babies are boys, i.e., that the true proportion
is equal to
.
In testing a claim about a proportion of a population, we set:
- The null hypothesis as the statement of equality:
- The alternative hypothesis as the statement that
is not equal to :
Thus, the correct choice is:
and
.
Step 2. Compute the Test Statistic
The test statistic for a hypothesis test for a proportion is calculated by
Given:
- Sample size:
- Number of boys: 425, so sample proportion:
- Claimed proportion:
.
Step 2.1. Calculate the Standard Error
First, compute
:
Then divide by
:
Take the square root:
Step 2.2. Calculate the
-Statistic
Now plug into the formula:
(Rounding to two decimal places,
.)
Final Answers:
-
Hypotheses:
and . -
Test Statistic:
.
Answered by UpStudy AI and reviewed by a Professional Tutor
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Beyond the Answer
To test the claim that
of newborn babies are boys, we will establish our hypotheses clearly. The null hypothesis,
, reflects the statement we want to test against, while the alternative hypothesis,
, proposes that the proportion of boys is higher than
. The correct pairing from your options is:
A.
Now, let’s calculate the test statistic. The formula for the test statistic
in this scenario is given by:
Where:
(the sample proportion),
(the claimed proportion),
and (the sample size).
and
Substituting in the values gives:
Calculating the denominator:
Now substituting back into the formula for
:
When rounding to two decimal places, the test statistic is approximately:
Test Statistic:
Historical Background: The study of birth ratios has fascinated statisticians and demographers for centuries. In many cultures, there’s been a belief in favorable or unfavorable birth ratios that serve various social, economic, and cultural narratives. Initially, the natural sex ratio at birth is often viewed to be around
boys for every
girls, but factors like maternal age, health, and environmental influences can impact this ratio.
Real-World Application: Understanding birth ratios is crucial in fields ranging from healthcare to social planning. For instance, if a region shows a significant anomaly in birth ratios, it may indicate underlying health issues, gender biases, or socio-economic factors that need addressing. Moreover, policies can be informed by these statistics to promote gender equality and resource allocation for neonatal care.