For this activity, you will be conducting your own statistical study. Use the following steps as a guide.

Question

Step 1: Identify your population and the characteristic of the population you are interested in finding.

Step 2: Write a survey question that asks about the characteristic of the population you are interested in finding. Some examples are listed below.

On average, how long does a customer have to wait in line to buy a ticket in a theater?
What is the average age of the United States senators in the 112th Congress?
What percentage of the residents in your neighborhood own a pet?
Step 3: Identify how you will choose your sample. Remember that random sampling methods tend to produce representative samples.

Step 4: Organize your data using a graph or table.

Step 5: Find the measures of center and variability, if applicable. Choose the measure that best summarizes your data.

Step 6: Draw inferences about your population using your sample.

Answer 1

Step 1: Identify Your Population and Characteristic

Population: College students at a local university
Characteristic: Average amount of time students spend on social media daily.

Step 2: Write a Survey Question

Survey Question: "On average, how many hours do you spend on social media each day?"

Step 3: Identify Sampling Method

Sampling Method: I will use stratified random sampling to ensure representation from different demographics. I will divide the population of college students into strata based on their year (e.g., freshman, sophomore, junior, senior) and then randomly select students from each strata.

Step 4: Organize Your Data

Assuming I've collected responses from 100 students, here's a hypothetical summary of their daily social media usage in hours:

| Hours Spent on Social Media | Number of Students | |-----------------------------|--------------------| | 0-1 hours | 10 | | 1-2 hours | 20 | | 2-3 hours | 30 | | 3-4 hours | 25 | | 4+ hours | 15 |

Graphical Representation

A histogram can be used to visualize the data distribution. Here’s a simple representation:

|                       *
|                       *           *
|             *         *           *
|             *         *           *           *
|             *         *           *           *
|   *    *    *         *           *           *
|   *    *    *         *           *           *
|___|____|____|____|____|____|____|____|____|____|____
    0    1    2    3    4    5+ Hours

Step 5: Find the Measures of Center and Variability

1. Mean Calculation:

   • Total hours from responses: (100.5) + (201.5) + (302.5) + (253.5) + (15*4.5) = 0 + 30 + 75 + 87.5 + 67.5 = 260
   • Mean = Total hours / Number of respondents = 260 / 100 = 2.6 hours

2. Median:

   • The median falls in the 2-3 hour range, since half (50) of the 100 respondents are above and below this range.

3. Mode:

   • The mode is 2-3 hours, as this interval had the highest frequency (30 students).

4. Variability:

   • Range: 0 to 4+ hours, which results in a range of 4 hours.
   • Standard deviation can also be calculated, but for simplicity, I will focus on the range and mean/median values.

Step 6: Draw Inferences About Your Population Using Your Sample

From the data collected and analyzed, we can infer that the average college student at our local university spends approximately 2.6 hours on social media each day. Additionally, the most common range of social media usage is 2-3 hours, suggesting that a significant portion of students engage heavily with social media. The variability indicates that while many students are in the moderate usage range, there are also a notable number of students who spend either very little or a significant amount of time (4+ hours) on social media.

This study suggests that while social media is a prevalent activity among college students, there exists a diverse pattern of usage that could be explored further, such as the impact on academic performance or mental well-being. Further research could involve qualitative aspects of why students choose to spend varying amounts of time on social media.