According to the National Center for Education Statistics, 37% of STEM gradu- sample of 40 random STEM majors at your college and find that 21 of them ar hypothesis test to determine whether your college differs from the national r that you would get, to at least four places.
According to the National Center for Education Statistics, 37% of STEM gradu- sample of 40 random STEM majors at your college and find that 21 of them ar hypothesis test to determine whether your college differs from the national r that you would get, to at least four places.
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.7: Probability
Problem 58E: What is meant by the sample space of an experiment?
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Question
![According to the National Center for Education Statistics, 37% of STEM graduates are women. You take a sample of 40 random STEM majors at your college and find that 21 of them are women. You want to do a hypothesis test to determine whether your college differs from the national rate. Calculate the test statistic that you would get, to at least four places.
[Input box]
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**Explanation for Educational Context:**
This problem involves performing a hypothesis test to compare a sample proportion to a known population proportion. Here are the specific steps and details:
1. **State the Hypotheses:**
- Null Hypothesis (H₀): The proportion of women in STEM at the college is equal to the national proportion, p₀ = 0.37.
- Alternative Hypothesis (H₁): The proportion of women in STEM at the college is not equal to the national proportion, p ≠ 0.37.
2. **Calculate the Test Statistic:**
A test statistic for a population proportion can be calculated using the following formula:
\[ z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}} \]
where:
- \(\hat{p}\) is the sample proportion.
- \(p_0\) is the population proportion.
- \(n\) is the sample size.
Given:
- Sample proportion, \(\hat{p} = \frac{21}{40} = 0.525\)
- Population proportion, \(p_0 = 0.37\)
- Sample size, \(n = 40\)
Substitute these values into the formula:
\[ z = \frac{0.525 - 0.37}{\sqrt{\frac{0.37 \cdot (1-0.37)}{40}}} \]
\[ z = \frac{0.155}{\sqrt{\frac{0.37 \cdot 0.63}{40}}} \]
\[ z = \frac{0.155}{\sqrt{0.2331 / 40}} \]
\[ z = \frac{0.155}{\sqrt{0.0058275}} \]
\[ z = \frac{0.155}{0.07634} \](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc8e28faf-547f-4c48-bb6d-e40546588d1c%2F8cbd78ee-ea31-40a9-b0e1-d8ccddacfc1a%2Fgs6nq8o_processed.jpeg&w=3840&q=75)
Transcribed Image Text:According to the National Center for Education Statistics, 37% of STEM graduates are women. You take a sample of 40 random STEM majors at your college and find that 21 of them are women. You want to do a hypothesis test to determine whether your college differs from the national rate. Calculate the test statistic that you would get, to at least four places.
[Input box]
---
**Explanation for Educational Context:**
This problem involves performing a hypothesis test to compare a sample proportion to a known population proportion. Here are the specific steps and details:
1. **State the Hypotheses:**
- Null Hypothesis (H₀): The proportion of women in STEM at the college is equal to the national proportion, p₀ = 0.37.
- Alternative Hypothesis (H₁): The proportion of women in STEM at the college is not equal to the national proportion, p ≠ 0.37.
2. **Calculate the Test Statistic:**
A test statistic for a population proportion can be calculated using the following formula:
\[ z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}} \]
where:
- \(\hat{p}\) is the sample proportion.
- \(p_0\) is the population proportion.
- \(n\) is the sample size.
Given:
- Sample proportion, \(\hat{p} = \frac{21}{40} = 0.525\)
- Population proportion, \(p_0 = 0.37\)
- Sample size, \(n = 40\)
Substitute these values into the formula:
\[ z = \frac{0.525 - 0.37}{\sqrt{\frac{0.37 \cdot (1-0.37)}{40}}} \]
\[ z = \frac{0.155}{\sqrt{\frac{0.37 \cdot 0.63}{40}}} \]
\[ z = \frac{0.155}{\sqrt{0.2331 / 40}} \]
\[ z = \frac{0.155}{\sqrt{0.0058275}} \]
\[ z = \frac{0.155}{0.07634} \
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