A drug, which is used for treating cancer, has potentially dangerous side effect

Question

A drug, which is used for treating cancer, has potentially dangerous side effects if it is taken in doses which are larger than 55.52 mg, the required dosage for the treatment. It is important that the variance of the amount of the active ingredient is 0.04. 25 tablets are randomly selected and the amount of the drug in each tablet is measured. It is determined that the variance of the amount of active ingredient is 0.0259 mg. Does the data suggests at = 0.01 that the variance of the drug in the tablets is less than the desired amount? Assume the population is normally distributed. Step 2 of 5 : Determine the critical value(s) of the test statistic. If the test is two-tailed, separate the values with a comma. Round your answer to three decimal places. PLEASE ONLY ANSWER THIS EXACT QUESTION: Step 2 of 5 : Determine the critical value(s) of the test statistic. If the test is two-tailed, separate the values with a comma. Round your answer to three decimal places. please highlight this exact final answer. PLEASE ROUND TO THREE DECIMAL PLACES!!! and highlight the answer to this problem.

Explanation / Answer

Given that,
population variance (^2) =0.04
sample size (n) = 25
sample variance (s^2)=0.0259
null, Ho: ^2 =0.04
alternate, H1 : ^2 !=0.04
level of significance, = 0.01
from standard normal table, two tailed ^2 /2 =42.98
since our test is two-tailed
reject Ho, if ^2 o < - OR if ^2 o > 42.98
we use test statistic chisquare ^2 =(n-1)*s^2/o^2
^2 cal=(25 - 1 ) * 0.0259 / 0.04 = 24*0.0259/0.04 = 15.54
| ^2 cal | =15.540
critical value
the value of |^2 | at los 0.01 with d.f (n-1)=24 is 42.98
we got | ^2| =15.540 & | ^2 | =42.98
make decision
hence value of | ^2 cal | < | ^2 | and here we do not reject Ho
^2 p_value =0.904
ANSWERS
---------------
null, Ho: ^2 =0.04
alternate, H1 : ^2 !=0.04
test statistic: 15.540
critical value: -42.98 , 42.98
p-value:0.904
decision: do not reject Ho

we do not have enough evidence to support the claim

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