**Problem Statement:**To test $ H_0: \sigma = 2.4 $ versus $ H_1: \sigma > 2.4 $, a random sample of size $ n = 16 $ is obtained from a population that is known to be normally distributed. Complete parts (a) through (d).---**(a)** If the sample standard deviation is determined to be $ s = 2.2 $, compute the test statistic.\[ \chi^2_0 = 12.604 \quad \text{(Round to three decimal places as needed.)} \]**(b)** If the researcher decides to test this hypothesis at the $ \alpha = 0.01 $ level of significance, determine the critical value.\[ \chi^2_{0.01} = \quad \text{(Round to three decimal places as needed.)} \]---*Options to Get Help:*- **Help me solve this**- **View an example**- **Get more help** *Actions Available:*- **Clear all**- **Check answer****Screenshot Details:**The screenshot shows an educational interface on a laptop with the problem statement and parts (a) and (b). There are options to get help and actions to clear responses or check the answer. **Graphical/Visual Elements:**There are no graphs or diagrams in this image. The interface includes options and action buttons but no visual aids related to the problem-solving.

Given data : sample size, n = 16 population standard deviation,σ= 2.4 sample…

Answered: To test Ho: o=2.4 versus H₁: o>2.4, a…

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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An ecologist is studying the impact of local polluted waters on the growth of alligators. The length of adult male alligators typically follows a normal distribution with a standard deviation of 2 feet. The ecologist wants to estimate the mean length of this population of alligators. Suppose she samples n alligators at random and uses the sample mean, X to as an estimator for u. a. What is the bias and variance of the estimator? (Note, these may be a function of n.) b. If n = 4, what is the probability that the estimator is within one foot of the true mean? (I.e. find P(|X – µ| < 1). c. What sample size, n, is required for the estimator to be within one foot of the true mean with 95% probability? (I.e. find the value of n that satisfies P(|X – µ| < 1) = 0.95.) d. Suppose the ecologist ends up sampling n = 9 alligators and calculates a sample mean of ī = 10.4 feet. Construct a 95% confidence interval for the population mean. e. Give an interpretation for the interval obtained in (d).
A random sample of 84 eighth grade students' scores on a national mathematics assessment test has a mean score of 290. This test result prompts a state school administrator to declare that the mean score for the state's eighth graders on this exam is more than 285. Assume that the population standard deviation is 36. At α=0.07, is there enough evidence to support the administrator's claim? Complete parts (a) through (e).
A sample of size 115 will be drawn from a population with mean 48 and standard deviation 12. Use the TI-83 Plus/TI-84 Plus calculator. Part 1 of 2 (a) Find the probability that x will be less than 45. Round the answer to at least four decimal places. The probability that x will be less than 45 is 0.0037 Part: 1/ 2 Part 2 of 2 (b) Find the 25 th percentile of x. Round the answer to at least two decimal places. The 25 th percentile is Skip Part Check Save For Later Subm © 2022 McGraw Hill LLC. All Rights Reserved. Terms of Use | Privacy Cente ......... .........a ... MacBook Air DII 80 F10 F7 F9 esc F4 F6 F2 F3 F1 @ 23 $ % & 1 2 3 4 6. 8.
A random sample of 90 eighth grade students' scores on a national mathematics assessment test has a mean score of 288. This test result prompts a state school administrator to declare that the mean score for the state's eighth graders on this exam is more than 280. Assume that the population standard deviation is 36. At α = 0.08, is there enough evidence to support the administrator's claim? Complete parts (a) through (e). (a) Write the claim mathematically and identify Ho and H₂. Choose the correct answer below. A. Ho: μ = 280 (claim) Ha:μ>280 Ho:μ≤280 Ha: μ> 280 (claim) B. Ho: μ = 280 P-value = (b) Find the standardized test statistic z. z = 2.11 (Round to two decimal places as needed.) (c) Find the P-value. E. Ho: μ≤280 (claim) Ha:μ>280 Ha: μ> 280 (claim) (Round to three decimal places as needed.) C. Ho: μ ≥280 (claim) Ha:μ< 280 F. Ho: μ< 280 H₂:μ ≥280 (claim)
A random sample of 82 eighth grade students' scores on a national mathematics assessment test has a mean score of 286. This test result prompts a state school administrator to declare that the mean score for the state's eighth graders on this exam is more than 280. Assume that the population standard deviation is 38. At α = 0.05, is there enough evidence to support the administrator's claim? Complete parts (a) through (e). (a) Write the claim mathematically and identify Ho and H₂. Choose the correct answer below. O A. Ho: ≤280 (claim) H₂:μ>280 O D. Ho: μ≤280 Ha: μ> 280 (claim) B. Ho: μ280 OF. Ho: μ = 280 H₂: µ>280 (claim)
A population has parameters u = 189.5 and o = 61.9. You intend to draw a random sample of size n = 113. What is the mean of the distribution of sample means? What is the standard deviation of the distribution of sample means? (Report answer accurate to 2 decimal places.)
In the year 2033, Sarai Patterson is a leading traveling nurse. Sarai is interested in reducing the mean recovery time for patients after experiencing a serious injury (assume recovery times are normally distributed). Suppose the mean recovery time is presently 8.6 months. Sarai takes a random sample of 46 patients that have experienced serious injury to participate in a new treatment program and finds the sample mean is 8.1 months and a sample standard deviation of 1.2 months. Using α = 0.05, answer the following questions. a) What is the setup for your null and alternative hypothesis? b) What is the value of the test statistic? c) What is/are the critical value(s)?
A random sample of n1 = 49 measurements from a population with population standard deviation ?1 = 3 had a sample mean of x1 = 9. An independent random sample of n2 = 64 measurements from a second population with population standard deviation ?2 = 4 had a sample mean of x2 = 11. Test the claim that the population means are different. Use level of significance 0.01.
A population has parameters u = 239.9 and o = 18.4. You intend to draw a random sample of size n = 76. What is the mean of the distribution of sample means? What is the standard deviation of the distribution of sample means? (Report answer accurate to 2 decimal places.)
A random sample of 82 eighth grade students' scores on a national mathematics assessment test has a mean score of 286. This test result prompts a state school administrator to declare that the mean score for the state's eighth graders on this exam is more than 280. Assume that the population standard deviation is 38. At α = 0.05, is there enough evidence to support the administrator's claim? Complete parts (a) through (e). (a) Write the claim mathematically and identify Ho and H₂. Choose the correct answer below. O A. Ho: μ≤280 (claim) H₂:μ>280 O D. Ho: μ≤280 Ha: μ> 280 (claim) O B. Ho: μ280 OF. Ho: μ = 280 Ha: μ>280 (claim)
Q3: The effective life of a component used in a jet-turbine aircraft engine is a random variable with mean 5000 hours and standard deviation 40 hours. The distribution of effective life is fairly close to a normal component that increases the mean life to 5030 hours and decreases the standard deviation to 30 hours. distribution. The engine manufacturer introduces an improvement into the manufacturing process for this Suppose that a random sample of n₁ = 16 components is selected from the "Old" process and a random sample of n₂ = 25 components is selected from the "Improved" process. What is the probability that difference in the two-sample means that the old and improved processes can be regarded as independent populations. 5 X₂X₁ is at least 15 hours? Assume
A population has a mean of 300 and a standard deviation of 40. Suppose a simple random sample of size 100 is selected and x¯ is used to estimate μ .What is the probability that the sample mean will be within +/- 5 of the population mean?

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