Sec 1.4 Homework

1.  ​A(n)  __________ is obtained by dividing the population into groups and selecting all individuals from within a random sample of the groups.

2. ​A(n) _________ is obtained by dividing the population into homogeneous groups and randomly selecting individuals from each group.

3.  Determine whether the following statement is true or false. Explain.

When taking a systematic random sample of size​ n, every group of size n from the population has the same chance of being selected.

Choose the correct answer below.

1. ​True, because any random sampling implies every group has an chance of selection.
2. ​True, because since k is chosen​ randomly, every group has an equal chance of selection.
3. ​False, because a systematic sample requires a frame.
4. ​False, because certain groups would never be selected.

4.  Determine whether the following statement is true or false. Explain.

A simple random sample is always preferred because it obtains the same information as other sampling plans but requires a smaller sample size.

Choose the correct answer below.

1. ​False, because other sampling techniques may provide more information for less cost than a simple random sample.
2. ​False, because simple random samples require a larger sample size than most other sampling methods.
3. ​True, because it does not require extra preparation and can return more information than the other sampling techniques.
4. ​True, because every individual has an equal chance of selection.

5.  Determine whether the following statement is true or false. Explain.

When conducting a cluster​ sample, it is better to have fewer clusters with more individuals when the clusters are heterogeneous.

Choose the correct answer below.

1. False. It is better to have fewer clusters when the clusters are homogeneous.
2. ​False, because the proportion of individuals per cluster to the population should not be affected by whether or not the clusters are heterogeneous.
3. ​True, because when the clusters are​ heterogeneous, they are scaled down versions of the population.
4. ​True, because heterogeneous clusters are not likely to resemble population​ heterogeneity, increasing the number of necessary individuals.

6.  Determine whether the following statement is true or false. Explain.

Inferences based on voluntary response samples are generally not reliable. Choose the correct answer below.

1. ​False, because a surveyor cannot force volunteers to respond.
2. ​False, because individuals who volunteer are least likely to have personal bias.
3. ​True, because the group that volunteers may not be a large enough sample size.
4. ​True, because it is often the case that the individuals who volunteer do not accurately represent the population.

7.  Determine whether the following statement is true or false. Explain.

When obtaining a stratified​ sample, the number of individuals included within each stratum must be equal.  Choose the correct answer below.

1. False. Within stratified​ samples, the number of individuals sampled from each stratum should be proportional to the size of the strata in the population.
2. False. When taking a stratified​ sample, a simple random sample is drawn from one stratum at random. All other strata will not be included in the sample.
3. False. A stratified sample is constructed by successively selecting a stratum at random and then selecting a random individual from within that stratum. With this​ process, it is unlikely that all strata will be sampled from the same number of times.
4. True. Sampling the same number of people from each stratum will result in a sample that is representative of the population at a lower cost than a simple random sample.

8.  To estimate the percentage of defects in a recent manufacturing​ batch, a quality control manager at Apple selects every 16th ipod that comes off the assembly line starting with the second until she obtains a sample of 120 ipods. What type of sampling is​ used?

1. Systematic
2. Cluster
3. Stratified
4. Simple random
5. Convenience

9.  To determine customer opinion of their inflight service​, Continental Airlines randomly selects 120 flights during a certain week and surveys all passengers on the flights. What type of sampling is​ used?

1. Convenience
2. Stratified
3. Simple random
4. Cluster
5. Systematic

10.  Maytag wants to administer a satisfaction survey to its current customers. Using their customer​ database, the company randomly selects 70 customers and asks them about their level of satisfaction with the company.

What type of sampling is​ used?

1. Stratified
2. Cluster
3. Systematic
4. Simple random
5. Convenience

11.  A internet site asks its members to call in their opinion regarding their reluctance to provide credit information online.

What type of sampling is​ used?

1. Systematic
2. Stratified
3. Convenience
4. Simple random
5. Cluster

12.  To determine her mood​, Carrie divides up her day into three​ parts: morning,​ afternoon, and evening. She then measures her mood at 2 randomly selected times during each part of the day.

What type of sampling is​ used?

1. Simple random
2. Convenience
3. Systematic
4. Stratified
5. Cluster

13.   A salesperson obtained a systematic sample of size 25 from a list of 500 clients. To do​ so, he randomly selected a number from 1 to 20​, obtaining the number 11. He included in the sample the 11th client on the list and every 20th client thereafter. List the numbers that correspond to the 25 clients selected.

Choose the correct answer below.

1. 25​, 45​, ​…, 500
2. 11​, 31​, ​…, 491
3. 11​, 31​, ​…, 486
4. 20​, 31​, ​…, 284

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