<p style="text-align:justify"><span style="font-size:14px"><span style="color:#000000"><strong>EXAMPLE&nbsp;1.12</strong></span></span></p>

<p style="text-align:justify">&nbsp;</p>

<p style="margin-left:8px; text-align:justify"><span style="font-size:14px"><span style="color:#000000">A study is done to determine the average tuition that LDR college undergraduate students pay per semester. Each student in the following samples is asked how much tuition he or she paid for the Fall semester. What is the type of sampling in each case?</span></span></p>

<p style="margin-left:8px; text-align:justify">&nbsp;</p>

<ol style="list-style-type:lower-alpha">
	<li style="text-align:justify">
	<p><span style="font-size:14px"><span style="color:#000000">A sample of 100 undergraduate LDR college students is taken by organizing the students&rsquo; names by classification (1<sup>st</sup> year, 2<sup>nd</sup> year,3<sup>rd</sup> year or 4<sup>th</sup> year), and then selecting 25 students from each.</span></span></p>
	</li>
	<li style="text-align:justify">
	<p><span style="font-size:14px"><span style="color:#000000">A random number generator is used to select a student from the alphabetical listing of all undergraduate students in the Fall semester. Starting with that student, every 50th student is chosen until 75 students are included in the sample.</span></span></p>
	</li>
	<li style="text-align:justify">
	<p><span style="font-size:14px"><span style="color:#000000">A completely random method is used to select 75 students. Each undergraduate student in the fall semester has the same probability of being chosen at any stage of the sampling process.</span></span></p>
	</li>
	<li style="text-align:justify">
	<p><span style="font-size:14px"><span style="color:#000000">The 1<sup>st</sup> year, 2<sup>nd</sup> year,3<sup>rd</sup> year or 4<sup>th</sup> year are numbered one, two, three, and four, respectively. A random number generator is used to pick two of those years. All students in those two years are in the sample.</span></span></p>
	</li>
	<li style="text-align:justify">
	<p><span style="font-size:14px"><span style="color:#000000">An administrative assistant is asked to stand in front of the library one Wednesday and to ask the first 100 undergraduate students he encounters what they paid for tuition the Fall semester. Those 100 students are the sample.</span></span></p>
	</li>
</ol>

<p style="margin-left:8px; text-align:justify"><span style="font-size:14px"><span style="color:#000000"><strong>Solution&nbsp;1.12</strong></span></span></p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:#000000">a. stratified; b. systematic; c. simple random; d. cluster; e. convenience</span></span></p>

<p style="text-align:justify">&nbsp;</p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:#000000"><strong>EXAMPLE&nbsp;1.13</strong></span></span></p>

<p style="text-align:justify">&nbsp;</p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:#000000">Determine the type of sampling used (simple random, stratified, systematic, cluster, or convenience).</span></span></p>

<p style="text-align:justify">&nbsp;</p>

<ol style="list-style-type:lower-alpha">
	<li>
	<p style="text-align:justify"><span style="font-size:14px"><span style="color:#000000">A soccer coach selects six players from a group of boys aged eight to ten, seven players from a group of boys aged 11 to 12, and three players from a group of boys aged 13 to 14 to form a recreational soccer team.</span></span></p>
	</li>
	<li>
	<p style="text-align:justify"><span style="font-size:14px"><span style="color:#000000">A pollster interviews all human resource personnel in five different high tech companies.</span></span></p>
	</li>
	<li>
	<p style="text-align:justify"><span style="font-size:14px"><span style="color:#000000">A high school educational researcher interviews 50 high school female teachers and 50 high school male teachers.</span></span></p>
	</li>
	<li>
	<p style="text-align:justify"><span style="font-size:14px"><span style="color:#000000">A medical researcher interviews every third cancer patient from a list of cancer patients at a local hospital.</span></span></p>
	</li>
	<li>
	<p style="text-align:justify"><span style="font-size:14px"><span style="color:#000000">A high school counselor uses a computer to generate 50 random numbers and then picks students whose names correspond to the numbers.</span></span></p>
	</li>
	<li>
	<p style="text-align:justify"><span style="font-size:14px"><span style="color:#000000">A student interviews classmates in his algebra class to determine how many pairs of jeans a student owns, on the average.</span></span></p>
	</li>
</ol>

<p style="margin-left:24px; text-align:justify">&nbsp;</p>

<p style="margin-left:24px; text-align:justify"><span style="font-size:14px"><span style="color:#000000"><strong>Solution</strong></span></span></p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:#000000">&nbsp; &nbsp; </span></span></p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:#000000">&nbsp;a. stratified; b. cluster; c. stratified; d. systematic; e. simple random; f. convenience</span></span></p>

