Probs & Stats A -- Stratified Random Samples

The athletic director at a university wants to interview all of the school's athletes about their satisfaction with their uniforms. She wants to randomly select two people from every team and interview them. Her co-worker suggests that she randomly pick ten athletes and interview them. Which statement best describes this scenario?

The athletic director wants to use stratified random sampling, while her co-worker suggests a simple random sampling method. hint: A stratified random sample involves dividing the population into homogeneous groups, different athletic teams, and then collecting data randomly. A simple random sample involves randomly selecting subjects, athletes from all the teams, from the population and collecting data.

In a grade of fifty students, twenty are in the computer club, and thirty are in the science club. After a simple random sampling of ten students, four students were chosen to represent the science club. How does this number of science club members compare to the number of science club members that would have been chosen if a stratified proportionate sample had been used instead?

There are more science club members in the stratified proportionate sample than in the simple random sample.

In a stratified proportionate sample of fifty online shoppers, twenty-two were men. If females represent 56% of the total population of online shoppers, is this sample representative of the population?

Yes; The percentage of women in the sample is the same as the percentage of women in the population.

A researcher wants to study the amount of protein in pet food. Which one of the following is most likely to give the researcher more accurate results?

divide the pet foods into two different groups, cat and dog, and take a sample from each group hint: Since different pet foods would have different protein contents, the better option is to divide or categorize the cat and dog foods into two different groups and take a sample from each group.

An example of a stratum in a stratified random sample from a study on texting while driving would be which of the following? Select all that apply.

drivers between the ages of 18 and 24 drivers of minivans drivers who are male hint: Drivers of a certain age who drive a certain car or who are of a certain gender are all samples of a population who share a certain characteristic, so they could be part of a selected stratum in a stratified random sample.

A sample of fifty scarves is taken from a shop to test the durability of fabrics. If 20% of scarves in a shop are silk and 80% are wool, which of the following statements is true?

A simple random sample of the scarves would be biased if the sample of fifty scarves included forty silk scarves. A stratified proportionate sample of the scarves would always have forty wool scarves and ten silk scarves. A stratified proportionate sample would divide the scarves into two subgroups: wool scarves and silk scarves.

hint:

A stratified random sample occurs when the population is divided into any type of group that shares the same characteristic (gender, prior activity level, destination in space), and then their data is randomly selected for the study. A simple random sample occurs when all astronauts have an equally likely chance of getting selected.

simple random sample

All astronauts who went into space are part of the study. Their data on time in space and muscle mass is collected, and a random sample from each group is chosen.

A startup company is looking into ways to invest in helping farmers produce better crops. Why would stratified random sampling be an effective way to study of farmers' needs?

It would allow the farmers who grow in very specific conditions to voice their needs and have them heard. It would reduce selection bias of the study's participants. It would ensure a sample of the population that accurately represents the population. hint: Stratified random sampling would reduce selection bias, ensure a proportionate and accurate sample of the population, and allow for the minority subgroups to have equal representation as the majority subgroups.

A hospital has thirty night nurses on duty and seventy day nurses on duty. A stratified proportionate sample of a total of twenty nurses was taken to ask their level of satisfaction with the hospital's cafeteria. Five night nurses and fifteen day nurses were part of that sample. Did the hospital perform the sampling correctly?

No; There should have been fourteen day nurses and six night nurses in the correct sample.

stratified random sample

The astronauts are divided into four groups based on their level of physical activity prior to going into space. Their data on time in space and muscle mass is collected, and a random sample from each group is chosen.

stratified random sample

The astronauts are divided into two groups, male and female. Their data on time in space and muscle mass is collected, and a random sample from each group is chosen.

A pet store has a total of two hundred fish in a tank. Of these, seventy-five are angel fish, and the remaining are goldfish. The pet owner chooses a stratified proportionate sample of forty fish to test for a certain bacterium. If he performed the sample correctly, how many angel fish and how many goldfish should he have chosen?

15 angel fish and 25 goldfish

Describe a study not mentioned in this lesson that uses stratified proportional random sampling. Explain why it is stratified and proportional and not simple random. Identify the sample size for the study and the proportionate sample for each of the strata.

Exemplar: Data was collected from registered members to get feedback about facilities in an outdoor club. Activities included tennis, swimming, and bowling. There is a total of one hundred members. If members are selected at random, the sample will not fairly represent those who attend each of these activities. In this case, a stratified random sampling will be more effective. A sample size of twenty was decided on. The registered members for each of the activities was determined - tennis: 20, pool: 50, bowling: 30 - this would be the strata. The proportionate sample for each activity was calculated using the formula: sample stratum count/ sample count ➗ population stratum count/population count Tennis: (Tennis stratum count)/20 = 20/100 tennis ∙ 100 = 400 tennis = 400/100 = 4 Pool: (pool stratum count)/20 = 50/100 pool ∙ 100 = 500 pool = 1000/100 = 10 bowling: (bowling stratum count)/20 = 50/100 bowling ∙ 100 = 600 bowling = 600/100 = 6 From each stratum, the calculated proportionate number was selected using simple random sample. So, four were selected from the tennis club to be in the sample, ten were selected from the swimmers, and six were selected from the bowling club.

Describe a study not mentioned in this lesson that requires a stratified random sample. Explain why this sampling technique is more effective than a simple random sample. How would you select the strata? What are the different members in the stratum?

Exemplar:A study is conducted to determine caloric consumption in adults over the age of eighteen. Since different people consume different levels of calories, taking a random sample of all adults over the age of eighteen may not be representative. It will be more helpful to group the adults into different categories based on age: adults 18-24, 25-34, 35-44, 45-54, 55-64, 65-74, and 74 and over. Each of these strata will have different caloric consumption since they have differing energy levels and metabolisms. The different categories will be the strata. The strata for this study is the different age groups. The different members of each stratum are the adults within each age group.

A researcher would like to study the average amount of debt owed by retired people in the United States. What could be an example of a strata sampled? Select all that would apply.

retirees from different states in the United States retirees who had different jobs in the United States retirees with different education levels hint: If the researcher would like to study the amount of debt owed by retired people in the U.S., the retirees from different states, the retirees who had different jobs, or the retirees with different education levels would be examples of strata that would help to give the researcher more accurate data on the average amount of debt in retired people. These strata share a common characteristic, and their data would be helpful to the objective of the study.

A researcher would like to study the amount of mercury in trout that live in different water conditions. How could the researcher divide the population of trout before taking a sample from each population for more accurate results?

river trout; stream trout; lake trout; ocean trout hint: The researcher will get a more accurate measure of the level of mercury in trout that live in different types of water if he divides the entire population of trout into categories based on the different types of water.