3. A college entrance exam company determined that a score of 22 on the mathematics portion of the exam suggests that a student is ready for college-level mathematics. To achieve this goal, the company recommends that students take a core curriculum of math courses in high school. Suppose a random sample of 250 students who completed this core set of courses results in a mean math score of 22.5 on the college entrance exam with a standard deviation of 3.5. Do these results suggest that students who complete the core curriculum are ready for college-level mathematics? That is, are they scoring above 22 on the math portion of the exam? Complete parts a) through d) below. a) State the appropriate null and alternative hypotheses. Fill in the correct answers below. The appropriate null and alternative hypotheses are Ho: (1) (2) versus H;: (3) (4) b) Verify that the requirements to perform the test using the t-distribution are satisfied. Check all that apply. A. The students were randomly sampled. B. The students' test scores were independent of one another. O c. The sample size is larger than 30. D. None of the requirements are satisfied. c) Use the P-value approach at the a= 0.05 level of significance to test the hypotheses in part (a). Identify the test statistic. to = (Round to two decimal places as needed.) Identify the P-value.
3. A college entrance exam company determined that a score of 22 on the mathematics portion of the exam suggests that a student is ready for college-level mathematics. To achieve this goal, the company recommends that students take a core curriculum of math courses in high school. Suppose a random sample of 250 students who completed this core set of courses results in a mean math score of 22.5 on the college entrance exam with a standard deviation of 3.5. Do these results suggest that students who complete the core curriculum are ready for college-level mathematics? That is, are they scoring above 22 on the math portion of the exam? Complete parts a) through d) below. a) State the appropriate null and alternative hypotheses. Fill in the correct answers below. The appropriate null and alternative hypotheses are Ho: (1) (2) versus H;: (3) (4) b) Verify that the requirements to perform the test using the t-distribution are satisfied. Check all that apply. A. The students were randomly sampled. B. The students' test scores were independent of one another. O c. The sample size is larger than 30. D. None of the requirements are satisfied. c) Use the P-value approach at the a= 0.05 level of significance to test the hypotheses in part (a). Identify the test statistic. to = (Round to two decimal places as needed.) Identify the P-value.
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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![**3. A college entrance exam company determined that a score of 22 on the mathematics portion of the exam suggests that a student is ready for college-level mathematics. To achieve this goal, the company recommends that students take a core curriculum of math courses in high school. Suppose a random sample of 250 students who completed this core set of courses results in a mean math score of 22.5 on the college entrance exam with a standard deviation of 3.5. Do these results suggest that students who complete the core curriculum are ready for college-level mathematics? That is, are they scoring above 22 on the math portion of the exam? Complete parts (a) through (d) below.**
**a) State the appropriate null and alternative hypotheses. Fill in the correct answers below.**
The appropriate null and alternative hypotheses are
\(H_0\): (1) ____________ (2) ____________ versus
\(H_1\): (3) ____________ (4) ____________ .
**b) Verify that the requirements to perform the test using the t-distribution are satisfied. Check all that apply.**
- [ ] A. The students were randomly sampled.
- [ ] B. The students' test scores were independent of one another.
- [ ] C. The sample size is larger than 30.
- [ ] D. None of the requirements are satisfied.
**c) Use the P-value approach at the \(\alpha = 0.05\) level of significance to test the hypotheses in part (a).**
- Identify the test statistic.
\(t_0 =\) ____________ (Round to two decimal places as needed.)
- Identify the P-value.
P-value = ____________ (Round to three decimal places as needed.)
**d) Write a conclusion based on the results. Choose the correct answer below.**
(5) ____________ the null hypothesis and claim that there (6) ____________ sufficient evidence to conclude that the population mean is (7) ____________ than 22.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff922576e-5855-4e0f-8aa5-b9c0343e784e%2F88a1d1b3-f634-43d0-b055-e1da5af456cf%2Frftvwmj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**3. A college entrance exam company determined that a score of 22 on the mathematics portion of the exam suggests that a student is ready for college-level mathematics. To achieve this goal, the company recommends that students take a core curriculum of math courses in high school. Suppose a random sample of 250 students who completed this core set of courses results in a mean math score of 22.5 on the college entrance exam with a standard deviation of 3.5. Do these results suggest that students who complete the core curriculum are ready for college-level mathematics? That is, are they scoring above 22 on the math portion of the exam? Complete parts (a) through (d) below.**
**a) State the appropriate null and alternative hypotheses. Fill in the correct answers below.**
The appropriate null and alternative hypotheses are
\(H_0\): (1) ____________ (2) ____________ versus
\(H_1\): (3) ____________ (4) ____________ .
**b) Verify that the requirements to perform the test using the t-distribution are satisfied. Check all that apply.**
- [ ] A. The students were randomly sampled.
- [ ] B. The students' test scores were independent of one another.
- [ ] C. The sample size is larger than 30.
- [ ] D. None of the requirements are satisfied.
**c) Use the P-value approach at the \(\alpha = 0.05\) level of significance to test the hypotheses in part (a).**
- Identify the test statistic.
\(t_0 =\) ____________ (Round to two decimal places as needed.)
- Identify the P-value.
P-value = ____________ (Round to three decimal places as needed.)
**d) Write a conclusion based on the results. Choose the correct answer below.**
(5) ____________ the null hypothesis and claim that there (6) ____________ sufficient evidence to conclude that the population mean is (7) ____________ than 22.
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