<p style="text-align:justify">&nbsp;</p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:#000000"><span style="background-color:white">If we were to examine two samples representing the same population, even if we used random sampling methods for the samples, they would not be exactly the same. Just as there is variation in data, there is variation in samples. As you become accustomed to sampling, the variability will begin to seem natural.</span></span></span></p>

<p style="text-align:justify">&nbsp;</p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:#000000"><strong>EXAMPLE&nbsp;1.14</strong></span></span></p>

<p style="text-align:justify">&nbsp;</p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:#000000">Suppose ABC College has 10,000 part-time students (the population). We are interested in the average amount of money a part-time student spends on books in the fall term. Asking all 10,000 students is an almost impossible task.</span></span></p>

<p style="text-align:justify">&nbsp;</p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:#000000">Suppose we take two different samples.</span></span></p>

<p style="text-align:justify">&nbsp;</p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:#000000">First, we use convenience sampling and survey ten students from a first term organic chemistry class. Many of these students are taking first term calculus in addition to the organic chemistry class. The amount of money they spend on books is as follows:</span></span></p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:#000000">Rs.128;&nbsp;Rs.87;&nbsp;Rs.173;&nbsp;Rs.116;&nbsp;Rs.130;&nbsp;</span></span></p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:#000000">Rs.204;&nbsp;Rs.147;&nbsp;Rs.189;&nbsp;Rs.93;&nbsp;Rs.153</span></span></p>

<p style="text-align:justify">&nbsp;</p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:#000000">The second sample is taken using a list of senior citizens who take P.E. classes and taking every fifth senior citizen on the list, for a total of ten senior citizens. They spend:</span></span></p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:#000000">Rs.50;&nbsp;Rs.40;&nbsp;Rs.36;&nbsp;Rs.15;&nbsp;Rs.50;&nbsp;</span></span></p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:#000000">Rs.100;&nbsp;Rs.40;&nbsp;Rs.53;&nbsp;Rs.22;&nbsp;Rs.22</span></span></p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:#000000">It is unlikely that any student is in both samples.</span></span></p>

<p style="text-align:justify">&nbsp;</p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:#000000">a. Do you think that either of these samples is representative of (or is characteristic of) the entire 10,000 part-time student population?</span></span></p>

<p style="text-align:justify">&nbsp;</p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:#000000"><strong>Solution&nbsp;1</strong></span></span></p>

<p style="text-align:justify">&nbsp;</p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:#000000">a. No. The first sample probably consists of science-oriented students. Besides the chemistry course, some of them are also taking first-term calculus. Books for these classes tend to be expensive. Most of these students are, more than likely, paying more than the average part-time student for their books. The second sample is a group of senior citizens who are, more than likely, taking courses for health and interest. The amount of money they spend on books is probably much less than the average parttime student. Both samples are biased. Also, in both cases, not all students have a chance to be in either sample.</span></span></p>

<p style="text-align:justify">&nbsp;</p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:#000000">b. Since these samples are not representative of the entire population, is it wise to use the results to describe the entire population? </span></span></p>

<p style="text-align:justify">&nbsp;</p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:#000000"><strong>Solution&nbsp;2</strong></span></span></p>

<p style="text-align:justify">&nbsp;</p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:#000000">b. No. For these samples, each member of the population did not have an equally likely chance of being chosen.</span></span></p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:#000000">Now, suppose we take a third sample. We choose ten different part-time students from the disciplines of chemistry, math, English, psychology, sociology, history, nursing, physical education, art, and early childhood development. (We assume that these are the only disciplines in which part-time students at ABC College are enrolled and that an equal number of part-time students are enrolled in each of the disciplines.) Each student is chosen using simple random sampling. Using a calculator, random numbers are generated and a student from a particular discipline is selected if he or she has a corresponding number. The students spend the following amounts:</span></span></p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:#000000">Rs.180;&nbsp;Rs.50;&nbsp;Rs.150;&nbsp;Rs.85;&nbsp;Rs.260;</span></span></p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:#000000">Rs.75;&nbsp;Rs.180;&nbsp;Rs.200;&nbsp;Rs.200;&nbsp;Rs.150</span></span></p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:#000000">c. Is the sample biased?</span></span></p>

<p style="text-align:justify">&nbsp;</p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:#000000"><strong>Solution&nbsp;3</strong></span></span></p>

<p>&nbsp;</p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:#000000">c. The sample is unbiased, but a larger sample would be recommended to increase the likelihood that the sample will be close to representative of the population. However, for a biased sampling technique, even a large sample runs the risk of not being representative of the population.</span></span></p>

<p style="text-align:justify">&nbsp;</p>

<p style="text-align:justify"><span style="font-size:14px"><span style="color:#000000">Students often ask if it is &quot;good enough&quot; to take a sample, instead of surveying the entire population. If the survey is done well, the answer is yes.</span></span></p>

<p>&nbsp;</p>