**Problem Statement:**A random sample of 75 eighth-grade students' scores on a national mathematics assessment test has a mean score of 278. 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 270. Assume that the population standard deviation is 34. At \(\alpha = 0.15\), is there enough evidence to support the administrator's claim? Complete parts (a) through (e).**Tasks:**(a) **Write the claim mathematically and identify \( H_0 \) and \( H_a \). Choose the correct answer below.**A. \( H_0: \mu < 270 \) \( H_a: \mu \ge 270 \) (claim)B. \( H_0: \mu \le 270 \) (claim) \( H_a: \mu > 270 \)C. \( H_0: \mu \ge 270 \) (claim) \( H_a: \mu < 270 \)D. \( H_0: \mu = 270 \) (claim) \( H_a: \mu \neq 270 \)E. \( H_0: \mu \le 270 \) \( H_a: \mu > 270 \) (claim)F. \( H_0: \mu = 270 \) \( H_a: \mu > 270 \) (claim)---(b) **Find the standardized test statistic \( z \), and its corresponding area.**\( z = \_\_\_ \) (Round to two decimal places as needed.)---(c) **Find the P-value.**P-value = \_\_\_ (Round to three decimal places as needed.)---**Explanation:**To determine which hypothesis to test, we need to consider the claim made by the administrator. The claim is that the mean score for the state's eighth graders is more than 270.From the options provided, the correct setup for the null (\( H_0 \)) and alternative (\( H_a \)) hypotheses can be identified:- **Null Hypothesis (\( H_0 \))**: \(\mu \le 270\)- **Alternative Hypothesis (\( H_a \))**: \(\mu > 270\) (claim)Thus, the correct answer for ### Hypothesis Testing: Mean Score Analysis of Eighth Grade StudentsA random sample of 75 eighth grade students' scores on a national mathematics assessment test has been collected. The sample has a mean score of 278. This result has prompted a state school administrator to declare that the mean score for the state's eighth graders on this exam is more than 270. Given the population standard deviation is 34 and α = 0.15, we will determine if there is enough evidence to support the administrator's claim. Follow the steps below:#### Steps to Perform Hypothesis Testing1. **State the Hypothesis:** - Null Hypothesis (H₀): μ ≤ 270 - Alternative Hypothesis (H₁): μ > 2702. **Calculate the Test Statistic (z):** \[ z = \frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}}} \] Where: - \(\bar{x}\) is the sample mean - μ is the population mean stated in the null hypothesis - σ is the population standard deviation - n is the sample size Substitute the given values: \[ z = \frac{278 - 270}{\frac{34}{\sqrt{75}}} \] (Round to two decimal places as needed.)3. **Find the P-value:** - Determine the probability that the test statistic is at least as extreme as the observed value under the null hypothesis. (Round to three decimal places as needed.)4. **Decision Rule:** - Compare the P-value with the significance level (α = 0.15): - If P-value < α, reject H₀ - If P-value ≥ α, fail to reject H₀ Choose the appropriate decision: - ☐ Fail to reject H₀ - ☐ Reject H₀5. **Conclusion:** - Interpret the decision in the context of the original claim: At the 15% significance level, there is ☐ enough evidence to ☐ the administrator's claim that the mean score for the state's eighth graders on the exam is more than 270.By following these steps, you can determine if the data provides enough evidence to support the administrator's claim that the mean score for the state's eighth graders

Name: **Problem Statement:**A random sample of 75 eighth-grade students' sc
Uploaded: 2024-03-20T07:07:12.000Z
Channel: Bartleby
Description: **Problem Statement:**A random sample of 75 eighth-grade students' scores on a national mathematics assessment test has a mean score of 278. This test result prompts a state school administrator to declare that the mean score for the state's eighth

Answered: Image /qna-images/answer/f81877e3-88c9-4015-bfd6-c9bb33dc3b7f.jpg

Math

Statistics

A random sample of 75 eighth grade students' scores on a national mathematics assessment test has a mean score of 278. 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 270. Assume that the population standard deviation is 34. At a = 0.15, is there enough evidence to support the administrator's claim? Complete parts (a) through (e). (Round to two decimal places as needed.) (c) Find the P-value. P-value = (Round to three decimal places as needed.) (d) Decide whether to reject or fail to reject the null hypothesis. Fail to reject Ho O Reject Ho (e) Interpret your decision in the context of the original claim. At the 15% significance level, there V enough evidence to V the administrator's claim that the mean score for the state's eighth graders on the exam is more than 270.

