{"id":187330,"date":"2025-02-04T06:40:08","date_gmt":"2025-02-04T06:40:08","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=187330"},"modified":"2025-02-04T06:40:10","modified_gmt":"2025-02-04T06:40:10","slug":"mendelian-genetics-when-mendel-conducted-his-famous-genetics-experiments-with-peas","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/02\/04\/mendelian-genetics-when-mendel-conducted-his-famous-genetics-experiments-with-peas\/","title":{"rendered":"Mendelian Genetics When Mendel conducted his famous genetics experiments with peas"},"content":{"rendered":"\n<p>Mendelian Genetics When Mendel conducted his famous genetics experiments with peas, one sample of offspring consisted of 428 green peas and 152 yellow peas.<\/p>\n\n\n\n<p>a. Find a 95% confidence interval estimate of the percentage of yellow peas.<\/p>\n\n\n\n<p>b. Based on his theory of genetics, Mendel expected that 25% of the offspring peas would be yellow. Given that the percentage of offspring yellow peas is not 25%, do the results contradict Mendel\u2019s theory? Why or why not?<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>In Gregor Mendel&#8217;s classic pea plant experiments, one sample comprised 428 green peas and 152 yellow peas. Let&#8217;s analyze this data to address the following:<\/p>\n\n\n\n<p><strong>a. 95% Confidence Interval for the Percentage of Yellow Peas<\/strong><\/p>\n\n\n\n<p>First, we calculate the sample proportion (( \\hat{p} )) of yellow peas:<\/p>\n\n\n\n<p>[ \\hat{p} = \\frac{152}{428 + 152} = \\frac{152}{580} \\approx 0.2621 ]<\/p>\n\n\n\n<p>To construct a 95% confidence interval for this proportion, we use the formula:<\/p>\n\n\n\n<p>[ \\hat{p} \\pm Z_{\\alpha\/2} \\times \\sqrt{\\frac{\\hat{p}(1 &#8211; \\hat{p})}{n}} ]<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( Z_{\\alpha\/2} ) is the critical value for a 95% confidence level, which is 1.96.<\/li>\n\n\n\n<li>( n ) is the total sample size, 580.<\/li>\n<\/ul>\n\n\n\n<p>Plugging in the values:<\/p>\n\n\n\n<p>[ 0.2621 \\pm 1.96 \\times \\sqrt{\\frac{0.2621 \\times (1 &#8211; 0.2621)}{580}} ]<\/p>\n\n\n\n<p>Calculating the margin of error:<\/p>\n\n\n\n<p>[ 1.96 \\times \\sqrt{\\frac{0.2621 \\times 0.7379}{580}} \\approx 1.96 \\times \\sqrt{0.000333} \\approx 1.96 \\times 0.0183 \\approx 0.0359 ]<\/p>\n\n\n\n<p>Thus, the confidence interval is:<\/p>\n\n\n\n<p>[ 0.2621 &#8211; 0.0359 \\approx 0.2262 ]<\/p>\n\n\n\n<p>[ 0.2621 + 0.0359 \\approx 0.2980 ]<\/p>\n\n\n\n<p>Converting these proportions to percentages:<\/p>\n\n\n\n<p>[ 22.62\\% \\text{ to } 29.80\\% ]<\/p>\n\n\n\n<p>Therefore, the 95% confidence interval for the percentage of yellow peas is approximately 22.62% to 29.80%.<\/p>\n\n\n\n<p><strong>b. Comparison with Mendel&#8217;s Expected 25%<\/strong><\/p>\n\n\n\n<p>Mendel&#8217;s genetic theory predicts that 25% of offspring peas should be yellow. The observed sample proportion is approximately 26.21%, and the 95% confidence interval ranges from 22.62% to 29.80%. Since 25% lies within this interval, the observed data does not significantly deviate from Mendel&#8217;s expected proportion.<\/p>\n\n\n\n<p><strong>Explanation<\/strong><\/p>\n\n\n\n<p>Confidence intervals provide a range of values within which we expect the true population parameter to lie, based on our sample data. In this case, the interval suggests that the true percentage of yellow peas in the population is likely between 22.62% and 29.80%. Mendel&#8217;s expected 25% falls comfortably within this range, indicating that the observed data aligns with his theoretical prediction.<\/p>\n\n\n\n<p>It&#8217;s important to note that sample data can exhibit natural variability due to random sampling error. The purpose of constructing a confidence interval is to account for this variability and assess whether observed differences are statistically significant or could have occurred by chance. In this scenario, the overlap between the confidence interval and Mendel&#8217;s expected proportion suggests that any discrepancy is likely due to random variation rather than a fundamental flaw in Mendel&#8217;s theory.<\/p>\n\n\n\n<p>Furthermore, the sample size of 580 peas is relatively large, which enhances the reliability of the confidence interval. Larger sample sizes tend to produce narrower confidence intervals, providing more precise estimates of the population parameter. The alignment between the observed data and Mendel&#8217;s expected ratio reinforces the validity of his genetic principles and demonstrates the robustness of his experimental results.<\/p>\n\n\n\n<p>In conclusion, the observed percentage of yellow peas is consistent with Mendel&#8217;s theoretical expectation, and the results do not contradict his genetic theory. The slight difference between the observed proportion and the expected 25% is well within the range of normal sampling variation.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Mendelian Genetics When Mendel conducted his famous genetics experiments with peas, one sample of offspring consisted of 428 green peas and 152 yellow peas. a. Find a 95% confidence interval estimate of the percentage of yellow peas. b. Based on his theory of genetics, Mendel expected that 25% of the offspring peas would be yellow. [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-187330","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/187330","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=187330"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/187330\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=187330"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=187330"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=187330"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}