2. You use the force gauge from the previous page to measure gallons of milk pro
ID: 3061778 • Letter: 2
Question
2. You use the force gauge from the previous page to measure gallons of milk produced at a dairy, since measuring weight can be an easy way to double-check that jugs are properly filled. Whole milk weighs about 8.6 1bs/gallon. If it is well established that the mean value for a gallon of milk is 8.60 lbs and the standard deviation is 0.05 Ibs, how many measurements would it take to determine if the filling machine is more than 0.02 Ibs in error at 95% certainty? a. Final Answer: b. You conduct the measurements using 30 samples (not the answer to part a)). You determine that your standard deviation is 0.07 1bs. Is this variance larger than the established standard deviation of 0.05 lbs to 95% certainty? Justify your answer and clearly list the null (Ho) and alternate (Ha) hypotheses.Explanation / Answer
a) Given that,
Sample mean (Xbar) = 8.6
Sample standard deviation (s) = 0.05
Margin of error (E) = 0.02
The formula for sample size is,
n = [(Zc * s) / E]2
where Zc is the critical value for normal distribution.
Zc we can find in excel.
syntax :
=NORMSINV(probability)
where probability = 1 - a/2
a = 1 - C
C = 95% = 0.95
Zc = 1.96
n = [(1.96 * 0.05) / 0.02]2 = 24.01 or approximately equal to 24.
b) Here we have to test,
H0 : sigma2 = 0.052 Vs H1 : sigma2 > 0.052
where sigma2 is the population variance of the data.
sample size (n) = 30
sample standard deviation (s) = 0.07
The test statistic is,
X2 = (n-1)*s2 / sigma2
= (30-1) * 0.072 / 0.052 = 56.84
Now we have to find P-value for taking the decision.
P-value we can find in excel.
syntax :
=CHIDIST(x, deg_freedom)
where x is test statistic
deg_freedom = n-1 = 30-1 = 29
P-value = 0.0015
P-value < alpha
Reject H0 at 5% level of significance.
Conclusion : The variance is larger than the established standard deviation.
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