Math Problem Statement
A random sample of 133 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 Address the following questions, assuming as necessary that all test assumptions are verified. Part 1 A test is run to answer the research question, ’Is there any difference between women and men in the average relationship length?’ Which test is correct to use, if we do not know the population standard deviation? Answer 1 Question 1 What is the null hypothesis? Answer 2 Question 1 The p-value of the test is 0.65. What is the decision of the test? Answer 3 Question 1 Part 2 A test is run to answer the research question, ’Is the average relationship length equal to 38?’ Which test is correct to use, if we know the population standard deviation? Answer 4 Question 1 The test statistic is -1.24. This means that the difference between the sample mean and the possible population mean, as stated in the null hypothesis (i.e. 38), is: Answer 5 Question 1 The p-value of the test is 0.216. What is the decision of the test?
Solution
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Math Problem Analysis
Mathematical Concepts
Hypothesis Testing
Two-sample t-test
One-sample z-test
Formulas
t-test formula: t = (X̄1 - X̄2) / sqrt[(s1^2/n1) + (s2^2/n2)]
z-test formula: z = (X̄ - μ) / (σ/√n)
Theorems
Central Limit Theorem
Law of Large Numbers
Suitable Grade Level
Undergraduate
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