Q. 73 Name the sampling method used in... [FREE SOLUTION]

91影视

Introductory Statistics

Barbara Illowsky, Susan Dean

$Math Studyset 91影视 Explanations$ Math

OER 2018 Edition 路 902 pages

ISBN: 9781938168208

Chapter 1: Q. 73 (page 54)

Name the sampling method used in each of the following situations:
a. A woman in the airport is handing out questionnaires to travelers asking them to evaluate the airport鈥檚 service. She does not ask travelers who are hurrying through the airport with their hands full of luggage, but instead asks all travelers who are sitting near gates and not taking naps while they wait.
b. A teacher wants to know if her students are doing homework, so she randomly selects rows two and five and then calls on all students in row two and all students in row five to present the solutions to homework problems to the class.
c. The marketing manager for an electronics chain store wants information about the ages of its customers. Over the next two weeks, at each store location, $100$ randomly selected customers are given questionnaires to fill out asking for information about age, as well as about other variables of interest.
d. The librarian at a public library wants to determine what proportion of the library users are children. The librarian has a tally sheet on which she marks whether books are checked out by an adult or a child. She records this data for every fourth patron who checks out books.
e. A political party wants to know the reaction of voters to a debate between the candidates. The day after the debate, the party鈥檚 polling staff calls $1, 200$ randomly selected phone numbers. If a registered voter answers the phone or is available to come to the phone, that registered voter is asked whom he or she intends to vote for and whether the debate changed his or her opinion of the candidates.

Short Answer

Expert verified

Sampling method:

(a) Convenience sampling

(b) Cluster sampling

(d) Systematic sampling

(e) Random sampling

Step by step solution

Given information

Given multiple scenarios.

Explanation (part a)

In this scenario, the woman simply hands over the questionnaire to the people who are near the gate and taking a nap. This implies she targets the people who would not mind filling out the questionnaire for her. She is taking any random selection of the people, or using another probabilistic technique to select the people. Hence it is convenience sampling method.

Explanation (part b)

In this method, the teacher divides the class into different rows. Each row may consist of intelligent, average, and weak students. thus each row can be considered to be a heterogenous set of students. These rows can be considered as clusters. the teacher selects any two clusters and includes all its subjects in the final sample. This method of sampling where the population is divided into clusters, and now any few clusters are completely included in the sample is called cluster sampling.

Explanation (part c)

In this scenario, the population consists of customers of different locations. these locations are considered strata. Each strata consists of customers of the same location, hence each strata is homogenous with respect to location. in the final sample, the marketing manager involves $100$ customers of each strata. Like this, each strata gets to participate in the sample. Such a method of sampling is called stratified sampling.

Explanation (part d)

In this method, the librarian selects every $4^{t h}$ patron from the list. This method where the first subjects are selected arbitrarily and the following subjects are selected as per a simple rule like every k^th subject in the list is included in the sample is called systematic sampling. Hence the method used b the librarian is called systematic sampling.

Explanation (part e)

In this method of sampling $1, 200$ random numbers are selected, and all those who are registered become part of the sample, his method of sampling does not divide the population into subgroups or uses any specific rule for the selection of subjects to the sample. It is a simple method in which random selection of the phone number is made. this method of sampling is called random sampling.