(d) Test the hypothesis at the a = 0.10 level of significance with n= 400 students. Assume that the sample mean is still 526 and the sample standard deviation is still 114. Is a sample mean of 526 significantly more than 520? Conduct a hypothesis test using the P-value approach. Find the test statistic.
(d) Test the hypothesis at the a = 0.10 level of significance with n= 400 students. Assume that the sample mean is still 526 and the sample standard deviation is still 114. Is a sample mean of 526 significantly more than 520? Conduct a hypothesis test using the P-value approach. Find the test statistic.
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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Question 10
Answer part D only!!
![A math teacher claims that she has developed a review course that increases the scores of students on the math portion of a college entrance exam. Based on data from the administrator of the exam, scores are normally distributed with a mean (μ) of 520. The teacher obtains a random sample of 2200 students, puts them through the review class, and finds that the mean math score of the 2200 students is 526 with a standard deviation of 114. Complete parts (a) through (d) below.
**(b) Test the hypothesis at α = 0.10 level of significance. Is a mean math score of 526 statistically significantly higher than 520? Conduct a hypothesis test using the P-value approach.**
Find the test statistic.
t₀ = 2.47
(Round to two decimal places as needed.)
Find the P-value.
The P-value is 0.007.
(Round to three decimal places as needed.)
Is the sample mean statistically significantly higher?
- **A.** Yes, because the P-value is less than α = 0.10.
- B. No, because the P-value is greater than α = 0.10.
- C. No, because the P-value is less than α = 0.10.
- D. Yes, because the P-value is greater than α = 0.10.
**(c) Do you think that a mean math score of 526 versus 520 will affect the decision of a school admissions administrator? In other words, does the increase in the score have any practical significance?**
- A. Yes, because the score became more than 1.15% greater.
- **B. No, because every increase in score is practically significant.**
- **C. No, because the score became only 1.15% greater.**
- D. Yes, because every increase in score is practically significant.
**(d) Test the hypothesis at the α = 0.10 level of significance with n = 400 students. Assume that the sample mean is still 526 and the sample standard deviation is still 114. Is a sample mean of 526 significantly more than 520? Conduct a hypothesis test using the P-value approach.**
Find the test statistic.
t₀ = [blank]
(Round to two decimal places as needed.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1c1e1001-e949-4573-be36-b00de430b7d7%2F26bbb151-0e03-4888-926a-82e74232b022%2Fehuhanb_processed.png&w=3840&q=75)
Transcribed Image Text:A math teacher claims that she has developed a review course that increases the scores of students on the math portion of a college entrance exam. Based on data from the administrator of the exam, scores are normally distributed with a mean (μ) of 520. The teacher obtains a random sample of 2200 students, puts them through the review class, and finds that the mean math score of the 2200 students is 526 with a standard deviation of 114. Complete parts (a) through (d) below.
**(b) Test the hypothesis at α = 0.10 level of significance. Is a mean math score of 526 statistically significantly higher than 520? Conduct a hypothesis test using the P-value approach.**
Find the test statistic.
t₀ = 2.47
(Round to two decimal places as needed.)
Find the P-value.
The P-value is 0.007.
(Round to three decimal places as needed.)
Is the sample mean statistically significantly higher?
- **A.** Yes, because the P-value is less than α = 0.10.
- B. No, because the P-value is greater than α = 0.10.
- C. No, because the P-value is less than α = 0.10.
- D. Yes, because the P-value is greater than α = 0.10.
**(c) Do you think that a mean math score of 526 versus 520 will affect the decision of a school admissions administrator? In other words, does the increase in the score have any practical significance?**
- A. Yes, because the score became more than 1.15% greater.
- **B. No, because every increase in score is practically significant.**
- **C. No, because the score became only 1.15% greater.**
- D. Yes, because every increase in score is practically significant.
**(d) Test the hypothesis at the α = 0.10 level of significance with n = 400 students. Assume that the sample mean is still 526 and the sample standard deviation is still 114. Is a sample mean of 526 significantly more than 520? Conduct a hypothesis test using the P-value approach.**
Find the test statistic.
t₀ = [blank]
(Round to two decimal places as needed.)
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