Business Statistics 1.2, 1.3

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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.

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