BUSS1020 Lecture Notes - Lecture 9: Central Limit Theorem, Conditional Probability, Confidence Interval
5 Jun 2018
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The basic principles of hypothesis testing
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How to use hypothesis testing to test for a specific value of a mean or a proportion
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The assumptions of each hypothesis-testing procedure, how to evaluate them, and the
consequences if they are violated
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How to avoid the pitfalls involved in hypothesis testing
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The ethical issues involved in hypothesis testing
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LO:
Fundamentals of Hypothesis Testing
1.
= claim (often about population parameter: mean and proportion)
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the mean monthly mobile phone bill is μ (population mean) = $42
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Telstra’s market share proportion in mobile phone customers, π (population
proportion), is greater than 0.5
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Example
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Hypothesis:
H0 states a default or status quo claim or assertion
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H0is always about a population parameter, not about a sample statistic
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Tests usually begin by assuming the null hypothesis is true
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H0 can refer to the “status quo” or historical value or just a relevant value to the test
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H0 may or may not be rejected in the test.
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H0 cannot be proven (but can be rejected) by the test.
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Null Hypothesis (H0)
(Have to use roman character above)
e.g., The average diameter of a manufactured bolt is not equal to 30mm ( H1: μ≠30 )
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H1 opposes the null hypothesis in some way
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H1 challenges the “status quo”
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H1 is generally the hypothesis that the researcher is trying to find evidence for (or against) or is
most interested in.
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Alternative Hypothesis (H1):
9. Hypothesis Testing: One Sample
Wednesday, 9 May 2018
9:06 AM
Textbooks Page 1
Hypothesis testing process:
E.g. The population is aging; in 2000 the population mean age was 50. Is the mean age still 50
in 2014?
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Usually, we start with the alternative (interesting) hypothesis.
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H0: μ= 50
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H1: μ≠50
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Claim: The population mean age is 50.
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To test this, we sample the population and find the sample mean.
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A two tail test always involves an alternative hypothesis that contains an unequal sign
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Sample population
1.
Find sample mean
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Is there strong enough evidence against null hypothesis?
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Does it support H1 and reject H0 or vice versa
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Example:
Textbooks Page 2
If the sample mean is “close” to the stated population mean, the null hypothesis is not
rejected.
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If the sample mean is “far” from the stated population mean, the null hypothesis is rejected.
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How far is “far enough” to reject H0?
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The critical value of a test statistic creates a “line in the sand” for decision making -- it answers
the question of how far is far enough.
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The test statistic and critical value:
Two tail test: needs two critical values to separate into three regions
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Have to find sample mean --> if sample mean falls in the rejection region --> then reject null
hypothesis
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If sample mean falls in the non-ejection region --> supports null hypothesis
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Textbooks Page 3
Document Summary
How to use hypothesis testing to test for a specific value of a mean or a proportion. The assumptions of each hypothesis-testing procedure, how to evaluate them, and the consequences if they are violated. How to avoid the pitfalls involved in hypothesis testing. = claim (often about population parameter: mean and proportion) Example the (cid:373)ea(cid:374) (cid:373)o(cid:374)thly (cid:373)o(cid:271)ile pho(cid:374)e (cid:271)ill is (cid:894)populatio(cid:374) (cid:373)ea(cid:374)(cid:895) = . Telst(cid:396)a"s (cid:373)a(cid:396)ket sha(cid:396)e p(cid:396)opo(cid:396)tio(cid:374) i(cid:374) (cid:373)o(cid:271)ile pho(cid:374)e (cid:272)usto(cid:373)e(cid:396)s, (population proportion), is greater than 0. 5. H0 states a default or status quo claim or assertion. H0 is always about a population parameter, not about a sample statistic. Tests usually begin by assuming the null hypothesis is true. H0 (cid:272)a(cid:374) (cid:396)efe(cid:396) to the (cid:862)status (cid:395)uo(cid:863) o(cid:396) histo(cid:396)i(cid:272)al (cid:448)alue o(cid:396) just a (cid:396)ele(cid:448)a(cid:374)t (cid:448)alue to the test. H0 may or may not be rejected in the test. H0 cannot be proven (but can be rejected) by the test. (have to use roman character above)
