A survey of 9,000 office workers included several questions about office relatio
ID: 3173739 • Letter: A
Question
A survey of 9,000 office workers included several questions about office relationships. Of the respondents, 2, 331 reported that bosses scream at employees. (a) If you wish to test the claim that more than 1/4 of people say bosses scream at employees, what should the null hypothesis and alternative hypothesis be? (b) Using a 0.05 significance level to test the claim, (i) find the value of the test statistic, and its P-value. (ii) find the critical region for the test statistic. (c) What do you conclude?Explanation / Answer
Given that,
possibile chances (x)=2331
sample size(n)=9000
success rate ( p )= x/n = 0.259
success probability,( po )=0.25
failure probability,( qo) = 0.75
null, Ho:p=0.25
alternate, H1: p>0.25
level of significance, = 0.05
from standard normal table,right tailed z /2 =1.64
since our test is right-tailed
reject Ho, if zo > 1.64
we use test statistic z proportion = p-po/sqrt(poqo/n)
zo=0.259-0.25/(sqrt(0.1875)/9000)
zo =1.9718
| zo | =1.9718
critical value
the value of |z | at los 0.05% is 1.64
we got |zo| =1.972 & | z | =1.64
make decision
hence value of | zo | > | z | and here we reject Ho
p-value: right tail - Ha : ( p > 1.9718 ) = 0.02432
hence value of p0.05 > 0.02432,here we reject Ho
ANSWERS
---------------
null, Ho:p=0.25
alternate, H1: p>0.25
test statistic: 1.9718
critical value: 1.64
decision: reject Ho
p-value: 0.02432
more than 1/4 people say bosses scream at employees
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