Assigned Exercises from Chapter 1 (There may be errors from the scanning process.)
 
 

1. 14. (a) No. Such regularity holds only in the long run. 
If it were true, you could look at the first 39 digits and
 know whether or not the 40th was a 0. (b) Yes. All pair of
 digits (there are 100, from 00 to 99) are equally likely. 
(This is property 3 from the text.) (c) No. Four random digits
 have chance 1/10000 to be 0000, so this sequence will occasionally
 occur. 0000 is no more or less random than 1234 or 2718, or any
 other four digit sequence.

1.16. The distribution of 80     Diameter 1/8 2/8 3/8 4/8 5/8 6/8 7/8
the diameters (in inches)         Frequency 10 10  10   20 10  10  10

is on the right. The population mean (the average diameter of all
 80 circles) is therefore 4/8 or 1/2 inch.


If you wish to work with this exercise on your own, you may find it useful to note that the distribution of the sample means would be almost exactly the same if there were only eight circles: two half-inch circles, and one of each of the rest (if you allow any circle to be picked more than once in your samples) - The experiment

is then greatly simplified!
A pair of relative frequency his

tograms (using only students who
appeared to do the exercise cor
rectly) is very helpful in Section 3. 
Shown are the approximate theoret
ical sampling distributions, with the
approximating normal distributions
superimposed over the histograms.
As illustrated, place them one above
the other, and use identical scales
(vertical and horizontal). Finally, 
use classes of approximately equal

width in both histograms. The means from part (b) will be one of 4/32=1/8,
5/32, 6/32, ..., 28/32=7/8; if each of these is a class in itself, then responses to (d) might be grouped as 16/128-18/128, 19/128-22/128, 23/128-26/128, ....
The histograms are then easy to compare visually. Since the numbers of samples
of sizes 4 and 16 differ, use of relative frequency on the vertical scale is essential to comparability.

Section 3: Population information from a sample

1.18. 2.503 cm is a parameter; 2.515 cm is a statistic.
1.29. The  histogram appears on 
the right. The center (median) is 5, the  
minimum is 1, and the maximum is 9. In all, 
32 of the 50 samples, or 64%, had one of 4, 
5, or 6 unemployed students. In its overall 
symmetric (roughly normal) pattern, this 
histogram is similar to Figure 1-2 in SCC.

1.40. To be more confident that the randomly varying sample statistic will land within a given margin of error of the true population parameter, we must allow a larger margin of error. So the margin of error for 95% confidence is larger than for 90% confidence. More on this tradeoff in Chapter 8.
 

Section 5: The practical side of sampling
 

1.41. (a) Nonsampling error: a response error. (b) Nonsampling error: a processing error. (c) Sampling error: a voluntary response sample.
 
 

1.42. (a) Sampling error: the sample only includes persons with listed phone numbers. (b) Nonsampling error: nonresponse. (c) Sampling error: a convenience sample.
 
 

1.43. (a) Only adults with phones were contacted. Alaska and Hawaii were omitted. Possibly, women axe overrepresented (see Example 14). (b) Processing errors (responses which are recorded incorrectly, e.g.), nonresponse (failure to reach, or uncooperativeness of, some members of the original sample), response error (inaccurate responses from the persons in the sample). (c) Neither: the margin of error only accounts for sampling variation.
 
 

1.57. (a) About 20% of the sample, or 40 women (there will, of course, be some variability). (b) A stratified sample, so that the number of men and women in the sample can be specified and adequate precision obtained for both groups.
 
 

1.63. Step 1. The population is all books in "large libraries." The librarians should specify what library or libraries they are interested in. Step 2. The variables are height of the book, or just which of the four height categories each book falls into. Step 3. The sampling frame is provided by the library's catalog system (card files, or a computer database).
 
 

Step 4. Now the fun begins. If the librarians are sure that all large libraries have the same size distribution of books, we need sample only one library (as the statement of the problem suggests). A SRS would do, but a stratified sample is preferable. Ask the librarians to set up strata of books shelved together (i.e., with call numbers in some range). Be sure to ask if there is separate "oversize" shelving. Within each stratum, a systematic sample is much easier than a SRS when you have a box from the card catalog in your hand. Then locate and measure the books whose cards fell in the sample.. To sample many libraries, a multistage sample (first libraries, then books) is needed. There are many possible variations on the technique described here, especially if the library has a computer database of its books.