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?

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?

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