Save Question 30 (3 points) A manufacturer finds that in a random sample of 100

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Save Question 30 (3 points) A manufacturer finds that in a random sample of 100 of its CD players, 96% have no defects. The manufacturer wishes to make a claim about the percentage of nondefective CD players and is prepared to exaggerate. What is the highest rate of nondefective CD players that the manufacturer could claim under the following condition? His claim would not be rejected at the 0.05 significance level if this sample data were used. Assume that a left-tailed hypothesis test would be performed. O A) 96.6% B) 96.5% 0 C) 98.2% 110 D) 98.4%

Explanation / Answer

Given that,
possibile chances (x)=96
sample size(n)=100
success rate ( p )= x/n = 0.96
success probability,( po )=0.966
failure probability,( qo) = 0.034
null, Ho:p=0.966  
alternate, H1: p<0.966
level of significance, = 0.05
from standard normal table,left tailed z /2 =1.64
since our test is left-tailed
reject Ho, if zo < -1.64
we use test statistic z proportion = p-po/sqrt(poqo/n)
zo=0.96-0.966/(sqrt(0.032844)/100)
zo =-0.3311
| zo | =0.3311
critical value
the value of |z | at los 0.05% is 1.64
we got |zo| =0.331 & | z | =1.64
make decision
hence value of |zo | < | z | and here we do not reject Ho
p-value: left tail - Ha : ( p < -0.33107 ) = 0.37029
hence value of p0.05 < 0.37029,here we do not reject Ho
ANSWERS
---------------
null, Ho:p=0.966
alternate, H1: p<0.966
test statistic: -0.3311
critical value: -1.64
decision: do not reject Ho
p-value: 0.37029

he can use the value proportion values as 96.6% at maximum

[ANSWER] 96.6%

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