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# Weight 8.

A manufacturing company of chocolate candies uses machines to package candies as they
move along a filling line. Although the packages are labeled as 8 ounces, the company wants
the packages to contain 8.17 ounces so that virtually none of the packages contain less than 8
ounces. A sample of 50 packages is selected periodically, and the packaging process is
stopped if there is evidence that the mean amount packaged is different from 8.17 ounces.
Suppose that the file Cookies.xls contains the weights in a particular sample of 50 packages
(see Blackboard). From the past it is known that the standard deviation is σ=0.050 (use this
known value from the past instead of the sample standard deviation!).
a) At the 0.05 level of significance, is there evidence that the mean amount is
different from 8.17 ounces?
b) Construct a 95% confidence interval for the population mean, but now use the
sample standard deviation. Is your method valid? If necessary include your
assumption(s).
c) What sample size is needed to have 95% confidence of estimating the population
mean within ±0.005 ounce?
Note: use the template on the following page for a).

TEMPLATES. Use these templates whenever you are solving a testing problem.
x= n= s= σ= N= p= (whatever is appropriate!).
(i) H0:
H1:
(ii) Test statistic:
Reject for
(iii) Assumptions:
(iv) Calculated test statistic:
p-value of this statistical problem:
critical value:
(v) Decision:
because
and conclude

Explanation:
(ii) Test statistic:
Reject for large /small/large and small values
(iii) Assumptions: of course: assumptions about the populations so that the statistic has
the desired properties
(iv) Calculated test statistic:
p-value of this statistical problem:
critical value: Note: only p-value of critical value is enough unless we ask for both
(v) Decision: reject or do not reject H0
Because compare p-value or critical value with your criterion
and conclude what does (non)rejection mean for the non-statistician?
Weight 8.24 8.08 8.18 8.16 8.11 8.16 8.17 8.15 8.07 8.1 8.15 8.12 8.15 8.23 8.16 8.11 8.07 8.18 8.2 8.15 8.17 8.12 8.12 8.19 8.21 8.22 8.17 8.16 8.18 8.17 8.17 8.11 8.24 8.1 8.25 8.17 8.17 8.18 8.18 8.08 8.21 8.16 8.18 8.11 8.18 8.16 8.16 8.13 8.11 8.15

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