Math Problem Statement
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? Answer 1 Question 1
Report the absolute value of the test statistic [use at least 2dp]: Answer 2 Question 1 Report the 𝑝 -value [use at least 3dp]: Answer 3 Question 1 What is a suitable conclusion about the difference between women and men in the average relationship length? Answer 4 Question 1
Part 2 Is the average relationship length equal to 38? Which test are you going to use? Answer 5 Question 1
Report the absolute value of the test statistic [use at least 2dp]: Answer 6 Question 1 Report the 𝑝 -value [use at least 3dp]: Answer 7 Question 1 What is the decision of the test? Answer 8 Question 1
What is a suitable conclusion?
Solution
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Math Problem Analysis
Mathematical Concepts
Statistics
Hypothesis Testing
Two-sample t-test
One-sample t-test
Formulas
Two-sample t-test formula: t = (X̄1 - X̄2) / sqrt(s1²/n1 + s2²/n2)
One-sample t-test formula: t = (X̄ - μ) / (s/√n)
Theorems
Central Limit Theorem
t-distribution
Suitable Grade Level
College level (Statistics, Research Methods)
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