need help solving. Show steps please! A drug company is considering marketing a
ID: 3323667 • Letter: N
Question
need help solving. Show steps please! A drug company is considering marketing a new local anesthetic. The effective time of the anesthetic the drug company is currently producing has a normal distribution with an average of 7.4 minutes with a standard deviation of 1.2 minutes. The precision of effective time is extremely important to surgeons during operations, expecting precisely at 7.4 minutes A sample of size 36 results in a sample mean of 7.1 minutes and standard deviation of 0.9 minute. Is the standard deviation of new drug at 1.2 minutes at 0.05 significance level?Explanation / Answer
Given that,
population standard deviation ()=1.2
sample standard deviation (s) =0.9
sample size (n) = 36
we calculate,
population variance (^2) =1.44
sample variance (s^2)=0.81
null, Ho: =1.2
alternate, H1 : !=1.2
level of significance, = 0.05
from standard normal table, two tailed ^2 /2 =49.802
since our test is two-tailed
reject Ho, if ^2 o < - OR if ^2 o > 49.802
we use test statistic chisquare ^2 =(n-1)*s^2/o^2
^2 cal=(36 - 1 ) * 0.81 / 1.44 = 35*0.81/1.44 = 19.69
| ^2 cal | =19.69
critical value
the value of |^2 | at los 0.05 with d.f (n-1)=35 is 49.802
we got | ^2| =19.69 & | ^2 | =49.802
make decision
hence value of | ^2 cal | < | ^2 | and here we do not reject Ho
^2 p_value =0.9827
ANSWERS
---------------
null, Ho: =1.2
alternate, H1 : !=1.2
test statistic: 19.69
critical value: -49.802 , 49.802
decision: do not reject Ho
yes, we conclude that standard dviation of new drug is 1.2
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