A common characterization of obese individuals is that their body mass index is

Question

A common characterization of obese individuals is that their body mass index is at least 30 [BMI weight/(height)2, where height is in meters and weight is in kilograms]. An article reported that in a sample of female workers, 268 had BMIs of less than 25, 156 had BMIs that were at least 25 but less than 30, and 121 had BMIs exceeding 30. Is there compelling evidence for concluding that more than 20% of the individuals in the sampled population are obese? (a) State the appropriate hypotheses with a significance level of 0.05. Ho: p>0.20 Hai p = 0.20 O Ho: p=0.20 Ha: p 0.20 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) P-value

Explanation / Answer

Given that,
possibile chances (x)=121
sample size(n)=545
success rate ( p )= x/n = 0.222
success probability,( po )=0.2
failure probability,( qo) = 0.8
null, Ho:p<0.2  
alternate, H1: p>0.2
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=0.22202-0.2/(sqrt(0.16)/545)
zo =1.2851
| zo | =1.2851
critical value
the value of |z | at los 0.05% is 1.64
we got |zo| =1.285 & | z | =1.64
make decision
hence value of |zo | < | z | and here we do not reject Ho
p-value: right tail - Ha : ( p > 1.28506 ) = 0.09939
hence value of p0.05 < 0.09939,here we do not reject Ho
ANSWERS
---------------
test statistic: 1.28
p-value: 0.0994

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