Please see attached mathematical statistics question and additional info below. If n = 13 and the significance level alpha = 0.025, how to determine c? In Exercise 4.2.18, we found a confidence interval for the variance $\sigma^2$ using the variance $S^2$ of a random sample of size $n$ arising from $N(\mu, \sigma^2)$, where the mean $\mu$ is unknown. In testing $H_0 : \sigma^2 = \sigma_0^2$ against $H_1 : \sigma^2 > \sigma_0^2$, use the critical region defined by \[\frac{(n-1)S^2}{\sigma_0^2} \geq c.\]That is, reject $H_0$ and accept $H_1$ if $S^2 \geq c\sigma_0^2/(n-1)$. If $n = 13$ and the significance level $\alpha = 0.025$, determine $c$. **4.2.18.** Let $ X_1, X_2, \cdots, X_n $ be a random sample from $ N(\mu, \sigma^2) $, where both parameters $\mu$ and $\sigma^2$ are unknown. A confidence interval for $\sigma^2$ can be found as follows.We know that $(n-1)S^2/\sigma^2$ is a random variable with a $\chi^2(n-1)$ distribution. Thus we can find constants $a$ and $b$ so that $P((n-1)S^2/\sigma^2 < b) = 0.975$ and $P(a < (n-1)S^2/\sigma^2 < b) = 0.95$.---**(a)** Show that this second probability statement can be written as\[ P((n-1)S^2/b < \sigma^2 < (n-1)S^2/a) = 0.95. \]**(b)** If $n = 9$ and $s^2 = 7.93$, find a 95% confidence interval for $\sigma^2$.**(c)** If $\mu$ is unknown, how would you modify the preceding procedure for finding a confidence interval for $\sigma^2$?---**Solution.****(a)**\[ a < (n-1)S^2/\sigma^2 \iff \sigma^2 < (n-1)S^2/a; \]and\[ (n-1)S^2/\sigma^2 < b \iff \sigma^2 > (n-1)S^2/b. \]Hence the second probability statement can be written as\[ P((n-1)S^2/b < \sigma^2 < (n-1)S^2/a) = 0.95. \]---**(b)** Since $\alpha = 0.05$, $n = 9$, $b = \chi^2_{\alpha/2,n-1} = \chi^2_{0.025,8} = 17.54$, and \(a = \chi^2_{1-\alpha/

Solution for the above question is given below:

In Exercise 4.2.18 we found a confidence interval for the variance o using the variance S? of a random sample of size n arising fromN (u, o2), where the mean u is unknown. In testing Ho : o? = of against Ho : o? > of, use the critical region defined by n-Ds > c. That is, reject Ho and accept H1 if S > co/(n – 1). If n = 13 and the significance level a = 0.025, determine c.

In Exercise 4.2.18 we found a confidence interval for the variance o using the variance S? of a random sample of size n arising fromN (u, o2), where the mean u is unknown. In testing Ho : o? = of against Ho : o? > of, use the critical region defined by n-Ds > c. That is, reject Ho and accept H1 if S > co/(n – 1). If n = 13 and the significance level a = 0.025, determine c.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

Please answer the question in the picture below to answer the question in the other picture
Can you please explain the process of solving this part of a statistics question? Specifically 0.039(0.961)/98=0.0196
De SFU The analgesic effects of music are well known, but most of the studies have been done with adults and most of the music has been classical. You want to know whether children who choose their own music or audiobook to listen to after a surgery experience less pain and whether that depends on a severity of a surgery. To answer this question, you asked children who underwent minor and major surgeries to listen to music or a story of their choice, or to sit with noise-cancelling headphones for 30 minutes and then to point to a pain face that best illustrated their level of pain. PAIN MEASUREMENT SCALE
need answer and explanation
2) Researchers are interested in whether there is any relationship between a person's IQ (x- variable) and how long they live (y-variable). Answer the questions below by using the data provided. Show your work and use the back of the page if necessary. X Y 10 3 6. 6. 7 4 3 4 a) What type of statistical analysis would be most appropriate to use in this scenario? Please justify your answer. b) Please state the null and alternative hypotheses. c) Please report the results of your statistical analyses and make a decision about whether to reject or fail to reject the null hypothesis Use alpha = .05 (two-tailed). %3D
An independent measures study with n = 6 in each sample produces a sample mean difference of 8 points and Sm1-m2= 2. What is the value for the T statistic? A. 1 B. 2 C. 4 D. 4/-8
The average income of a large sample of households is $63,000 and the s.d. is $7,000. Assume that the data is approximately bell-shaped. What percent of these households have incomes between $42,000 and $77,000? Don’t forget to properly justify your answer using the empirical rule.
Please answer the question in the picture below to answer the question in the other picture
please answer in text form and in proper format answer with must explanation , calculation for each part and steps clearly
Please manually solve this not using excel. Thx
Determine what would be the most appropriate method of Colleting data today and the Scale of Measurement that will be used in a study to “Find the Number of schools that closed down in 2020 due to the CONVIRUS… Briefly explain justification of your choices in Number 1…