Question

QUESTION 1

A Pew Research Center survey on Teens, Social Media & Technology at the beginning of 2015 included 10601060 teens, of which 614614 were white, non‑Hispanic; 101101 were black, non‑Hispanic; 236236 were Hispanic; and 109 were other races or ethnic groups. Each teen sampled was asked about technology usage, including access to mobile devices, social media usage, and video game playing. The margin of error (we will give more detail in later chapters) was reported as ±3.7%±3.7% for the entire sample. When considering technology usage of only the Hispanic teens, the margin of error was reported as ±8.1%±8.1% .

Which of the descriptions correctly explains the fact that estimates for Hispanic teens were less precise than for the entire sample?

It is hard to say without more information, but there must be some factor or combination of factors which is causing there to be more variation of technology usage amongst Hispanic teens than non‑Hispanics.

The sample size for all teens is larger than the sample size for Hispanic teens. Larger samples yield more information, which means more accuracy, which means a smaller margin of error.

There is no legitimate reason for such a difference to occur. The data must have been tampered with.

The sample size for all teens is more than twice the sample size for Hispanic teens. Therefore the margins of error also have a ratio of more than two to one.

QUESTION 2

The sampling examples below use either the stratified or the cluster method of sampling.

Select the examples that use the stratified method.

A questionnaire is created to gauge student opinion on a new university cafeteria. A sample of 40 freshmen, 50 sophomores, 60 juniors, and 50 seniors is selected to fill out the questionnaire.

A health agency needs to assess the performance of hospitals in a region but does not have the resources to evaluate each hospital. To reduce costs, the agency selects 5 of the 23 hospitals in the region and samples data related to performance from randomly chosen days and times.

A landlord wants to know the average income of his tenants. He selects three of his eight apartment complexes and collects income information from several randomly chosen tenants within the selected complexes.

A potato field is believed to be infected with a plant disease. The field is divided into 10 equal areas, and 25 potatoes are selected from each area to be tested for the disease.

A city council wants to know if elementary students in its city are meeting national standards. Eight schools are selected from the city's 30 total elementary schools, and the test scores of all students in the selected schools are evaluated

QUESTION 3

On January 30, 2015, the Los Angeles Times ran an online poll on its website and asked readers the question,

If the NFL comes to Los Angeles, which team would be the best fit? The St. Louis Rams, San Diego Chargers and Oakland Raiders are all on year‑to‑year leases, unhappy with their current venues, and mulling a possible relocation to L.A.

Readers clicked on one of three buttons to vote: a picture of the Oakland Raiders logo, a picture of the San Diego Chargers logo, and a picture of the St. Louis Rams logo. In all, 12,212 (33%)12,212 (33%) selected the Oakland Raiders, 2038 (6%)2038 (6%) selected the San Diego Chargers, and 22,721 (61%)22,721 (61%) selected the St. Louis Rams.

(a) What is the sample size for this poll?

2,0382,038

36,97136,971

22,72122,721

12,212

Answer 1

1) The margin of error: In a confidence interval, the range of values above and below the sample statistic is called the margin of error. The formula for calculating ME is as follows:

Margin of error = Critical value x Standard error of the statistic

Where z = critical value

p = proportion

n = sample size

So, more is the sample size less will be the margin of error

hence,

The descriptions correctly explain the fact that estimates for Hispanic teens were less precise than for the entire sample

Given: The margin of error (we will give more detail in later chapters) was reported as ±3.7% for the entire sample. When considering technology usage of only the Hispanic teens, the margin of error was reported as ±8.1%

Hence the answer will be

The sample size for all teens is larger than the sample size for Hispanic teens. Larger samples yield more information, which means more accuracy, which means a smaller margin of error.

2) Select the examples that use the stratified method.

Definition: Stratified sampling refers to a type of sampling method. With stratified sampling, the researcher divides the population into separate groups, called strata. Then, a probability sample (often a simple random sample ) is drawn from each group.

Thus from the examples given following are divided into groups or strata. The groups are highlighted in bold.

A questionnaire is created to gauge student opinion on a new university cafeteria. A sample of 40 freshmen, 50 sophomores, 60 juniors, and 50 seniors is selected to fill out the questionnaire.

A potato field is believed to be infected with a plant disease. The field is divided into 10 equal areas, and 25 potatoes are selected from each area to be tested for the disease.

3)

Sample size will be given by the total number of clicks

Sample size = 12212+22721+2038 = 36,971

Please like the solution if it helps you. Thank u