Workers at a certan soda drink factory collected data on the volumes (in ounces)
ID: 3334250 • Letter: W
Question
Workers at a certan soda drink factory collected data on the volumes (in ounces) of a simple random sample of 15 cans of the soda drink Those volumes have a mean of 12 19 oz and a standard deviation of 0 14 oz, and they appear to be from a normally distributed population If the workers want the filing process to work so that almost al cans have volumes between 11.93 oz and 12 61 oz, the range rule of thumb can be used to estimate that the standard deviation should be less than 0 17 oz Use the sample data to test the clam that the population of volumes has a standard deviation less than 0.17 oz Use a 0 025 signficance level Complete parts (a) through (d) below a. Idenbify the null and altemative hypotheses Choose the correct answer below OA H>017 oz OB. H0 020170Z H1 (017oz H1.0-017oz H1 :Explanation / Answer
Given that,
population standard deviation ()=0.17
sample standard deviation (s) =0.14
sample size (n) = 15
we calculate,
population variance (^2) =0.0289
sample variance (s^2)=0.0196
null, Ho: >=0.17
alternate, claim that population voulume has a standard deviation less than 0.17 H1 : <0.17
level of significance, = 0.025
from standard normal table,left tailed ^2 /2 =26.119
since our test is left-tailed
reject Ho, if ^2 o < -26.119
we use test statistic chisquare ^2 =(n-1)*s^2/o^2
^2 cal=(15 - 1 ) * 0.0196 / 0.0289 = 14*0.0196/0.0289 = 9.495
| ^2 cal | =9.495
critical value
the value of |^2 | at los 0.025 with d.f (n-1)=14 is 26.119
we got | ^2| =9.495 & | ^2 | =26.119
make decision
hence value of | ^2 cal | < | ^2 | and here we do not reject Ho
^2 p_value =0.7984
ANSWERS
---------------
a.
Ho: =0.17
H1 : <0.17
b.
test statistic: 9.495
c.
p-value:0.7984
d.
decision: do not reject Ho, greater, no
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