// Numbas version: exam_results_page_options
{"name": "Obliczenie przedzia\u0142u ufno\u015bci", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Obliczenie przedzia\u0142u ufno\u015bci", "tags": [], "metadata": {"description": "<p>Dane s\u0105 \u015brednia i odchylenie standardowe 1000-elementowej pr&oacute;by. Nale\u017cy wyznaczy\u0107 95% przedzia\u0142 ufno\u015bci dla \u015bredniej w populacji.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>W badaniu spytano $\\var{samplesize}$ mieszka\u0144c&oacute;w Gda\u0144ska o subiektywn\u0105 ocen\u0119 dost\u0119pno\u015bci transportu zbiorowego w miejscu zamieszkania w skali od $\\var{bottom}$ ({expb}) do $\\var{top}$ ({expt}).</p>\n<p>Wsr&oacute;d tych respondent&oacute;w \u015brednia wynosi\u0142a $\\var{samplemean}$, a odchylenie standardowe $\\var{sstdev}$.</p>\n<p></p>\n<p>Zaokr\u0105glij wszystkie wyniki do 2 miejsc po przecinku.</p>\n<p></p>", "advice": "\n\t<p><strong>a) </strong></p>\n\t    <p>The $z$-score is given by&nbsp;</p>\n\t    <p>\\[z=\\frac{\\var{score}-\\var{samplemean}}{\\var{sstdev}}=\\var{zscore}\\]</p>\n\t    <p>(To 3 decimal places).</p>\n\t    <p><strong>b)</strong></p>\n\t    <p>The lower bound for the 95% confidence interval is given by:</p>\n\t    <p>Lower bound = $\\displaystyle 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