Math Problem Statement

sample.csv

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A random sample of 104 married or de facto couples in the Sydney region has been selected to study non-verbal communication. An experiment was conducted requiring the subject to guess words shown to the partner, without any verbal communication. Some of the variables recorded for each couple are listed below.

Variable Description subid Subject ID sex sex of guesser years the length of the relationship (in years) percentage the percentage of correct guesses Import the data set included in the file sample.csv in Excel. To do this, you need to click on the link above and save the data file in a convenient location on your PC (in your browser, File and Save). Next open Excel, click File in the Menu, select Open and navigate to the file you previously saved – or simply double-click on it, Excel should open automatically. Use Excel and/or probTool, and appropriate hypothesis tests, to address the following research questions. Assume all the test assumptions are verified. Part 1 Is there any difference between women and men in the average relationship length? Which test are you going to use? a) one sample t-test b) two sample t-test c) paired t-test d) z-test

Solution

The dataset contains the following columns:

  • SubID: Subject ID
  • sex: Sex of the guesser (male or female)
  • years: Length of the relationship (in years)
  • percentage: Percentage of correct guesses.

Part 1: Test for Differences in Relationship Length Between Women and Men

We are comparing the average relationship length between two independent groups (women and men). The appropriate test for this would be the two-sample t-test because:

  • We are comparing means from two independent groups (men and women).
  • We assume the data follows a normal distribution or has sufficient sample size for the central limit theorem to apply.

Selected test:

b) two-sample t-test

Shall I proceed with the hypothesis test?

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Math Problem Analysis

Mathematical Concepts

Statistics
Hypothesis Testing
T-Test

Formulas

Two-sample t-test formula: t = (X̄1 - X̄2) / sqrt((s1^2/n1) + (s2^2/n2))

Theorems

Central Limit Theorem
Student's t-distribution

Suitable Grade Level

Undergraduate