# Statistics explained in this solution

Prepare answers to the following assignments from the e-text, Applied Statistics in Business and Economics, by Doane and Seward:

Chapter 8 - Chapter Exercises

8.48
A sample of 20 pages was taken without replacement from the 1,591-page phone directory Ameritech Pages Plus Yellow Pages. On each page, the mean area devoted to display ads was measured (a display ad is a large block of multicolored illustrations, maps, and text). The data (in square millimeters) are shown below:
0 260 356 403 536 0 268 369 428 536
268 396 469 536 162 338 403 536 536 130
(a) Construct a 95 percent confidence interval for the true mean. (b) Why might normality be an issue here? (c) What sample size would be needed to obtain an error of ±10 square millimeters with 99 percent confidence? (d) If this is not a reasonable requirement, suggest one that is. (Data are from a project by MBA student Daniel R. Dalach.) DisplayAds

8.64
Biting an unpopped kernel of popcorn hurts! As an experiment, a self-confessed connoisseur of cheap popcorn carefully counted 773 kernels and put them in a popper. After popping, the unpopped kernels were counted. There were 86. (a) Construct a 90 percent confidence interval for the proportion of all kernels that would not pop. (b) Check the normality assumption. (c) Try the Very Quick Rule. Does it work well here? Why, or why not? (d) Why might this sample not be typical?

Chapter 9 - Chapter Exercises

9.54
Faced with rising fax costs, a firm issued a guideline that transmissions of 10 pages or more should be sent by 2-day mail instead. Exceptions are allowed, but they want the average to be 10 or below. The firm examined 35 randomly chosen fax transmissions during the next year, yielding a sample mean of 14.44 with a standard deviation of 4.45 pages. (a) At the .01 level of significance, is the true mean greater than 10? (b) Use Excel to find the right-tail p-value.

9.56
A coin was flipped 60 times and came up heads 38 times. (a) At the .10 level of significance, is the coin biased toward heads? Show your decision rule and calculations. (b) Calculate a p-value and interpret it.

9.62
The Web-based company Oh Baby! Gifts has a goal of processing 95 percent of its orders on the same day they are received. If 485 out of the next 500 orders are processed on the same day, would this prove that they are exceeding their goal, using _ = .025? (See story.news.yahoo.com accessed June 25, 2004.)

9.64
An auditor reviewed 25 oral surgery insurance claims from a particular surgical office, determining that the mean out-of-pocket patient billing above the reimbursed amount was \$275.66 with a standard deviation of \$78.11. (a) At the 5 percent level of significance, does this sample prove a violation of the guideline that the average patient should pay no more than \$250 out-of-pocket? State your hypotheses and decision rule. (b) Is this a close decision?

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There are 6 problems that cover topics such as p-value, significance, standard deviation, and confidence intervals.

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Prepare answers to the following assignments from the e-text, Applied Statistics in Business
and Economics, by Doane and Seward:

Chapter 8 – Chapter Exercises

8.48
A sample of 20 pages was taken without replacement from the 1,591-page phone directory
Ameritech Pages Plus Yellow Pages. On each page, the mean area devoted to display ads was
measured (a display ad is a large block of multicolored illustrations, maps, and text). The data
(in square millimeters) are shown below:
0 260 356 403 536 0 268 369 428 536
268 396 469 536 162 338 403 536 536 130

(a) Construct a 95 percent confidence interval for the true mean. (b) Why might normality be
an issue here? (c) What sample size would be needed to obtain an error of ±10 square
millimeters with 99 percent confidence? (d) If this is not a reasonable requirement, suggest one
that is. (Data are from a project by MBA student Daniel R. Dalach.) DisplayAds

8.64
Biting an unpopped kernel of popcorn hurts! As an experiment, a self-confessed connoisseur of
cheap popcorn carefully counted 773 kernels and put them in a popper. After popping, the
unpopped kernels were counted. There were 86. (a) Construct a 90 percent confidence interval
for the proportion of all kernels that would not pop. (b) Check the normality assumption. (c) Try
the Very Quick Rule. Does it work well here? Why, or why not? (d) Why might this sample not
be typical?

Chapter 9 – Chapter Exercises

9.54
Faced with rising fax costs, a firm issued a guideline that transmissions of 10 pages or more
should be sent by 2-day mail instead. Exceptions are allowed, but they want the average to be
10 or below. The firm examined 35 randomly chosen fax transmissions during the next year,
yielding a sample mean of 14.44 with a standard deviation of 4.45 pages. (a) At the .01 level of
significance, is the true mean greater than 10? (b) Use Excel to find the right-tail p-value.

9.56
A coin was flipped 60 times and came up heads 38 times. (a) At the .10 level of significance, is
the coin biased toward heads? Show your decision rule and calculations. (b) Calculate a p-value
and interpret it.

9.62
The Web-based company Oh Baby! Gifts has a goal of processing 95 percent of its orders on the
same day they are received. If 485 out of the next 500 orders are processed on the same day,
would this prove that they are exceeding their goal, using α = .025? (See
story.news.yahoo.comaccessed June 25, 2004.)

9.64
An auditor reviewed 25 oral surgery insurance claims from a particular surgical office,
determining that the mean out-of-pocket patient billing above the reimbursed amount was
\$275.66 with a standard deviation of \$78.11. (a) At the 5 percent level of significance, does this
sample prove a violation of the guideline that the average patient should pay no more than
\$250 out-of-pocket? State your hypotheses and decision rule. (b) Is this a close decision?