The Practice of Statistics for AP - 4th Edition
4th Edition
ISBN: 9781429245593
Author: Starnes, Daren S., Yates, Daniel S., Moore, David S.
Publisher: Macmillan Higher Education
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Chapter 9.2, Problem 47E
To determine
The corrections to be made in hypothesis test run to check the claim that more than three quarters of school engaged in bullying behavior.
Expert Solution & Answer
Explanation of Solution
Given:A hypothesis test is run to verify the claim that more than three quarters of school engaged in bullying behavior.
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
Z=ˆp−p0√p0(1−p0)n
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
H0:p=0.75Ha:p>0.75
The proportion of students in middle school who engaged in bullying
from sample is
ˆp=445558=0.797
p0=0.75 (from null hypothesis)
The sample of 558 students in middle school are selected randomly
np0=558*0.75=418np0≥10n(1−p0)=558*(1−0.75)=140n(1−p0)≥10
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
Z=ˆp−p0√p0(1−p0)nZ=0.797−0.75√0.75(1−0.75)558=0.0470.018=2.6
The p value is P(Z = 2.6)
using standard Z table we get
P(Z < 2.6) = 0.9953P(Z ≥ 2.6) = 1 – P(Z < 2.6) = 1 – 0.9953 = 0.0047
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
Ch. 9.1 - Prob. 1.1CYUCh. 9.1 - Prob. 1.2CYUCh. 9.1 - Prob. 2.1CYUCh. 9.1 - Prob. 2.2CYUCh. 9.1 - Prob. 2.3CYUCh. 9.1 - Prob. 1ECh. 9.1 - Prob. 2ECh. 9.1 - Prob. 3ECh. 9.1 - Prob. 4ECh. 9.1 - Prob. 5E
Ch. 9.1 - Prob. 6ECh. 9.1 - Prob. 7ECh. 9.1 - Prob. 8ECh. 9.1 - Prob. 9ECh. 9.1 - Prob. 10ECh. 9.1 - Prob. 11ECh. 9.1 - Prob. 12ECh. 9.1 - Prob. 13ECh. 9.1 - Prob. 14ECh. 9.1 - Prob. 15ECh. 9.1 - Prob. 16ECh. 9.1 - Prob. 17ECh. 9.1 - Prob. 18ECh. 9.1 - Prob. 19ECh. 9.1 - Prob. 20ECh. 9.1 - Prob. 21ECh. 9.1 - Prob. 22ECh. 9.1 - Prob. 23ECh. 9.1 - Prob. 24ECh. 9.1 - Prob. 25ECh. 9.1 - Prob. 26ECh. 9.1 - Prob. 27ECh. 9.1 - Prob. 28ECh. 9.1 - Prob. 29ECh. 9.1 - Prob. 30ECh. 9.1 - Prob. 31ECh. 9.1 - Prob. 32ECh. 9.2 - Prob. 1.1CYUCh. 9.2 - Prob. 2.1CYUCh. 9.2 - Prob. 3.1CYUCh. 9.2 - Prob. 33ECh. 9.2 - Prob. 34ECh. 9.2 - Prob. 35ECh. 9.2 - Prob. 36ECh. 9.2 - Prob. 37ECh. 9.2 - Prob. 38ECh. 9.2 - Prob. 39ECh. 9.2 - Prob. 40ECh. 9.2 - Prob. 41ECh. 9.2 - Prob. 42ECh. 9.2 - Prob. 43ECh. 9.2 - Prob. 44ECh. 9.2 - Prob. 45ECh. 9.2 - Prob. 46ECh. 9.2 - Prob. 47ECh. 9.2 - Prob. 48ECh. 9.2 - Prob. 49ECh. 9.2 - Prob. 50ECh. 9.2 - Prob. 51ECh. 9.2 - Prob. 52ECh. 9.2 - Prob. 53ECh. 9.2 - Prob. 54ECh. 9.2 - Prob. 55ECh. 9.2 - Prob. 56ECh. 9.2 - Prob. 57ECh. 9.2 - Prob. 58ECh. 9.2 - Prob. 59ECh. 9.2 - Prob. 60ECh. 9.2 - Prob. 61ECh. 9.2 - Prob. 62ECh. 9.3 - Prob. 1.1CYUCh. 9.3 - Prob. 1.2CYUCh. 9.3 - Prob. 1.3CYUCh. 9.3 - Prob. 2.1CYUCh. 9.3 - Prob. 3.1CYUCh. 9.3 - Prob. 3.2CYUCh. 9.3 - Prob. 63ECh. 9.3 - Prob. 64ECh. 9.3 - Prob. 65ECh. 9.3 - Prob. 66ECh. 9.3 - Prob. 67ECh. 9.3 - Prob. 68ECh. 9.3 - Prob. 69ECh. 9.3 - Prob. 70ECh. 9.3 - Prob. 71ECh. 9.3 - Prob. 72ECh. 9.3 - Prob. 73ECh. 9.3 - Prob. 74ECh. 9.3 - Prob. 75ECh. 9.3 - Prob. 76ECh. 9.3 - Prob. 77ECh. 9.3 - Prob. 78ECh. 9.3 - Prob. 79ECh. 9.3 - Prob. 80ECh. 9.3 - Prob. 81ECh. 9.3 - Prob. 82ECh. 9.3 - Prob. 83ECh. 9.3 - Prob. 84ECh. 9.3 - Prob. 85ECh. 9.3 - Prob. 86ECh. 9.3 - Prob. 87ECh. 9.3 - Prob. 88ECh. 9.3 - Prob. 89ECh. 9.3 - Prob. 90ECh. 9.3 - Prob. 91ECh. 9.3 - Prob. 92ECh. 9.3 - Prob. 93ECh. 9.3 - Prob. 94ECh. 9.3 - Prob. 95ECh. 9.3 - Prob. 96ECh. 9.3 - Prob. 97ECh. 9.3 - Prob. 98ECh. 9.3 - Prob. 99ECh. 9.3 - Prob. 100ECh. 9.3 - Prob. 101ECh. 9.3 - Prob. 102ECh. 9.3 - Prob. 103ECh. 9.3 - Prob. 104ECh. 9.3 - Prob. 105ECh. 9.3 - Prob. 106ECh. 9.3 - Prob. 107ECh. 9.3 - Prob. 108ECh. 9 - Prob. 1CRECh. 9 - Prob. 2CRECh. 9 - Prob. 3CRECh. 9 - Prob. 4CRECh. 9 - Prob. 5CRECh. 9 - Prob. 6CRECh. 9 - Prob. 7CRECh. 9 - Prob. 8CRECh. 9 - Prob. 9CRECh. 9 - Prob. 1PTCh. 9 - Prob. 2PTCh. 9 - Prob. 3PTCh. 9 - Prob. 4PTCh. 9 - Prob. 5PTCh. 9 - Prob. 6PTCh. 9 - Prob. 7PTCh. 9 - Prob. 8PTCh. 9 - Prob. 9PTCh. 9 - Prob. 10PTCh. 9 - Prob. 11PTCh. 9 - Prob. 12PTCh. 9 - Prob. 13PT
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