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: 9780137493470Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoLarson 8th EditionCh. 7 - Hypothesis Testing with One SampleProblema 7.5.30
Capitolo 7, Problema 7.5.30

Hypothesis Testing Using Rejection Regions In Exercises 23–30, (a) identify the claim and state H0 and Ha, (b) find the critical value(s) and identify the rejection region(s), (c) find the standardized test statistic X^2, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. Assume the population is normally distributed.


Salaries The annual salaries (in dollars) of 12 randomly chosen nursing supervisors are shown in the table at the left. At α=0.10, is there enough evidence to reject the claim that the standard deviation of the annual salaries is \$18,630?


tab2

Guida verificata passo dopo passo
1
Step 1: Identify the claim and state the null hypothesis (H0) and the alternative hypothesis (Ha). The claim is that the standard deviation of the annual salaries is \$18,630. Thus, H0: σ = 18,630 (the standard deviation equals \$18,630), and Ha: σ ≠ 18,630 (the standard deviation does not equal \$18,630).
Step 2: Determine the critical value(s) and rejection region(s). Since the test involves the standard deviation and the population is normally distributed, use the chi-square distribution. The degrees of freedom (df) are calculated as n - 1, where n is the sample size. Here, n = 12, so df = 11. Using α = 0.10 for a two-tailed test, find the critical chi-square values from a chi-square table or calculator.
Step 3: Calculate the standardized test statistic X². First, compute the sample variance (s²) using the formula s² = Σ(x - x̄)² / (n - 1), where x̄ is the sample mean. Then, use the formula X² = (n - 1) * s² / σ² to calculate the test statistic, where σ² is the square of the claimed standard deviation.
Step 4: Compare the test statistic X² to the critical values. If X² falls within the rejection region (either below the lower critical value or above the upper critical value), reject the null hypothesis. Otherwise, fail to reject the null hypothesis.
Step 5: Interpret the decision in the context of the original claim. If the null hypothesis is rejected, conclude that there is enough evidence to reject the claim that the standard deviation of the annual salaries is \$18,630. If the null hypothesis is not rejected, conclude that there is not enough evidence to reject the claim.

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:
5m

Concetti chiave

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

Hypothesis Testing

Hypothesis testing is a statistical method used to make decisions about a population based on sample data. It involves formulating two competing hypotheses: the null hypothesis (H0), which represents a statement of no effect or no difference, and the alternative hypothesis (Ha), which represents the claim being tested. The goal is to determine whether there is enough evidence in the sample data to reject H0 in favor of Ha.
Video consigliato:
Percorso guidato
06:21
Step 1: Write Hypotheses

Critical Value and Rejection Region

The critical value is a threshold that determines the boundary for rejecting the null hypothesis in hypothesis testing. It is derived from the significance level (α), which indicates the probability of making a Type I error. The rejection region is the range of values for the test statistic that leads to the rejection of H0. If the calculated test statistic falls within this region, we reject the null hypothesis.
Video consigliato:
Percorso guidato
05:50
Critical Values: t-Distribution

Standard Deviation and Chi-Square Test

The standard deviation is a measure of the amount of variation or dispersion in a set of values. In the context of hypothesis testing for standard deviation, the Chi-Square test is used to determine if the sample standard deviation significantly differs from a hypothesized population standard deviation. The test statistic is calculated using the sample data, and its value is compared to the critical value to make a decision regarding the null hypothesis.
Video consigliato:
Percorso guidato
08:45
Calculating Standard Deviation
Pratica correlata
Domanda del libro di testo

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.


Repeat Customers A used textbook selling website claims that at least 60% of its new customers will return to buy their next textbook.

101
views
Domanda del libro di testo

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.


Survey A polling organization reports that the number of responses to a survey mailed to 100,000 U.S. residents is not 100,000.

58
views
Domanda del libro di testo

Finding a P-Value In Exercises 13–18, find the P-value for the hypothesis test with the standardized test statistic z. Decide whether to reject H0 for the level of significance alpha.

Left-tailed test


z= 1.95

alpha=0.08

57
views
Domanda del libro di testo

Hypothesis Testing Using Rejection Regions In Exercises 7–12, (a) identify the claim and state H0 and Ha, (b) find the critical value(s) and identify the rejection region(s), (c) find the standardized test statistic z, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim.


Changing Jobs A researcher claims that 40% of U.S. adults would consider changing jobs. In a random sample of 50 U.S. adults, 25 say they would consider changing jobs. At α=0.10, is there enough evidence to reject the researcher’s claim?

77
views
Domanda del libro di testo

Stating Hypotheses In Exercises 11–16, the statement represents a claim. Write its complement and state which is H0 and which is Ha.


μ < 128

47
views
Domanda del libro di testo

Stating Hypotheses In Exercises 11–16, the statement represents a claim. Write its complement and state which is H0 and which is Ha.


p = 0.21

66
views