Random Sampling Homework 1.
To obtain a sample of 25 students from among the 500 students present in school today, a surveyor decides to pick every twentieth student waiting in line to attend a required assembly in the gym. a. Explain why this procedure will not result in a simple random sample of the students present that day. This is a systematic random sample and not a SRS because not every group of 25 students has the same chance of being selected. For example, some classes will arrive at the same time and therefore only one or no students from a certain class will be selected. A whole class could not possibly be selected this way. b. Describe a procedure that will result in a simple random sample of the students present that day. (Be specific) The surveyor could number an alphabetical list of students prednet in school today from 1 to 500. They could use a random number generator on a calculator to generate 25 UNIQUE random numbers from 1 to 500. The students corresponding to those 25 numbers w ould be asked to participate.
2. A cable company plans to survey potential customers in a small city currently served by satellite dishes. Two sampling methods are being considered. Method A is to randomly select a sample of 25 city blocks and survey every family living on those blocks. Method B is to randomly select a sample of families from each of the five natural neighborhoods making up the city.
a. What is the statistical name for the sampling technique used in Method A, and what is a possible reason for using it rather than an SRS? Method A is a random cluster sample because the population is broken up into heterogeneous groups and an entire group (in this case a cluster of 25 city blocks) is selected for the sample. It is easier than a SRS because one does not have to deal with selecting individuals out of the entire population. b. What is the statistical name for the sampling technique used in Method B, and what is a possible reason for using it rather than an SRS? Method B is a stratified random sample because the population is broken up into homogenous groups (neighborhoods in this case) and a certain number of families are chosen out of each stratum. Stratified samples give comparative information that a SRS cannot offer due to the fact that each stratum (neighborhood) is represented in the sample. 3. A firm wants to understand the attitudes of its minority managers toward its system for assessing management performance. Below is a list of all the firms managers who are members of minority groups. Use table B starting at line 139 to choose a simple random sample of 6 to be interviewed in detail about the performance appraisal system. Assign #01-­‐28 to the firm’s managers who are members of minority groups. 01-­‐ Agarwal 06-­‐ Castillo 11-­‐ Gates 16-­‐ Kim 20-­‐ Peters 25-­‐ Santiago 02-­‐ Anderson 07-­‐ Cross 12-­‐ Goel 17-­‐Liao 21-­‐ Pliego 26-­‐ Shen 03-­‐ Baxter 08-­‐ Dewald 13-­‐ Gomez 18-­‐Mourning 22-­‐ Puri 27-­‐Vega 04-­‐ Bonds 09-­‐ Fernandez 14-­‐ Hernandez 19-­‐Naber 23-­‐ Richards 28-­‐ Wang 05-­‐ Bowman 10-­‐ Fleming 15-­‐ Huang 24-­‐ Rodriguez Take the numbers in groups of 2 since the largest possible number from our population has two digits. 55, 58, 89, 94, 04, 70, 70, 84, 10, 98, 43, 56, 35, 69, 34, 48, 39, 45, 17, 19, 12, 97, 51, 32, 58, 13 The managers selected are 04-­‐ Bonds, 10-­‐ Fleming, 17-­‐ Liao, 19-­‐ Naber, 12-­‐Goel, 13-­‐ Gomez Random Sampling Homework 4. A furniture maker buys hardwood in large batches. The supplier is supposed to dry the wood before shipping (would that isn’t dry won’t hold its size and shape). The furniture maker chooses five pieces of wood from each batch and tests their moisture content. If any piece exceeds 12% moisture content, the entire batch is sent back. a.) Identify the population in the above setting. All pieces of hardwood in a batch b.) Identify the sample in the above setting. The five pieces of wood randomly selected from the batch and tested for moisture content. 5. You want to take simple random sample (SRS) of 50 of the 816 students who live in a dormitory on campus. You label the students 001 to 816 in alphabetical order. In the table of random digits, you read the entries 95592 94007 69769 33547 72450 16632 81194 The first three students in your sample have labels (a) 955, 929, 400 (b) 400, 769, 769 (c) 929, 400, 769 (d) 400, 769, 335 6. A TV station wishes to obtain information on the TV viewing habits in its market area. The market area contains one city of population 170,000, another city of 70,000, and four towns of about 5000 inhabitants each. The station suspects that the viewing habits may be different in larger and smaller cities and in the rural areas. Which of the following sampling designs would give the type of information that the station requires? (A) A cluster sample using the cities and towns as clusters. (B) A convenience sample from the market area (C) A simple random sample from the whole market area (D) A stratified sample from the cities and towns in the market area 7. Bias in a sampling method is (A) any error in the sample result, that is, any deviation of the sample result from the truth about the population (B) the random error due to using chance to select a sample (C) any error due to practical difficulties such as contacting the subjects selected (D) any systematic error that tends to occur in the same direction whenever you use this sampling method 8. For your final project in AP Statistics, you decide to survey Penncrest students about their iPad usage. You label every table in the cafeteria with a number from 1-­‐65. You randomly select 5 tables and then you survey every student at each of those five tables. What type of sampling method are you using to collect your data? A) Simple Random Sample B) Stratified Sampling C) Cluster Sampling D) Systematic Random Sampling 9. Which of the following is a true statement? (A) If bias is present in a sampling procedure, it can be overcome by dramatically increasing the sample size (B) Sampling error can be eliminated only if a survey is both extremely well designed and extremely well conducted (C) Sampling error concerns natural variation between samples, is always present, and can be predicted using probability (D) Sampling error is generally larger when the sample size is larger Random Sampling Homework