Introduction to Statistical Methods
Introduction to Statistical Methods STAT 301
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Mrs. Triston Collier
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This 2 page Class Notes was uploaded by Mrs. Triston Collier on Thursday September 17, 2015. The Class Notes belongs to STAT 301 at University of Wisconsin - Madison taught by Staff in Fall. Since its upload, it has received 27 views. For similar materials see /class/205083/stat-301-university-of-wisconsin-madison in Statistics at University of Wisconsin - Madison.
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Date Created: 09/17/15
STAT 301 TA Lisa Chung lchungstatwiscedu DISCUSSION 13 Dec 6 2004 0 Two Types of Hypothesis Alternative hypothesis H1 the claim we wish to establish Null hypothesis H0 the current belief H0 H1 MltM0 111 MgtM0 MO 0 Test Statistic A sample statistic used to decide whether to reject H0 Never say reject H1 0 Rejection Region The numerical values of the test statistic for which H0 will be rejected 0 Two Types of Errors and Their Probabilities Type 1 error wrong rejection of H0 when H0 is true Type 11 error wrong retention of H0 when H1 is true 04 Pmaking type 1 error size of the test level of signi cance 3 Pmaking type 11 error 0 PValue observed signi cance level The probability calculated under H0 that the test statistic takes a value equal to or more extreme than the value actually observed The P value serves as a measure of the strength of evidence against H0 A small P value means that the null hypothesis is strongly rejected or the result is highly statistically signi cant 0 Summary of Steps 1 List H0 and H1 2 Using Z to determine rejection region 3 Compute Z0175 from the data 4 Draw conclusion 5 Compute P value Example 1 With a random sample of size n 1447 someone proposes X 7 125 X 125 to be a con dence interval for In What then is the level of con dence Example 2 Suppose you are to verify the claim that u gt 20 on the basis of a random sample of size 707 and you know that a 56 a If you set the rejection region to be R X 2 21317 what is the level of signi cance of your test b Find the numerical value of c so that the test B X 2 c has a 5 level of signi cance Example 3 A sample of 40 sales receipts from a university bookstore has i 121 and s102 Use these values to perform a test of a H0 p 125 versus H1 p lt 125 with 04 05 Off Hour W 100 300 pm 1 1275A MSC7 262 1577 STAT 301 TA Lisa Chung lchungstatwiscedu b H0 311 125 versus H1 311 7 125 with 04 05 Example 4 It is claimed that a new treatment is more effective than the standard treatment for prolonging the lives of terminal cancer patients The standard treatment has been in use for a long time and from records in medical journals the mean survival period is known to be 42 years The new treatment is administered to 80 patients and their duration of survival recorded The sample mean and the standard deviation are found to be 45 and 11 years respectively Is the claim supported by these results Test at 04 005 Also calculate the P value Example 5 Calculating from a random sample of 36 observations one obtains the results i 804 and s 162 In the context of each of the following hypothesis testing problems determine the P value of these results and state Whether or not it signi es a strong rejection of H0 a Test H0 311 85 versus H1 311 lt 85 b Test H0 u 76 versus H1 417 76 Off Hour W 100 300 pm 2 1275A MSC 262 1577
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