Skip to main content
Ch. 7 - Hypothesis Testing with One Sample
Larson - Elementary Statistics: Picturing the World 8th Edition
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Not the one you use?Change textbook
All textbooksLarson 8th EditionCh. 7 - Hypothesis Testing with One SampleProblem 7.1.52a
Chapter 7, Problem 7.1.52a

Writing Hypotheses: Internet Provider An Internet provider is trying to gain advertising deals and claims that the mean time a customer spends online per day is greater than 28 minutes. You are asked to test this claim. How would you write the null and alternative hypotheses when


a. you represent the Internet provider and want to support the claim?

Verified step by step guidance
1
Understand the context: The Internet provider claims that the mean time a customer spends online per day is greater than 28 minutes. This is a one-tailed hypothesis test because the claim specifies a direction ('greater than').
Define the null hypothesis (H₀): The null hypothesis represents the default or status quo assumption. In this case, it would state that the mean time a customer spends online per day is less than or equal to 28 minutes. Mathematically, H₀: μ ≤ 28, where μ represents the population mean.
Define the alternative hypothesis (H₁): The alternative hypothesis represents the claim being tested. Since the Internet provider wants to support the claim that the mean time is greater than 28 minutes, the alternative hypothesis is H₁: μ > 28.
Verify the hypotheses: Ensure that the null and alternative hypotheses are mutually exclusive and collectively exhaustive. This means that one and only one of these hypotheses can be true based on the evidence from the data.
Write the hypotheses clearly: Null hypothesis (H₀): μ ≤ 28. Alternative hypothesis (H₁): μ > 28. These hypotheses will guide the statistical test to determine whether there is sufficient evidence to support the provider's claim.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
2m
Was this helpful?

Key Concepts

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

Null Hypothesis (H0)

The null hypothesis is a statement that indicates no effect or no difference, serving as a default position that there is no relationship between two measured phenomena. In this context, it would assert that the mean time customers spend online per day is less than or equal to 28 minutes, which the Internet provider is trying to challenge.
Recommended video:
Guided course
06:21
Step 1: Write Hypotheses

Alternative Hypothesis (H1)

The alternative hypothesis is a statement that contradicts the null hypothesis, suggesting that there is an effect or a difference. For the Internet provider's claim, the alternative hypothesis would state that the mean time customers spend online per day is greater than 28 minutes, which is what they aim to support.
Recommended video:
Guided course
06:21
Step 1: Write Hypotheses

Hypothesis Testing

Hypothesis testing is a statistical method used to make decisions about the validity of a hypothesis based on sample data. It involves calculating a test statistic and comparing it to a critical value to determine whether to reject the null hypothesis in favor of the alternative hypothesis, thus providing evidence for the Internet provider's claim.
Recommended video:
Guided course
06:21
Step 1: Write Hypotheses
Related Practice
Textbook Question

Interpreting a Decision In Exercises 43–48, determine whether the claim represents the null hypothesis or the alternative hypothesis. If a hypothesis test is performed, how should you interpret a decision that

         

a. rejects the null hypothesis?


A recent study claims that at least 20% of renters are behind on rent payments in New Jersey. 

Textbook Question

Graphical Analysis In Exercises 13 and 14, state whether each standardized test statistic X^2 allows you to reject the null hypothesis. Explain.


a. X^2=2.091

Textbook Question

Interpreting a Decision In Exercises 43–48, determine whether the claim represents the null hypothesis or the alternative hypothesis. If a hypothesis test is performed, how should you interpret a decision that

         

a. rejects the null hypothesis?


Gas Mileage An automotive manufacturer claims that the standard deviation for the gas mileage of one of the vehicles it manufactures is 3.9 miles per gallon.

Textbook Question

In Exercises 3–6, determine whether a normal sampling distribution can be used. If it can be used, test the claim.

Claim: p ≠0.15, α=0.05. Sample statistics: p_hat = 0.12, n=500

Textbook Question

Graphical Analysis In Exercises 9–12, state whether each standardized test statistic t allows you to reject the null hypothesis. Explain.


a. t = 1.4


Textbook Question

A nutrition bar manufacturer claims that the standard deviation of the number of grams of carbohydrates in a bar is 1.11 grams. A random sample of 26 bars has a standard deviation of 1.19 grams. At α=0.05, is there enough evidence to reject the manufacturer’s claim? Assume the population is normally distributed.