Week7.pdf - Lecture 1 Hypothesis Tests for \u00b5 and Introducing P-values Slide 7.3 7.120 Week 7 Announcement We are in the process of marking your

# Week7.pdf - Lecture 1 Hypothesis Tests for µ and...

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Lecture 1: Hypothesis Tests for μ , and Introducing P -values Slide 7.3 / 7.120 Week 7 Announcement We are in the process of marking your mid-term exams. You will get your marks soon. The assignment (15%) (a.k.a., the Stats Project) will be made available athe end this week (Week 7), two weeks before it is due for submission. This activity will require the use of RStudio. The Week 7 online tutorial is due Sunday, 6pm. Chapter 7 : Statistical Inference: Hypothesis Testing & Central Limit Theorem MATH1041: Page 782 / 898
Lecture 1: Hypothesis Tests for μ , and Introducing P -values Slide 7.4 / 7.120 The Agenda Slide Overarching aim of the course: introducing Statistics, the study of collecting, analysing and interpreting data (fundamental to any quantitative research) First class of Week 7 Last time: Confidence intervals The t -distribution Today: Hypothesis tests for μ , and introducing p -values The Central Limit Theorem Chapter 7 : Statistical Inference: Hypothesis Testing & Central Limit Theorem MATH1041: Page 783 / 898
Lecture 1: Hypothesis Tests for μ , and Introducing P -values Slide 7.5 / 7.120 Confidence Intervals Revision TRUE or FALSE? 1 If you have a 95% confidence interval [ 100.5, 110.2 ] for the true mean, there is a 95% probability that the true mean value is between 100.5 and 110.2. 2 It is better to have a narrow (shorter) confidence interval than a wide one, as it gives us more certain information (if the same confidence level is used each time). 3 If your study involves twenty 95% confidence intervals, then you expect about one to not contain μ . Chapter 7 : Statistical Inference: Hypothesis Testing & Central Limit Theorem MATH1041: Page 784 / 898
Lecture 1: Hypothesis Tests for μ , and Introducing P -values Slide 7.6 / 7.120 Lecture 1 Learning Outcomes [ Ch7-L1-O1 ] Understand the reasoning of hypothesis testing [ Ch7-L1-O2 ] Understand what p -values are and their limitations By the end of this lecture you should be able to: perform tests about the mean μ interpret correctly the results of a test procedure Chapter 7 : Statistical Inference: Hypothesis Testing & Central Limit Theorem MATH1041: Page 785 / 898
Lecture 1: Hypothesis Tests for μ , and Introducing P -values Slide 7.7 / 7.120 Introduction So far we have used statistics to estimate an unknown parameter ( e.g. , the mean or the standard deviation), and we have learnt how to construct an interval where we believe the true parameter lies (with some high level of confidence). Now, suppose we claim that our unknown parameter ( e.g. , the mean μ of some random variable of interest) belongs to some set of hypothesized values. These hypothesized values will depend on the research question. So now we would like to prove that our claim is true . Chapter 7 : Statistical Inference: Hypothesis Testing & Central Limit Theorem MATH1041: Page 786 / 898
Lecture 1: Hypothesis Tests for μ , and Introducing P -values Slide 7.8 / 7.120 Introduction Example 7.49 Suppose we make a claim that next year, students will sleep less than this current year.

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