{"id":113,"date":"2018-03-27T23:50:00","date_gmt":"2018-03-27T21:50:00","guid":{"rendered":"https:\/\/kindsonthegenius.com\/blog\/2018\/03\/27\/hypothesis-testing-question-21-walf-wolfowitz-run-test-for-large-sample-step-by-step-procedure\/"},"modified":"2020-08-22T20:33:48","modified_gmt":"2020-08-22T18:33:48","slug":"hypothesis-testing-question-21-walf-wolfowitz-run-test-for-large-sample-step-by-step-procedure","status":"publish","type":"post","link":"https:\/\/kindsonthegenius.com\/blog\/hypothesis-testing-question-21-walf-wolfowitz-run-test-for-large-sample-step-by-step-procedure\/","title":{"rendered":"Hypothesis Testing Question 21 – Wald-Wolfowitz Run Test for Large Sample (Step by Step Procedure)"},"content":{"rendered":"
This is how to Perform Wald-Wolfowitz Run Test<\/div>\n

Question 21<\/b><\/span><\/span><\/span><\/span>
\nThe following arrangement of men, M, and women, W, lined up to purchase tickets for a rock concert:<\/p>\n

<\/a><\/div>\n

Test for randomness at the \u03b1<\/b> = 0.05 significance level<\/p>\n


\n<\/span>Solution Steps <\/span><\/b><\/span>
\nIn this case, we see that the sample size is fairly large, so we are going to use a slightly different method in this case. We are going to calculate the mean runs and the standard deviation.<\/p>\n

Then we go ahead to find the z-statistic. We would use the following 7 steps to disolve this problem.<\/p>\n

Step 1: State the null and alternate hypothesis<\/a>
\nStep 2: Determine the number of runs<\/a>
\nStep 3: Calculate the mean runs<\/a>
\nStep 4: Calculate the Standard deviation<\/a>
\nStep 5: Calculate the z-Statistic<\/a>
\nStep 6: Determine the Critical value<\/a>
\nStep 7: Draw a conclusion<\/a><\/p>\n

<\/ins>
\n<\/b><\/p>\n

Step 1: State the null and alternate hypothesis<\/h3>\n

H0<\/sub>: Arrangement is random
\nH1<\/sub>: Arrangment is not random<\/p>\n

 <\/p>\n

Step 2: Determine the Number of Runs<\/h3>\n

This means that you need to mark each of the categories so you can easily count them
\nHere I mark each run alternatively with red for M and black wor W. The outcome is given below.<\/p>\n

 <\/p>\n

<\/a><\/div>\n

The number of runs is given by R = 27
\nThe number of Men, n1<\/sub> = 30
\nThe number of Women, n2<\/sub> = 18<\/p>\n

<\/ins>
\n<\/b><\/p>\n

Step 3: Calculate the Mean runs<\/h3>\n

The mean is given by the formula<\/p>\n

<\/a><\/div>\n
<\/div>\n

We can go ahead to substitute the value of n1 = 30 and n2 = 18<\/p>\n

<\/a><\/div>\n

 <\/p>\n

Step 4: Calculate the Standard Deviation<\/h3>\n

You can\u00a0 find the standard deviation for a runs test using the formula<\/p>\n

<\/a><\/div>\n

We can go ahead to substitute the value of n1<\/sub> = 30 and n2<\/sub> = 18<\/p>\n

 <\/p>\n

<\/a><\/div>\n

 <\/p>\n

Step 5: Calculate the z-Statistic<\/h3>\n

The z-Statistic can be calculated using the formula<\/p>\n

<\/a><\/div>\n

Then we can substitute the value of
\nR = 27
\n\u03bcR<\/sub> = 23.5
\n\u03c3R<\/sub> = 3.2083<\/p>\n

<\/a><\/div>\n

<\/ins>
\n<\/b><\/p>\n

Step 6: Determine the Critical Value<\/h3>\n

Look up the value of the critical value from statistical table of normal distribution
\nWe get a critical value for of 1.96<\/b><\/p>\n

 <\/p>\n

Step 7: State the Decision<\/h3>\n

Since the calculated value of z = 1.0909 is within the accept region(less than the critical value of 1.96), we therefore accept (fail to reject) the null hypothesis and conclude that there is not real evidence that the arrangement is not random<\/p>\n

 <\/p>\n

Leave a comment if you have any observation or difficulty following this lesson
\nThank you for solving.<\/p>\n","protected":false},"excerpt":{"rendered":"

This is how to Perform Wald-Wolfowitz Run Test Question 21 The following arrangement of men, M, and women, W, lined up to purchase tickets for … <\/p>\n","protected":false},"author":2,"featured_media":690,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_mi_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0},"categories":[223],"tags":[],"_links":{"self":[{"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/posts\/113"}],"collection":[{"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/comments?post=113"}],"version-history":[{"count":10,"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/posts\/113\/revisions"}],"predecessor-version":[{"id":1238,"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/posts\/113\/revisions\/1238"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/media\/690"}],"wp:attachment":[{"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/media?parent=113"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/categories?post=113"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/tags?post=113"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}