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# (Solved) MATH225 Week 1 Assignment Comparing Sampling Methods

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Question

When is using a simple random sample appropriate?

• A simple random sample should always be used if possible.
• A simple random sample should be used if the population is not well understood or there are no groups within the population that need to be analyzed individually.
• A simple random sample should be used when the population has well-

Â Question

A professor is interested in the average length of books in her library. She has divided her books into a few different categories:Â 235Â books on mathematics,Â 290Â books on sports, andÂ 166Â books on interior design. Rather than examining all the books, she plans to use a stratified sample ofÂ 50Â books. How many of the sports books should she choose? Enter a whole number.

Question

Donald is studying the eating habits of all students attending his school. He samples the population by dividing the students into groups by grade level and randomly selecting a proportionate number of students from each group. He then collects data from the sample. Which type of sampling is used?

• Systematic sampling
• Convenience sampling
• Stratified sampling
• Cluster sampling

Question

When is cluster sampling appropriate?

• Cluster sampling is a good choice when the population has multiple distinct groups that are each likely to be representative of the population as a whole.
• Cluster sampling is a good choice when the population has multiple distinct groups that are internally homogenous but not representative of the population as a whole.
• Cluster sampling is useful if the population is not well understood or there are no groups within the population that need to be analysed individually.
• Cluster sampling is a useful method when the individuals in the population are generated in a continuous stream, like on an assembly line.

Question

In order to study the wrist sizes of people in her town, Kathryn samples the population by dividing the residents by age and randomly selecting a proportionate number of residents from each age group. Which type of sampling is used?

• cluster sampling
• convenience sampling
• stratified sampling
• systematic sampling

Question

When considering different sampling methods, cluster sampling includes the steps: _______.

• use simple random sampling to select a set of groups; every individual in the chosen groups is included in the sample
• list the members of the population; use simple random sampling to select a starting point in the population; let k = (number of individuals in the population)/(number of individuals needed in the sample); choose every kth individual in the list starting with the one that was randomly selected
• divide the population into groups; use simple random sampling to identify a proportionate number of individuals from each group
• identify individuals of the population that are easily accessible; obtain data from these individuals

Question

An executive for a large national restaurant chain with multiple locations in each of 513 counties wants to personally sample the cleanliness of the chain’s restaurants throughout the country by visiting restaurants. The executive wants a good-quality sample but wants to minimize travel time and expenses. Which of the following sampling methods would be most appropriate?

• Obtain a convenience sample by visiting the 100 restaurants that are closest to the executive’s office.
• Obtain a systematic sample by selecting every 20th restaurant from a list that orders all restaurants by date of opening.
• Obtain a stratified sample by visiting 1 randomly selected restaurant in every county.
• Obtain a cluster sample by randomly selecting 20 counties and visiting every restaurant within those counties

Question

In order to study the mean pulse rate of people in his town, Jerry samples the population by dividing the residents by regions and randomly selecting 12 of the regions. He collects data from all residents in the selected regions. Which type of sampling is used?

Cluster sampling

• Convenience sampling
• Stratified sampling

Question

In reference to different sampling methods, is the following statement true or false?

Cluster sampling includes the steps: divide the population into groups; use simple random sampling to identify a proportionate number of individuals from each group.

• True
• False

Question

The management of a large airline wants to estimate the average time after take-off taken before the crew begins serving snacks and beverages on their flights. Assuming that management has easy access to all of the information that would be required to select flights by each proposed method, which of the following would be reasonable methods of stratified sampling?

Select all that apply.

• For each day of the week, randomly select 5% of all flights that depart on that day of the week.
• Divide all flights into the following 4 groups on the basis of scheduled departure time: before 9:00 am, 9:00 am to 1:00 pm, 1:00 pm to 5:00 pm, and after 5:00 pm. Randomly select 5% of the flights in each group.
• For each crew member the airline employs randomly select 5 flights that the crew member works.
• Divide the airports from which the airline’s flights depart into 4 regions: Northeast, Northwest, Southwest, and Southeast. Randomly select 5% of all flights departing from airports in each region.

Question

When is stratified sampling appropriate?