{"id":115,"date":"2018-03-27T20:36:00","date_gmt":"2018-03-27T18:36:00","guid":{"rendered":"https:\/\/kindsonthegenius.com\/blog\/2018\/03\/27\/hypothesis-testing-question-20-run-test-suppose-we-flib-a-coin\/"},"modified":"2020-08-22T20:33:36","modified_gmt":"2020-08-22T18:33:36","slug":"hypothesis-testing-question-20-run-test-suppose-we-flib-a-coin","status":"publish","type":"post","link":"https:\/\/kindsonthegenius.com\/blog\/hypothesis-testing-question-20-run-test-suppose-we-flib-a-coin\/","title":{"rendered":"Hypothesis Testing Question 20 – Run Test( Suppose we flip a coin…)"},"content":{"rendered":"

Question 20<\/b><\/span>
\nSuppose we flip a coin n = 15 times and come up with the following arrangements<\/p>\n

H T T T H H T T T T H H T H H<\/p>\n

(H = head, T = tail)<\/p>\n

Test at the alpha = 0.05 significance level whether this arrangement may be regarded as random.<\/p>\n

 <\/p>\n

Solution Steps<\/b><\/span>
\nStep 1:<\/b> State the null and alternate hypothesis
\nH0<\/sub>: Arrangement is random
\nH1<\/sub>: Arrangement is not random<\/p>\n

 <\/p>\n

Step 2<\/b>: Calculate the Test Statistic (Number of Runs)
\nNormally you separate each of the runs so that you would be able to count them.<\/p>\n

H\u00a0 TTT\u00a0 <\/span>HH\u00a0 TTTT\u00a0 <\/span>HH\u00a0 T\u00a0<\/span> HH<\/p>\n

Number of runs is given by r = 7
\nNumber of H, n1<\/sub> = 7
\nNumber of T, n2<\/sub> =8<\/p>\n

Test Statistic = 7 (number of runs)<\/p>\n

 <\/p>\n

Step 3: <\/b>Lookup Critical values in table of runs tests
\nAt\u00a0 \"varepsilon\u00a0 = 0.05 significance, n1<\/sub> = 7, n2<\/sub> =8
\nUpper critical value =\u00a0 4
\nLower critical value = 13<\/p>\n

 <\/p>\n

Step 4: <\/b>Make Your Decision
\nSince r = 10 which is between 4 and 13, we accept the null hypothesis (we fail to reject it)<\/p>\n

 <\/p>\n

Step 5:<\/b> Draw a Conclusion
\nThere are not enough evidence to reject the claim hat the pattern of occurrence of heads and tails is determined by a random process<\/p>\n

<\/ins>
\n<\/ins><\/p>\n","protected":false},"excerpt":{"rendered":"

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