### Chi-Square Goodness-of-Fit Test A chi-square goodness-of-fit test using a significance level of $\alpha = 0.05$ was conducted to investigate whether the number of babies born in a town is uniformly distributed across the months of the year. The test produced a test statistic of $\chi^{2} = 5.6$ with a corresponding $p$-value of 0.90. Which of the following is correct?- **A)** Births are uniformly distributed across months.- **B)** There is sufficient evidence to suggest that the distribution of births is not uniformly distributed across months.- **C)** There is sufficient evidence to suggest that the distribution of births is uniformly distributed across months.- **D)** There is insufficient evidence to suggest that the distribution of births is not uniformly distributed across months.- **E)** There is insufficient evidence to suggest that the distribution of births is uniformly distributed across months.### Explanation:In this scenario, we are dealing with a chi-square goodness-of-fit test. The null hypothesis for this test states that the distribution of births is uniformly distributed across the months. The alternative hypothesis states that it is not uniformly distributed. The test statistic $ \chi^{2} = 5.6 $ and the $ p$-value is 0.90. Since the $ p$-value (0.90) is greater than the significance level $ \alpha = 0.05 $, we fail to reject the null hypothesis. Therefore, there is insufficient evidence to suggest that the distribution of births is not uniformly distributed across the months.Thus, the correct statement is:**D) There is insufficient evidence to suggest that the distribution of births is not uniformly distributed across months.** ### Research Claim and Hypothesis TestingA researcher is investigating the claim that the proportion of television viewers who identify one of four shows as their favorite is the same for all four shows. A $\chi^2$ (chi-square) goodness-of-fit test is used to evaluate this claim at a significance level of $\alpha = 0.05$. The test produced a test statistic $\chi^2 = 8.95$ with a corresponding p-value of 0.03. Which of the following is correct?### Answer Choices**A.** There is sufficient evidence to reject the null hypothesis at the 0.05 level since the test statistic is greater than the p-value.**B.** There is not sufficient evidence to reject the null hypothesis at the 0.05 level since the test statistic is greater than the p-value.**C.** There is sufficient evidence to reject the null hypothesis at the 0.05 level since the p-value is less than the significance level.**D.** There is not sufficient evidence to reject the null hypothesis at the 0.05 level since the p-value is less than the significance level.**E.** There is sufficient evidence to reject the null hypothesis at the 0.05 level since the test statistic is greater than the significance level.### Explanation of Chi-Square Goodness-of-Fit TestThe chi-square ($\chi^2$) goodness-of-fit test is used to determine whether there is a significant difference between the expected frequencies and the observed frequencies in one or more categories.1. **Null Hypothesis ($H_0$)**: The proportion of television viewers who identify one of four shows as their favorite is the same for all four shows.2. **Alternative Hypothesis ($H_a$)**: The proportion of television viewers who identify one of four shows as their favorite is not the same for all four shows.### Decision Rule- **Significance Level ($\alpha$)**: 0.05When conducting a hypothesis test, compare the p-value with the significance level:- **If p-value $\leq \alpha$**: Reject the null hypothesis ($H_0$)- **If p-value $> \alpha$**: Do not reject the null hypothesis ($H_0$)Given:- Test statistic $\chi^2 = 8.95$-

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A chi-square goodness-of-fit test using a significance level of a = 0.05 was conducted to investigate whether the number of babies born in a town is uniformly distributed across the months of the year. The test produced a test statistic of x² = 5.6 with a corresponding p-value of 0.90. Which of the following is correct? A Births are uniformly distributed across months. There is sufficient evidence to suggest that the distribution of births is not uniformly distributed across months. C There is sufficient evidence to suggest that the distribution of births is uniformly distributed across months. There is insufficient evidence to suggest that the distribution of births is not uniformly distributed across months. E There is insufficient evidence to suggest that the distribution of births is uniformly distributed across months.

A chi-square goodness-of-fit test using a significance level of a = 0.05 was conducted to investigate whether the number of babies born in a town is uniformly distributed across the months of the year. The test produced a test statistic of x² = 5.6 with a corresponding p-value of 0.90. Which of the following is correct? A Births are uniformly distributed across months. There is sufficient evidence to suggest that the distribution of births is not uniformly distributed across months. C There is sufficient evidence to suggest that the distribution of births is uniformly distributed across months. There is insufficient evidence to suggest that the distribution of births is not uniformly distributed across months. E There is insufficient evidence to suggest that the distribution of births is uniformly distributed across months.

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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Researchers measured skulls from different time periods in an attempt to determine whether interbreeding of cultures occurred. Results are given below. Assume that both samples are independent simple random samples from populations having normal distributions. Use a 0.05 significance level to test the claim that the variation of maximal skull breadths in 4000 B.C. is the same as the variation in A.D. 150. n x 4000 B.C. 30 131.92 mm A.D. 150 30 136.92 mm 5.16 mm 5.31 mm What are the null and alternative hypotheses? Hoo #0₂ H₁:0₁ = 0₂ 2 2 OC H₂O²=0² H₁ <0 2 2 Identify the test statistic. F= (Round to two decimal places as needed.) B. H₂O=0₂ H₁0² #03 *D. Hollo² = 0² 2 2 2 H₁0₁20₂ 2