Question 7 | of 17 Step 1 of 5 in an effort to make a healthier product, the Ori

Question

Question 7 | of 17 Step 1 of 5 in an effort to make a healthier product, the Oriental Spice Sauce company has reduced the amount of sodium in their pr addition, the standard deviation of the amount of sodium should be 70. To make sure this new product continues sample of 19 bottles is taken and the standard deviation for the sample was 72.2109. Is there evidence at -0.01 that the st the sodium content exceeds the desired level? Assume the population is normally distributed. oduct to 1100 mg. in andard deviation of Step 1 of S: State the null and alternative hypotheses. Round to four decimal places when necessary Answer 2 Points Keypad Tables Nez ev

Explanation / Answer

Given that,
population standard deviation ()=70
sample standard deviation (s) =72.2109
sample size (n) = 19
we calculate,
population variance (^2) =4900
sample variance (s^2)=5214.41407881
null, Ho: ^2 =4900
alternate, H1 : ^2 >4900
level of significance, = 0.01
from standard normal table,right tailed ^2 /2 =34.805
since our test is right-tailed
we use test statistic chisquare ^2 =(n-1)*s^2/o^2
^2 cal=(19 - 1 ) * 5214.41407881 / 4900 = 18*5214.41407881/4900 = 19.15
| ^2 cal | =19.15
critical value
the value of |^2 | at los 0.01 with d.f (n-1)=18 is 34.805
we got | ^2| =19.15 & | ^2 | =34.805
make decision
hence value of | ^2 cal | < | ^2 | and here we do not reject Ho
^2 p_value =0.3826
ANSWERS
---------------
null, Ho: ^2 =4900
alternate, H1 : ^2 >4900
One tailed, ^2 /2 =34.805
test statistic: 19.15
decision: do not reject Ho
there is not suffcient evidence to show that standard deviation of the sodium content exceeds the normal level

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