A random sample of 75 eighth grade students' scores on a national mathematics assessment test has a mean score of 278. 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 270. Assume that the population standard deviation is 34. At a = 0.15, is there enough evidence to support the administrator's claim? Complete parts (a) through (e). (Round to two decimal places as needed.) (c) Find the P-value. P-value = (Round to three decimal places as needed.) (d) Decide whether to reject or fail to reject the null hypothesis. Fail to reject Ho O Reject Ho (e) Interpret your decision in the context of the original claim. At the 15% significance level, there V enough evidence to V the administrator's claim that the mean score for the state's eighth graders on the exam is more than 270.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

Suppose that the heights of adult women in the United States are normally distributed with a mean of 65 inches and a standard deviation of 2.5 inches. Jennifer is taller than 70% of the population of U.S. women. How tall (in inches) is Jennifer? Carry your intermediate computations to at least four decimal places. Round your answer to one decimal place.
Calcium levels in people are normally distributed with a mean of 9.4 and a standard deviation of 0.4 . Individuals with calcium levels in the bottom 10% dL of the population are considered to have low calcium levels. Find the calcium level that is the borderline between low calcium levels and those not considered low. Carry your intermediate computations to at least four decimal places. Round your answer to one decimal place.
For a data set of the pulse rates for a sample of adult females, the lowest pulse rate is 37 beats per minute, the mean of the listed pulse rates is x=73.0 beats per minute, and their standard deviation is s=20.5 beats per minute. a. What is the difference between the pulse rate of 37 beats per minute and the mean pulse rate of the females? b. How many standard deviations is that [the difference found in part (a)]? c. Convert the pulse rate of 37 beats per minutes to a z score. d. If we consider pulse rates that convert to z scores between −2and 2 to be neither significantly low nor significantly high, is the pulse rate of 37 beats per minute significant?
The data set of size 40 has mean 15 and standard deviation 2. Approximately how many observations lie between 13 and 17?
For a data set of the pulse rates for a sample of adult females, the lowest pulse rate is 35 beats per minute, the mean of the listed pulse rates is x = 71.0 beats per minute, and their standard deviation is s= 14.2 beats per minute. a. What is the difference between the pulse rate of 35 beats per minute and the mean pulse rate of the females? b. How many standard deviations is that [the difference found in part (a)]? c. Convert the pulse rate of 35 beats per minutes to a z score. d. If we consider pulse rates that convert to z scores between -2 and 2 to be neither significantly low nor significantly high, is the pulse rate of 35 beats per minute significant? a. The difference is beats per minute. (Type an integer or a decimal. Do not round.) b. The difference is standard deviations, (Round to two decimal places as needed.) c. The z score is z=. (Round to two decimal places as needed.) d. The lowest pulse rate is
For a data set of the pulse rates for a sample of adult females, the lowest pulse rate is 37 beats perminute, the mean of the listed pulse rates is x=77.0 beats per minute, and their standard deviation is s=24.8 beats per minute. a. What is the difference between the pulse rate of 37 beats per minute and the mean pulse rate of the females? b. How many standard deviations is that [the difference found in part (a)]? c. Convert the pulse rate of 37 beats per minutes to a z score. d. If we consider pulse rates that convert to z scores between −2 and 2 to be neither significantly low nor significantly high, is the pulse rate of 37 beats per minute significant?
For a data set of the pulse rates for a sample of adult females, the lowest pulse rate is 34 beats per minute, the mean of the listed pulse rates is x=72.0 beats per minute, and their standard deviation is s=13.8 beats per minute. a. What is the difference between the pulse rate of 34 beats per minute and the mean pulse rate of the females? b. How many standard deviations is that [the difference found in part (a)]? c. Convert the pulse rate of 34 beats per minutes to a z score. d. If we consider pulse rates that convert to z scores between −2 and 2 to be neither significantly low nor significantly high, is the pulse rate of 34 beats per minute significant?
A random sample of 88 eighth grade students' scores on a national mathematics assessment test has a mean score of 281. 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 275. Assume that the population standard deviation is 40. At a = 0.03, is there enough evidence to support the administrator's claim? Complete parts (a) through (e). ..... (a) Write the claim mathematically and identify H, and Ha. Choose the correct answer below. ' O A. Ho: µs 275 Hai H> 275 (claim) B. H0: μ 275 c. Ho: μ 275 Ο Ε. Ho: μ = 275 Ha: µ> 275 (claim) OF H : μ2 275 (claim) Ha: µ<275
The reading speed of second grade students in a large city is approximately normal, with mean of 91 words per minute (wpm) and a standard deviation of 10 wpm. Complete parts (a) through (f). O B. If 100 different students were chosen from this population, we would expect to read exactly 95 words per minute. O C. If 100 different students were chosen from this population, we would expect to read less than 95 words per minute. (b) What is the probability that a random sample of 13 second grade students from the city results in a mean reading rate of more than 95 words per minute? The probability is 0.0746. (Round to four decimal places as needed.) Interpret this probability. Select the correct choice below and fill in the answer box within your choice. O A. If 100 independent samples of n = 13 students were chosen from this population, we would expect sample(s) to have a sample mean reading rate of exactly 95 words per minute. O B. If 100 independent samples of n = 13 students were…
Use z scores to compare the given values. The tallest living man at one time had a height of 238 cm. The shortest living man at that time had a height of 142.4 cm. Heights of men at that time had a mean of 175.45 cm and a standard deviation of 5.59 cm. Which of these two men had the height that was more extreme? ... Since the z score for the tallest man is z = 0 and the z score for the shortest man is z = the man had the height that was Im- more extreme. (Round to two decimal places.) shortest tallest
Solve for C)
Suppose that the antenna lengths of woodlice are approximately normally distributed with a mean of 0.22 inches and a standard deviation of 0.05 inches. What proportion of woodlice have antenna lengths that are at most 0.18 inches? Round your answer to at least four decimal places.