{"id":36210,"date":"2024-04-26T22:59:58","date_gmt":"2024-04-26T22:59:58","guid":{"rendered":"http:\/\/localhost\/branding\/null-and-alternate-hypotheses\/"},"modified":"2024-04-26T22:59:58","modified_gmt":"2024-04-26T22:59:58","slug":"null-and-alternate-hypotheses","status":"publish","type":"post","link":"https:\/\/sheilathewriter.com\/blog\/null-and-alternate-hypotheses\/","title":{"rendered":"Null and alternate hypotheses"},"content":{"rendered":"

Null and alternate hypotheses\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/p>\n

\u00a0<\/p>\n

Week X Y XY XX 1 29 21 609 841 2 35 32 1120 1225 3 41 11 451 1681 4 32 26 832 1024 Total \u2211X = 137 \u2211Y = 90 \u2211 XY = 3012 \u2211XX = 4771 Given n = 4, \u2211X = 137 Mean = \u2211X \/ n Standard Deviation (s) = \u221a \u2211{(X – x)(X – x)} \/ n Mean = 137 \/ 4 Standard Deviation (s) = \u221a 17689 \/ 4 Mean = 34.25 Standard Deviation (s) = \u221a 4422.25 Standard Deviation (s) = 66.5 The null and alternate hypothesis here becomes:<\/p>\n

H0: \u03bc \u2265 34.25<\/p>\n

H1: \u03bc < 34.25<\/p>\n

The hypothesis test statistics is:<\/p>\n

Z = (x-\u03bc) \/ (\u03c3-\u221an)<\/p>\n

= (34.25-35) \/ (0.05-\u221a100)<\/p>\n

= -0.75 \/ -9.95<\/p>\n

= 0.075<\/p>\n

Probability (p) value when (\u03c3) = 0.05, and its meaning<\/p>\n

p-value = P(Z>0.075) = 0.0001<\/p>\n

The probability of getting a sample whose mean is 34.25 or more when H0 is true is 0.0001.<\/p>\n

Comparing the p \u2013 value to alpha <\/p>\n

For a large test statistic, the critical value is large and its p-value is small than even the alpha value.A rejection is made if test statistics is found in the rejection region.<\/p>\n","protected":false},"excerpt":{"rendered":"

Null and alternate hypotheses\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0 Week X Y XY XX 1 29 21 609 841 2 35 32 1120 1225<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[],"tags":[],"class_list":["post-36210","post","type-post","status-publish","format-standard","hentry"],"yoast_head":"\nNull and alternate hypotheses - sheilathewriter<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/sheilathewriter.com\/blog\/null-and-alternate-hypotheses\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Null and alternate hypotheses - sheilathewriter\" \/>\n<meta property=\"og:description\" content=\"Null and alternate hypotheses\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0 Week X Y XY XX 1 29 21 609 841 2 35 32 1120 1225\" \/>\n<meta property=\"og:url\" content=\"https:\/\/sheilathewriter.com\/blog\/null-and-alternate-hypotheses\/\" \/>\n<meta property=\"og:site_name\" content=\"sheilathewriter\" \/>\n<meta property=\"article:published_time\" content=\"2024-04-26T22:59:58+00:00\" \/>\n<meta name=\"author\" content=\"admin\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"admin\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/sheilathewriter.com\/blog\/null-and-alternate-hypotheses\/\",\"url\":\"https:\/\/sheilathewriter.com\/blog\/null-and-alternate-hypotheses\/\",\"name\":\"Null and alternate hypotheses - 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