Concept explainers
The corrections to be made in hypothesis test run to check the claim that more than three quarters of school engaged in bullying behavior.
Explanation of Solution
Given:A hypothesis test is run to verify the claim that more than three quarters of school engaged in bullying behavior.
Sample size = n = 558
Number of students who behaved with physical aggression in last 30 days = 445
Concept used:The conditions to satisfy to run one sample Z test
1) The sample should be random
2) np = 10
3) n(1-p) = 10
4) There should be at least 10% of people of population in the sample.
Test statistic
If p value is less than the level of significance, we have sufficient evidence to reject the null hypothesis.
Calculation:Let p be the proportion of students in middle school who engaged in bullying
Null Hypothesis and alternate hypothesis are shown below
The proportion of students in middle school who engaged in bullying
from sample is
The sample of 558 students in middle school are selected randomly
Here there will be at least 5580 students in middle school, so 10% condition is satisfied.
So here we run a one sample Z test. Test statistic is calculated as shown below
The p value is P(Z = 2.6)
using standard Z table we get
The probability that null hypothesis is true is 0.0047
The p value(0.0047) is less than level of significance 0.05, So we have sufficient evidence to reject the null hypothesis.
Conclusion:
At 5% level of significance, we have sufficient evidence that more than three quarters of school students engaged in bullying behavior.
Chapter 9 Solutions
The Practice of Statistics for AP - 4th Edition
Additional Math Textbook Solutions
Basic Business Statistics, Student Value Edition (13th Edition)
Statistical Reasoning for Everyday Life (5th Edition)
Fundamentals of Statistics (5th Edition)
- MATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th...StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C...StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage Learning
- Elementary Statistics: Picturing the World (7th E...StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman