Table of contents

1. Intro to Stats and Collecting Data55m
2. Describing Data with Tables and Graphs1h 55m
3. Describing Data Numerically1h 45m
4. Probability2h 16m
5. Binomial Distribution & Discrete Random Variables2h 33m
6. Normal Distribution and Continuous Random Variables1h 38m
7. Sampling Distributions & Confidence Intervals: Mean1h 53m
8. Sampling Distributions & Confidence Intervals: Proportion1h 12m
- Sampling Distribution of Sample Proportion
  29m
- Confidence Intervals for Population Proportion
  42m
9. Hypothesis Testing for One Sample2h 19m
10. Hypothesis Testing for Two Samples3h 26m
11. Correlation1h 6m
12. Regression1h 35m
13. Chi-Square Tests & Goodness of Fit1h 57m
14. ANOVA1h 0m

9. Hypothesis Testing for One Sample

Steps in Hypothesis Testing

Statistics

9. Hypothesis Testing for One Sample

Steps in Hypothesis Testing

Previous problemNext problem

2:05 minutes

Problem 7.1.29

Textbook Question

Stating the Null and Alternative Hypotheses In Exercises 25–30, write the claim as a mathematical statement. State the null and alternative hypotheses, and identify which represents the claim.

Paying for College According to a recent survey, 54% of today’s college students used student loans to pay for college.

Verified step by step guidance

Identify the claim: The problem states that 54% of today's college students used student loans to pay for college. This is the claim we will test.

Define the population proportion: Let p represent the proportion of college students who use student loans to pay for college.

Write the claim as a mathematical statement: The claim is that p = 0.54.

State the null hypothesis (H₀): The null hypothesis always includes equality. Here, H₀: p = 0.54.

State the alternative hypothesis (H₁): The alternative hypothesis depends on the context. If we are testing whether the proportion is different from 54%, then H₁: p ≠ 0.54. If we are testing whether it is greater or less than 54%, the alternative hypothesis would be H₁: p > 0.54 or H₁: p < 0.54, respectively.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above

Video duration:

Play a video:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Null Hypothesis

The null hypothesis (H0) is a statement that indicates no effect or no difference in a statistical test. It serves as a default position that assumes any observed effect is due to sampling variability. In this context, it would state that the proportion of college students using loans is equal to 54%, suggesting that there is no significant change from the reported figure.

Alternative Hypothesis

The alternative hypothesis (H1) is a statement that contradicts the null hypothesis, indicating that there is an effect or a difference. It represents the claim that researchers aim to support. In this case, it would assert that the proportion of college students using loans is not equal to 54%, suggesting a significant change in the usage of student loans.

Statistical Significance

Statistical significance refers to the likelihood that a relationship observed in data is not due to chance. It is often determined through p-values in hypothesis testing. If the results show statistical significance, it implies that the alternative hypothesis may be accepted, indicating a meaningful difference in the proportion of students using loans compared to the stated 54%.

Watch next

Master Step 1: Write Hypotheses with a bite sized video explanation from Patrick

Start learning

Related Videos

Related Practice

Textbook Question

Graphical Analysis In Exercises 17–20, match the alternative hypothesis with its graph. Then state the null hypothesis and sketch its graph.

Ha: μ > 3

views

Textbook Question

Identifying a Test In Exercises 21–24, determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed.

Ha: μ ≤ 8.0

H0: μ > 8.0

views

Textbook Question

Stating the Null and Alternative Hypotheses In Exercises 25–30, write the claim as a mathematical statement. State the null and alternative hypotheses, and identify which represents the claim.

Tablets A tablet manufacturer claims that the mean life of the battery for a certain model of tablet is more than 8 hours.

views

Textbook Question

Stating the Null and Alternative Hypotheses In Exercises 25–30, write the claim as a mathematical statement. State the null and alternative hypotheses, and identify which represents the claim.

Attendance An amusement park claims that the mean daily attendance at the park is at least 20,000 people.

views

Textbook Question

Stating the Null and Alternative Hypotheses In Exercises 25–30, write the claim as a mathematical statement. State the null and alternative hypotheses, and identify which represents the claim.

College Debt According to a recent survey, 14% of adults currently carry student loan debt.

views

Textbook Question

Identifying Type I and Type II Errors In Exercises 31–36, describe type I and type II errors for a hypothesis test of the indicated claim.

Security A campus security department publicizes that at most 25% of applicants become campus security officers.

views

Textbook Question

Identifying Type I and Type II Errors In Exercises 31–36, describe type I and type II errors for a hypothesis test of the indicated claim.

Phone Repairs A cell phone repair shop advertises that the mean cost of repairing a phone screen is less than $120.

views

Textbook Question

Identifying the Nature of a Hypothesis Test In Exercises 37–42, state and in words and in symbols. Then determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed. Explain your reasoning. Sketch a normal sampling distribution and shade the area for the P-value.

Golf A golf analyst claims that the standard deviation of the 18-hole scores for a golfer is less than 2.1 strokes.

views

Show more practices

Download the Mobile app

Privacy

Do not sell my personal information

Accessibility

Patent notice

Sitemap