{"id":46105,"date":"2024-04-15T22:07:35","date_gmt":"2024-04-15T22:07:35","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=46105"},"modified":"2024-04-15T22:07:35","modified_gmt":"2024-04-15T22:07:35","slug":"which-one-of-the-following-theories-is-not-correct-in-the-context-of-central-limit-theorem","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/which-one-of-the-following-theories-is-not-correct-in-the-context-of-central-limit-theorem\/","title":{"rendered":"Which one of the following theories is not correct in the context of Central Limit Theorem?"},"content":{"rendered":"<p>\r\n    <!-- Check if it's an AMP page -->\r\n            <!-- Non-AMP version -->\r\n        <div class=\"mcq-container\" data-quiz-id=\"quizState_6a977648c64bd\">\r\n                                            <div class=\"option\" data-option-key=\"option1\" data-is-correct=\"false\">\r\n                    If a population from which a sample is drawn is normally distributed the sampling distribution of mean (SDM) will be normal for all sample sizes                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option2\" data-is-correct=\"false\">\r\n                    The mean of the SDM is the population mean                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option3\" data-is-correct=\"true\">\r\n                    If the population is not normal from which the sample is drawn, the SDM is not normal for any sample size                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option4\" data-is-correct=\"false\">\r\n                    If the population is not normal from which a sample is drawn, the SDM approaches normality as the sample size increases                <\/div>\r\n                            \r\n            <!-- Feedback messages for non-AMP -->\r\n            <div class=\"feedback\" data-feedback=\"wrong\">Answer is Right!<\/div>\r\n            <div class=\"feedback\" data-feedback=\"right\">Answer is Wrong!<\/div>\r\n        <\/div>\r\n\r\n        <script>\r\n        document.addEventListener('DOMContentLoaded', function () {\r\n            var containers = document.querySelectorAll('.mcq-container');\r\n\r\n            containers.forEach(function(container) {\r\n                var options = container.querySelectorAll('.option');\r\n                var feedbackSelect = container.querySelector('[data-feedback=\"select\"]');\r\n                var feedbackWrong = container.querySelector('[data-feedback=\"wrong\"]');\r\n                var feedbackRight = container.querySelector('[data-feedback=\"right\"]');\r\n\r\n                options.forEach(function(option) {\r\n                    option.addEventListener('click', function() {\r\n                        var selectedOption = option.getAttribute('data-option-key');\r\n                        var isCorrect = option.getAttribute('data-is-correct') === 'true';\r\n\r\n                        \/\/ Remove previous selections\r\n                        options.forEach(function(opt) {\r\n                            opt.classList.remove('correct', 'incorrect');\r\n                        });\r\n\r\n                        \/\/ Add the correct\/incorrect class\r\n                        if (isCorrect) {\r\n                            option.classList.add('correct');\r\n                            feedbackRight.hidden = false;\r\n                            feedbackWrong.hidden = true;\r\n                        } else {\r\n                            option.classList.add('incorrect');\r\n                            feedbackRight.hidden = true;\r\n                            feedbackWrong.hidden = false;\r\n                        }\r\n\r\n                        \/\/ Hide select feedback\r\n                        feedbackSelect.hidden = true;\r\n                    });\r\n                });\r\n            });\r\n        });\r\n        <\/script>\r\n    \r\n    <!--more--><\/p>\n<p>The correct answer is: C. If the population is not normal from which the sample is drawn, the SDM is not normal <div class=\"youtube-subscribe-container\">\r\n        <a href=\"https:\/\/www.youtube.com\/channel\/UCNHT8lW-JmLC68rjBfZhdkg?sub_confirmation=1\" target=\"_blank\" class=\"youtube-subscribe-button\">\r\n            <span class=\"youtube-icon\">\r\n                <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 576 512\">\r\n                    <path d=\"M549.7 124.1c-6.3-23.7-24.8-42.3-48.3-48.6C458.8 64 288 64 288 64S117.2 64 74.6 75.5c-23.5 6.3-42 24.9-48.3 48.6-11.4 42.9-11.4 132.3-11.4 132.3s0 89.4 11.4 132.3c6.3 23.7 24.8 41.5 48.3 47.8C117.2 448 288 448 288 448s170.8 0 213.4-11.5c23.5-6.3 42-24.2 48.3-47.8 11.4-42.9 11.4-132.3 11.4-132.3s0-89.4-11.4-132.3zm-317.5 213.5V175.2l142.7 81.2-142.7 81.2z\"\/>\r\n                <\/svg>\r\n            <\/span>\r\n            Subscribe on YouTube\r\n        <\/a>\r\n    <\/div> for any sample size.<\/p>\n<p>The Central Limit Theorem (CLT) states that, given a sufficiently large sample size, the sampling distribution of the mean of a variable will be approximately normally distributed, regardless of the distribution of the variable in the population. This means that, even if the population is not normally distributed, the sample mean will be approximately normally distributed if the sample size is large enough.<\/p>\n<p>The CLT is a powerful tool that can be used to make inferences about a population based on a sample. However, it is important to note that the CLT only applies to the sampling distribution of the mean. The CLT does not apply to the sampling distribution of other statistics, such as the median or the mode.<\/p>\n<p>In addition, the CLT only applies to sufficiently large sample sizes. The exact sample size required for the CLT to apply depends on the distribution of the variable in the population. For example, if the population is normally distributed, the <div class=\"telegram-channel-container\">\r\n        <a href=\"https:\/\/t.me\/pscnotes2025\" target=\"_blank\" class=\"telegram-channel-button\">\r\n            <span class=\"telegram-icon\">\r\n                <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 496 512\">\r\n                    <path fill=\"white\" d=\"M248,8C111,8,0,119,0,256s111,248,248,248s248-111,248-248S385,8,248,8z M362,177L320,367c-3,14-10,18-20,14l-56-41l-27,26 c-3,3-5,5-10,5l4-63L323,196c5-5-1-7-8-3l-98,62l-42-13c-9-3-10-9,2-14l162-63C351,160,365,164,362,177z\"\/>\r\n                <\/svg>\r\n            <\/span>\r\n            Join Our Telegram Channel\r\n        <\/a>\r\n    <\/div> CLT will apply with a sample size of 30 or more. However, if the population is not normally distributed, a larger sample size may be required for the CLT to apply.<\/p>\n<p>Overall, the CLT is a powerful tool that can be used to make inferences about a population based on a sample. However, it is important to note that the CLT only applies to the sampling distribution of the mean, and that the CLT only applies to sufficiently large sample sizes.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Subscribe on YouTube<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[12],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.2 (Yoast SEO v23.3) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Which one of the following theories is not correct in the context of Central Limit Theorem?<\/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:\/\/exam.pscnotes.com\/mcq\/which-one-of-the-following-theories-is-not-correct-in-the-context-of-central-limit-theorem\/\" \/>\n<meta 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