### Chi-Square Test for Dice FairnessA gambler complained about the dice, suspecting they were loaded. Each die was rolled 300 times, and the frequencies of each outcome were recorded as follows:| Outcome | 1 | 2 | 3 | 4 | 5 | 6 ||---------|----|----|----|----|----|----|| Observed Frequency \( O \) | 62 | 48 | 61 | 30 | 51 | 48 |The objective is to determine if the dice are unbalanced using a 1% level of significance. If the die is balanced, all outcomes should have the same expected frequency.#### Questions(a) **What is the level of significance?**- Enter the level of significance in the provided box.**State the null and alternate hypotheses:**- \( H_0 \): The distributions are the same.- \( H_1 \): The distributions are different.There are multiple-choice options for hypothesis statements; select the correct one.(b) **Find the value of the chi-square statistic for the sample.**- Round the expected frequencies to at least three decimal places and the test statistic to three decimal places. Enter your answer in the provided box.**Are all the expected frequencies greater than 5?**- Yes- No**What sampling distribution will you use?**- Student’s \( t \)- Uniform- Normal- Chi-square**What are the degrees of freedom?**- Enter the degrees of freedom in the provided box.These analyses guide the decision on whether the dice are fair or loaded based on observed data versus expected outcomes assuming a fair die. **Title: Analyzing Hypothesis Testing in Statistics**Are all the expected frequencies greater than 5? - [ ] Yes - [ ] No **What sampling distribution will you use?** - [ ] Student's t - [ ] Uniform - [ ] Normal - [ ] Chi-square **What are the degrees of freedom?** [Text Box] (c) **Estimate the P-value of the sample test statistic.** - [ ] P-value > 0.100 - [ ] 0.050 < P-value < 0.100 - [ ] 0.025 < P-value < 0.050 - [ ] 0.010 < P-value < 0.025 - [ ] 0.005 < P-value < 0.010 - [ ] P-value < 0.005 (d) **Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis of independence?** - [ ] Since the P-value > α, we fail to reject the null hypothesis. - [ ] Since the P-value > α, we reject the null hypothesis. - [ ] Since the P-value ≤ α, we reject the null hypothesis. - [ ] Since the P-value ≤ α, we fail to reject the null hypothesis. (e) **Interpret your conclusion in the context of the application.** - [ ] At the 1% level of significance, the evidence is sufficient to conclude that the distribution of observed outcomes for the die is different from the expected distribution of a fair die. - [ ] At the 1% level of significance, the evidence is insufficient to conclude that the distribution of observed outcomes for the die is different from the expected distribution of a fair die. **Explanation of Use:**This template guides students through a hypothesis testing procedure using statistical methods. Students must:- Determine if expected frequencies exceed 5, choosing the correct option.- Select an appropriate sampling distribution.- Calculate the degrees of freedom.- Estimate the P-value range for their test statistic.- Decide to reject or fail to reject the null hypothesis based on the P-value.- Interpret the results within the context, considering the significance level.This process aids in understanding the practical application of statistical tests in experiments, emphasizing critical decision-making steps for hypothesis validation.

Let us first test whether “The population of advertising expenses follows normal probability…

A gambler complained about the dice. They seemed to be loaded! The dice were taken off the table and tested one at a time. One die was rolled 300 times and the following frequencies were recorded. Outcome Observed frequency O 4 6 62 48 61 30 51 48 Do these data indicate that the die is unbalanced? Use a 1% level of significance. Hint: If the die is balanced, all outcomes should have the same expected frequency. (a) What is the level of significance?

A gambler complained about the dice. They seemed to be loaded! The dice were taken off the table and tested one at a time. One die was rolled 300 times and the following frequencies were recorded. Outcome Observed frequency O 4 6 62 48 61 30 51 48 Do these data indicate that the die is unbalanced? Use a 1% level of significance. Hint: If the die is balanced, all outcomes should have the same expected frequency. (a) What is the level of significance?

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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