Question

Find quantitative data about something that you are interested in. Make sure to get data on at least 50 individuals. 50 football players height

a. You don’t need to collect the data yourself, but you do need to find out and explain how the data was collected.

b. In order to be useful, this sample needs to be representative of some population.

       i. What population is represented by your sample

  ii. Describe biases that may result from your sampling method.

2. Select a level of significance.

3. Describe your data:

a. What are your observational units?

b. What is the variable you’re interested in?

c. What is your sample size?

d. Create a dotplot or histogram or some kind of chart that lets you see the shape of your data, and discuss the shape and any interesting characteristics of your data.

4. Use the theory method to find a confidence interval for the population mean at the level of confidence appropriate to your selected level of significance.

a. Don’t forget to show how you can tell that your method is valid for your data.

5. Explain the relationship between your sample mean, your confidence interval, and the population mean.

6. Discuss the usefulness and limitations of your confidence interval.

Answer 1

Note:

Hey there! Thank you for the question. As the question has asked, we have not collected the actual data, but explained the method of data collection, identified the relevant population, and explained the possible biases. The type of data mentioned here is that of “50 football players height”, which is a quantitative data. We have explained everything based on this variable.

You have posted 6 different questions. Thus, as per our policy regarding answering multiple questions, we have solved the first question for you (Parts a, b. i., b. ii.).

a.

A possible data collection procedure is as follows:

• Gain access to a list of all registered football players in the country, along with their details. If this is too large a data, select a particular league, and consider the list of all the players of this league.
• Use a random selection method, such as a random number table, a random number generating software, etc. to select 50 players from the list.
• Note down the heights of all these 50 players.

There, you have your data.

b. i.

Loosely speaking, the sample represents the heights of all football players in the country.

However, as the data were collected only for the players of a particular league, in reality, the population represented by the sample is the population of heights of football players of the chosen league.

b. ii.

Although a random selection procedure was used, the data may not be fully free from biases. Some of the biases that might result from the described sampling method are as follows:

• Selection bias: By selecting players from a particular league, we fail to get a sample that is representative of the entire population of football players in the country. With such a sample, if we use the results to draw conclusion about football players in the country in general, we would be making selection bias.
• Exclusion bias: There is only one goalkeeper in each team (not considering the ones in reserve). As a result, the list of all players of a particular league will have fewer goalkeepers than players playing in any other positions. This is highly likely to lead to a sample with very few or no goalkeepers. Similarly, there is no surety that players playing in the different positions of the field would be properly represented in the sample. This might lead to an exclusion bias.

In order to avoid these biases, the whole population of football players in the country may be considered, and a separate random selection may be made from players playing in each of the different positions (stratified sampling).