Math Problem Statement
A random sample of 145 students enrolled in statistics units in recent semesters at Macquarie University has been selected to study participation in lectures, measured as the number of polling quizzes answered, and academic performance. Some of the variables recorded for each student are listed below.
Variable Description subid Subject ID liveStream either “True”, if the student mostly watched the lectures via the live-stream, or “False”, if the student mostly came to classes numQuizzes the number of polling quizzes answered unitMark the final unit mark 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 students coming to classes and live-streamers in the average number of polling quizzes answered?’ Which test is correct to use, if we 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 0.24. 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 number of polling quizzes answered equal to 38?’ Which test is correct to use, if we do not know the population standard deviation? Answer 4 Question 1
The test statistic is -2.67. 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 0.008. What is the decision of the test? Answer 6 Question 1
Solution
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Math Problem Analysis
Mathematical Concepts
Hypothesis Testing
Z-test
t-test
p-value
Formulas
Z-test formula: Z = (X̄1 - X̄2) / (σ / √n)
t-test formula: t = (X̄ - μ) / (s / √n)
Theorems
Central Limit Theorem
Law of Large Numbers
Suitable Grade Level
Undergraduate Statistics
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