The manufacturers of Oriental Spice Sauce are concerned that the sodium levels i
ID: 3334268 • Letter: T
Question
The manufacturers of Oriental Spice Sauce are concerned that the sodium levels in their product vary too much. A package of the sauce is supposed to contain 1000 mg of sodium with a standard deviation of 150 mg.A sample of 17 packages was analyzed and the sample standard deviation was 246.4609 mg.Is there evidence at = 0.025 that the standard deviation of the sodium content exceeds the desired level? 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 CLEARLY list the answers:
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.
thank you
Explanation / Answer
Given that,
population standard deviation ()=150
sample standard deviation (s) =246.4609
sample size (n) = 17
we calculate,
population variance (^2) =22500
sample variance (s^2)=60742.97522881
null, Ho: =150
alternate, H1 : >150
level of significance, = 0.025
from standard normal table,right tailed ^2 /2 =28.845
since our test is right-tailed
we use test statistic chisquare ^2 =(n-1)*s^2/o^2
^2 cal=(17 - 1 ) * 60742.97522881 / 22500 = 16*60742.97522881/22500 = 43.2
| ^2 cal | =43.2
critical value
the value of |^2 | at los 0.025 with d.f (n-1)=16 is 28.845
we got | ^2| =43.2 & | ^2 | =28.845
make decision
hence value of | ^2 cal | > | ^2 | and here we reject Ho
^2 p_value =0.0003
ANSWERS
---------------
null, Ho: =150
alternate, H1 : >150
test statistic: 43.2
critical value: 28.845
p-value:0.0003
decision: reject Ho
it exceeds the desired level
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