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Chapter 21: Problem 1

Choose a random sample of 100 married couples. Ask each member of the couple how much time they spend looking at their smartphone while at home. Compare the mean times for the two members of couples.

Short Answer

Expert verified
Organize data into spouses' groups, calculate means for each, then compare them.

Step by step solution

01

Collect Data

Gather data from 100 married couples by asking each member how much time they spend looking at their smartphone while at home.
02

Organize Data

Organize the collected data into two separate groups: one for data from husbands and another for data from wives.
03

Calculate the Mean for Husbands

Sum up the total time spent on smartphones by all husbands and divide by the number of husbands (100) to find the mean time for husbands. Use the formula: \( \text{Mean} = \frac{\text{Total Time of Husbands}}{100} \).
04

Calculate the Mean for Wives

Sum up the total time spent on smartphones by all wives and divide by the number of wives (100) to find the mean time for wives. Use the formula: \( \text{Mean} = \frac{\text{Total Time of Wives}}{100} \).
05

Compare the Means

Compare the mean times calculated in Step 3 and Step 4. Determine which group, husbands or wives, spends more time on smartphones on average.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Data Collection
Data collection is the foundational step in any statistical analysis. It involves gathering information that is relevant to your research question or hypothesis. In our example, the task requires us to collect data from 100 married couples, focusing on the time each member spends on their smartphone while at home. Here's a simple way to approach data collection:
  • Identify the target population 鈥� in this case, married couples.
  • Define the data points needed 鈥� this would be the smartphone usage time for both members of each couple.
  • Use consistent methods 鈥� ask all participants the same questions under the same conditions to ensure uniformity.
Proper data collection ensures that the data you use is both reliable and valid, setting the stage for meaningful analysis.
Calculating the Mean
Once the data is collected, calculating the mean is a key step. The mean, or average, provides a single value that summarizes a large set of observations, helping us comprehend the overall dataset. For each group in our exercise 鈥� husbands and wives 鈥� you'll calculate the mean time they spend on their smartphones. Here's the process:
  • Add together all the individual times reported by husbands.
  • Divide the total by 100, the number of husbands, to get the mean for this group: \( \text{Mean for Husbands} = \frac{\text{Total Time of Husbands}}{100} \).
  • Repeat the process for the wives: \( \text{Mean for Wives} = \frac{\text{Total Time of Wives}}{100} \).
This calculation provides a simple average which is instrumental for further comparison in our study.
Efficient Data Organization
Data organization involves structuring and categorizing data so that it can be analyzed correctly. Proper organization helps minimize errors and eases the analysis process. For the smartphone usage study, organize the data into logical groups:
  • Create two categories: one for husbands and another for wives.
  • Within each category, list the individual time data collected from each participant.
  • Maintain the integrity of the original data entries to ensure accuracy during analysis.
Good data organization is crucial as it allows for efficient analysis and clear interpretation of the results.
Performing Data Comparison
Data comparison involves examining two or more datasets to determine differences, trends, or patterns. In this exercise, comparison is used to understand the differences in smartphone usage between husbands and wives. Once you have the means calculated for both husbands and wives, the next step is straightforward:
  • Compare the mean values to determine which group spends more time on smartphones.
  • Consider why there may be a difference 鈥� societal roles, interests, or technology habits could be factors.
  • Use the findings to draw informed conclusions or ask new questions like, "Does this affect family interaction time?"
Comparison not only highlights differences but also sparks deeper inquiry into the data, promoting a better understanding of the subject.

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