Domanda del libro di testo
Cola Weights The displayed results from Exercise 1 are from one-way analysis of variance. What is it about this test that characterizes it as one-way analysis of variance instead of two-way analysis of variance?
109
views
Ch. 12 - Analysis of Variance
Triola14th EditionElementary StatisticsISBN: 9780137366446
Non è quello che usi tu?Cambia libro di testoScegli un libro di testo diverso
TOC.tableOfContents
- Ch. 1 - Introduction to Statistics88
- Ch. 2 - Exploring Data with Tables and Graphs70
- Ch. 3 - Describing, Exploring, and Comparing Data66
- Ch. 4 - Probability112
- Ch. 5 - Discrete Probability Distributions109
- Ch. 6 - Normal Probability Distributions122
- Ch. 7 - Estimating Parameters and Determining Sample Sizes107
- Ch. 8 - Hypothesis Testing75
- Ch. 9 - Inferences from Two Samples94
- Ch. 10 - Correlation and Regression80
- Ch. 11 - Goodness-of-Fit and Contingency Tables29
- Ch. 12 - Analysis of Variance42
Triola14th EditionElementary StatisticsISBN: 9780137366446Non è quello che usi tu?Cambia libro di testo
Capitolo 12, Problema 12.CRE.8c
Win 4 Lottery Shown below is a histogram of digits selected in California’s Win 4 lottery. Each drawing involves the random selection (with replacement) of four digits between 0 and 9 inclusive.
c. Identify the frequencies, then test the claim that the digits are selected from a population in which the digits are all equally likely. Is there a problem with the lottery?
Guida verificata passo dopo passo1
Step 1: Extract the frequencies of each digit from the histogram. The frequencies are as follows: 0 (18), 1 (22), 2 (23), 3 (21), 4 (19), 5 (24), 6 (16), 7 (15), 8 (23), 9 (23).
Step 2: Formulate the null hypothesis (H₀) and alternative hypothesis (H₁). H₀: The digits are equally likely to be selected (uniform distribution). H₁: The digits are not equally likely to be selected.
Step 3: Calculate the expected frequency for each digit under the assumption of uniform distribution. Since there are 10 digits (0-9) and the total frequency is the sum of all observed frequencies, divide the total frequency by 10 to get the expected frequency for each digit.
Step 4: Use the Chi-Square Goodness-of-Fit Test formula: χ² = Σ((Oᵢ - Eᵢ)² / Eᵢ), where Oᵢ is the observed frequency and Eᵢ is the expected frequency for each digit. Compute the χ² statistic using the observed and expected frequencies.
Step 5: Compare the calculated χ² statistic to the critical value from the Chi-Square distribution table at the appropriate degrees of freedom (df = number of categories - 1) and significance level (e.g., α = 0.05). If χ² > critical value, reject H₀ and conclude that the digits are not equally likely. Otherwise, fail to reject H₀.
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:
7mConcetti chiave
Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.
Frequency Distribution
A frequency distribution is a summary of how often each value occurs in a dataset. In the context of the lottery, it shows the number of times each digit from 0 to 9 was drawn. This distribution helps identify patterns or anomalies in the data, such as whether certain digits are drawn more frequently than others.
Video consigliato:
Percorso guidato
06:38
Intro to Frequency Distributions
Chi-Square Goodness of Fit Test
The Chi-Square Goodness of Fit Test is a statistical method used to determine if a sample distribution matches an expected distribution. In this case, it tests the hypothesis that all digits in the lottery are equally likely to be drawn. A significant result would indicate that the observed frequencies differ from what would be expected under the assumption of equal likelihood.
Video consigliato:
Percorso guidato
06:34Step 2: Calculate Test Statistic
Random Sampling
Random sampling is a technique where each member of a population has an equal chance of being selected. In the lottery context, it implies that each digit should have an equal probability of being drawn in each drawing. If the sampling is not random, it could lead to biased results, affecting the fairness of the lottery.
Video consigliato:
Percorso guidato
05:11Sampling Distribution of Sample Proportion
Pratica correlata
Domanda del libro di testo
Quarters Assume that weights of quarters minted after 1964 are normally distributed with a mean of 5.670 g and a standard deviation of 0.062 g (based on U.S. Mint specifications).
b. If 25 quarters are randomly selected, find the probability that their mean weight is greater than 5.675 g.
104
views
Domanda del libro di testo
Normal Quantile Plot The accompanying normal quantile plot was obtained from the longevity times of presidents. What does this graph tell us?
154
views
Domanda del libro di testo
One vs. Two What is the fundamental difference between one-way analysis of variance and two-way analysis of variance?
104
views
Domanda del libro di testo
Win 4 Lottery Shown below is a histogram of digits selected in California’s Win 4 lottery. Each drawing involves the random selection (with replacement) of four digits between 0 and 9 inclusive.
b. Does the display depict a normal distribution? Why or why not? What should be the shape of the histogram?
141
views
Domanda del libro di testo
In Exercises 1–5, refer to the following list of numbers of years that deceased U.S. presidents, popes, and British monarchs lived after their inauguration, election, or coronation, respectively. (As of this writing, the last president is George H. W. Bush, the last pope is John Paul II, and the last British monarch is George VI.) Assume that the data are samples from larger populations.
[Image]
Exploring the Data Include appropriate units in all answers.
e. What is the level of measurement of the data (nominal, ordinal, interval, ratio)?
131
views