Skip to main content
Ch. 8 - Hypothesis Testing with Two Samples
Larson - Elementary Statistics: Picturing the World 8th Edition
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoLarson 8th EditionCh. 8 - Hypothesis Testing with Two SamplesProblema 8.10
Capitolo 8, Problema 8.10

In Exercises 7–10, the statement represents a claim. Write its complement and state which is Ho and which is Ha.


μ≠2.28

Guida verificata passo dopo passo
1
Identify the claim in the problem. The claim is μ≠2.28, which is a statement about the population mean (μ). This indicates that the mean is not equal to 2.28.
Understand the complement of the claim. The complement of μ≠2.28 is μ=2.28, which states that the population mean is equal to 2.28.
Determine the null hypothesis (Ho). The null hypothesis always represents the statement of equality, so Ho: μ=2.28.
Determine the alternative hypothesis (Ha). The alternative hypothesis represents the claim being tested, so Ha: μ≠2.28.
Summarize the hypotheses: Ho: μ=2.28 (null hypothesis) and Ha: μ≠2.28 (alternative hypothesis). The alternative hypothesis is the claim, and the null hypothesis is its complement.

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Durata del video:
2m

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

Null Hypothesis (Ho)

The null hypothesis, denoted as Ho, is a statement that indicates no effect or no difference in a statistical test. It serves as the default assumption that any observed effect is due to sampling variability. In this case, the null hypothesis would be that the population mean μ equals 2.28.
Video consigliato:
Percorso guidato
01:35
Step 1: Write Hypotheses Example 1

Alternative Hypothesis (Ha)

The alternative hypothesis, represented as Ha, is a statement that contradicts the null hypothesis. It suggests that there is an effect or a difference. For the given claim μ≠2.28, the alternative hypothesis would be that the population mean μ is not equal to 2.28, indicating a significant deviation from this value.
Video consigliato:
Percorso guidato
06:21
Step 1: Write Hypotheses

Complement of a Hypothesis

The complement of a hypothesis refers to the opposite scenario of the original claim. In hypothesis testing, if the null hypothesis states a specific value, the complement would encompass all other possibilities. For the claim μ≠2.28, the complement is μ=2.28, which is the condition under which the null hypothesis holds true.
Video consigliato:
Percorso guidato
4:23
Complementary Events
Pratica correlata
Domanda del libro di testo

Test the claim about the mean of the differences for a population of paired data at the level of significance α. Assume the samples are random and dependent, and the populations are normally distributed.

Claim: μd≤0 , α=0.10, Sample statistics: d̄ =6.5, sd=9.54, n=16

77
views
Domanda del libro di testo

Gas Mileage The table shows the gas mileages (in miles per gallon) of eight cars with and without using a fuel additive. At α=0.10, is there enough evidence to conclude that the additive improved gas mileage? Assume the populations are normally distributed.


48
views
Domanda del libro di testo

A pediatrician claims that the mean birth weight of a single-birth baby is greater than the mean birth weight of a baby that has a twin. The mean birth weight of a random sample of 85 single-birth babies is 3086 grams. Assume the population standard deviation is 563 grams. The mean birth weight of a random sample of 68 babies that have a twin is 2263 grams. Assume the population standard deviation is 624 grams. At α=0.10, can you support the pediatrician’s claim? Interpret the decision in the context of the original claim.

55
views
Domanda del libro di testo

Describe another way you can perform a hypothesis test for the difference between the means of two populations using independent samples with and known that does not use rejection regions.

76
views
Domanda del libro di testo

Independent and Dependent Samples In Exercises 5–8, classify the two samples as independent or dependent and justify your answer.

Sample 1: The commute times of 10 workers when they use their own vehicles

Sample 2: The commute times of the same 10 workers when they use public transportation

61
views
Domanda del libro di testo

Getting at the Concept Explain why the null hypothesis Ho: μ1=μ2 is equivalent to the null hypothesis .Ho: μ1-μ2=0

168
views