Business Statistics 1.2, 1.3
Systematic random sampling is
a statistical sampling technique that involves selecting every kth item in the population after a randomly selected starting point between 1 and k. The value of k is determined as the ratio of the population size over the desired sample size.
An agency has started charging a user fee to park at selected trailheads and cross-country ski lots. Some users object to this fee, claiming they already pay taxes for these areas. The agency has decided to randomly question selected users at fee areas in a region to assess the level of concern. a. Define the population of interest. b. Assume a sample of 250 is required. Suppose the agency questions the first 50 users encountered at each of 5 fee areas. Which sampling technique did the agency use?
a. People who park at the selected trailheads and cross-country ski lots. b. Convenience sampling
What are the disadvantages? Select all that apply. A. Expensive B. Possible nonresponse Bias C. Possible interview bias D. Difficult to format the data
B. Possible nonresponse bias
During a recent political campaign, a news organization poll of eligible voters showed that one candidate would beat the other in the general election 47% to 44.5%. Are these values statistics or parameters? Explain. The values are _______ because they are based on _________.
Statistics A sample of Eligible Voters
Explain the difference between stratified random sampling and cluster sampling.
Stratified random sampling divides a population into subgroups so that each population item belongs to only one subgroup. Cluster sampling divides a population into groups that are each intended to be mini-populations.
Cluster sampling is
a method by which the population is divided into groups, or clusters, that are each intended to be mini-populations. A simple random sample of m clusters is selected. The items chosen from a cluster can be selected using any probability sampling technique.
Stratified random sampling is
a method in which the population is divided into subgroups called strata so that each population item belongs to only one stratum. The objective is to form strata such that the population values of interest within each stratum are as much alike as possible. Sample items are selected from each stratum using the simple random sampling method.
Simple random sampling is
a method of selecting items from a population such that every possible sample of a specified size has an equal chance of being selected.
A company has 25,000 employees. The file containing the names is ordered by employee number from 1 to 25,000. If a sample of 100 employees is to be selected from the 25,000 using systematic random sampling, within what range of employee numbers will the first employee selected come from? The first employee selected must be in the range (use ascending order)
1-250
Explain why a census does not necessarily have to involve a population of people. Use an example to illustrate.
A census examines an entire population. Recording the make of each vehicle owned by a company is a census.
Define what is meant by a leading question.
A leading question is worded in a way that will influence the response of the question.
Describe the difference between a statistic and a parameter.
A parameter is a descriptive numerical measure computed from an entire population. A statistic is the corresponding measure for a sample.
Assume you have used an online service to make an airline reservation. The following day, you receive an e-mail containing a questionnaire asking you to rate the quality of the experience. Discuss both the advantages and disadvantages of using this form of questionnaire delivery. A. Inexpensive B. Easy C. Answers are anonymous D. High response rate
A. Inexpensive B. Easy
Suppose a student is asked to survey students at his university to determine if they are satisfied with the food service choices on campus. What types of biases must the student guard against in collecting the data? Assume that the student conducts a written survey. A. nonresponse bias B. selection bias C. leading or poorly worded questions D. interviewer bias E. Observer bias
A. nonresponse Bias B. Selection Bias C. Leading or poorly worded questions
Briefly explain what is meant by an experiment and an experimental design.
An experiment is any event for which the result is not known beforehand. Experimental design is a method for implementing an experiment and determining all of the information that should be recorded before, during and after the experiment is conducted.
Suppose a survey is conducted using a telephone survey method. The survey is conducted from 9 A.M. to 11 A.M. on Tuesday. Indicate what potential problems the data collectors might encounter.
Aside from the normal problems when conducting any telephone survey, the timing of the call would increase any nonresponse bias because many people who work during the day will not be able to answer the phone.
If a pet store wishes to determine the level of customer satisfaction with its services, would it be appropriate to conduct an experiment? Explain.
No, because a written or telephone survey would be a much easier and cheaper way to obtain the customer satisfaction data
Describe how systematic random sampling could be used to select a random sample of 1,000 customers who have a certificate of deposit at a commercial bank. Assume that the bank has 25,000 customers who own a certificate of deposit. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.
