Question

4. Susan is in charge of quality control at a small fruit juice bottling plant. Each bottle produced is supposed to contain exactly 12 fluid Ounces (fl oz) of juice. Susan decides to test this by randomly sampling 30 filled bottles and carefully measuring the amount of juice inside each. She will recalibrate the machinery if the average amount of juice per bottle differs from 12 fl oz at the 1% significance level. The sample of 30 bottles has an average of 11.92 fl oz per bottle and a standard deviation of 0.26 fl oz. Should Susan recalibrate the machinery? Justify your response with a complete hypothesis test following the methods of Section 6.2-HT. Parameter: Hypotheses: ah Sample statistic: Test statistic (including df): P-value: Conclusion (reject or do not reject): Conclusion in context:

Answer 1

Parameter: $\mu$ = 12

Hypothesis:

H0: $\mu$ = 12

Ha: $\mu$ $\neq$ 12

Sample statistics

$\bar{x}$ = 11.92 , S = 0.26

Test staistics

df = n - 1 = 30 - 1 = 29

t = ($\bar{x}$ - $\mu$ ) / ( S / sqrt(n) )

= ( 11.92 - 12) / ( 0.26 / sqrt(30) )

= -1.69

p-value =

From T table, with test statistics of 1.69 and df of 29,

p-value = 0.1018

Conclusion = Since p-value > 0.01 level, do not reject H0

Conlusion = We do not have sufficient evidence to support the claim that population average

amount differs from 12 fl oz.

Susan should not recaliberate the machinary.