The bank would need to randomly determine a starting point between 1 and ____ * 25 *select that numbered customer from a numbered list of all customers who own a certificate of deposit, and then select every ______ * 25 * th customer on the list until 1,000 customers are sampled. (Take 25,000 / 1,000 = 25. Range is 1-25. Selecting every 25th customer)
According to a report issued by an agency, it is estimated that southern fire ants spread at a rate of 4 to 5 miles a year. What data collection method do you think was used to collect this data? Explain your answer.
The data were collected by either direct observation or by experiment. Either the agency watched the spread of existing ants in the region, or it conducted an experiment to determine the spread of these ants under certain conditions.
If the manager at First City Bank surveys a sample of 100 customers to determine how many miles they live from the bank, is the mean travel distance for this sample considered a parameter or a statistic? Explain.
The mean travel distance is considered a statistic. Values computed from a sample are always considered statistics. In order for a value, such as an average, to be considered a parameter it must be computed from all items in the population.
Why is convenience sampling considered to be a nonstatistical sampling method?
The probability that an item is selected depends on the ease of selection.
As part of a consulting project for a local television station, a survey was conducted with 744 respondents. Of those responding, 32% indicated that they prefer to watch local news on this station. How might this survey have been conducted, and what type of bias could occur if that data collection method was used?
The survey may have been conducted by telephone interview. Some potential types of bias that could occur are interviewer bias, nonresponse bias, and selection bias.
According to the U.S. Bureau of Labor Statistics, the annual percentage increase in U.S. college tuition and fees in 1995 was 6.0%, in 1999 it was 4.0%, and in 2004 it was 9.5%. Are these percentages statistics or parameters? Explain.
These percentages are parameters since they would include all U.S. colleges.
A food distributor has a very large warehouse in which food is stored until it is delivered. The warehouse has 64 storage racks numbered 1-64. Each rack is three shelves high, labeled A, B, and C, and each shelf is divided into 80 sections, numbered 1-80. Products are located by rack number, shelf letter, and section number. Employees perform an inventory for a sample of products. Products are selected and counted, and the count is compared to the quantity recorded as in stock. Assume the company has selected breakfast cereals to inventory, and assume that breakfast cereals occupy racks 1 through 5. a. Assume that the company wishes to use cluster random sampling to select the sample. Discuss the steps the company would take to carry out the sampling. b. In this case, why might cluster sampling be preferred over simple random sampling? Discuss.
a. Randomly select a rack, randomly select a shelf, and randomly select a section. Then perform an inventory of a sample of the products in that location. b. With cluster sampling, the employees do not need to change location to inventory each product in the sample, as they would with simple random sampling.
Give the name of the kind of sampling that was most likely used in each of the cases described below. a. A news organization poll of 1,500 people to determine the president's approval rating b. A poll taken of each of a motorcycle manufacturer's dealerships in a region in December to determine an estimate of the average number of the manufacturer's motorcycles not yet sold by all of the manufacturer's dealerships in the country c. A quality-assurance procedure within a plant that manufactures corn chips tests every 1,500th bag of corn chips produced to make sure the bag is sealed properly d. A sampling technique in which a random sample from each of the tax brackets is obtained by a national tax collection agency to audit tax returns
a. Simple random sampling b. Cluster sampling c. Systematic random sampling d. Stratified random sampling
For each of the following situations, indicate what type of data collection method you would recommend and discuss why you have made that recommendation. a. collecting data on the percentage of drivers who wear their seatbelts b. collecting data on the price of a steak and cheese sub at sub shops in the state c. collecting data on customer satisfaction with the service provided by
a. The data should be collected with direct observation so that the data collected are accurate. b. The data should be collected by telephone or written surveys because they are the cheapest and easiest methods. c. The data should be collected by telephone or written surveys because they are the cheapest and easiest methods.
Indicate which sampling method would most likely be used in each of the following situations. a. an interview conducted with police chiefs of a sample of cities in California b. a poll of voters regarding a referendum calling for a national railways development program c. a survey of customers entering a shopping mall in
a. cluster sampling b. stratified random sampling c. convenience sampling
Assume you have received a class assignment to determine the attitude of students in your school toward the school's registration process. What are the validity issues you should be concerned with? To address the issue of __________ validity, the sampling method chosen must ensure that the results based on the sample will be able to be generalized to the population of all students. To have __________ validity, any extraneous factors influencing the group of sample students must be controlled. This would involve making sure the data gathering method, for instance a questionnaire, accurately determines the respondents attitude towards the registration process.
external internal
