SOLVED: The following hypotheses are given. H0 : π ≤ 0.81 H1 : π > 0.81 A sample of 80 observations revealed that p = 0.95. At the 0.01 significance level, can the null hypothesis be rejected? a. State the decision rule. (Round your answer to 2 decimal pl (2024)

`); let searchUrl = `/search/`; history.forEach((elem) => { prevsearch.find('#prevsearch-options').append(`

${elem}

`); }); } $('#search-pretype-options').empty(); $('#search-pretype-options').append(prevsearch); let prevbooks = $(false); [ {title:"Recently Opened Textbooks", books:previous_books}, {title:"Recommended Textbooks", books:recommended_books} ].forEach((book_segment) => { if (Array.isArray(book_segment.books) && book_segment.books.length>0 && nsegments<2) { nsegments+=1; prevbooks = $(`

  • ${book_segment.title}
  • `); let searchUrl = "/books/xxx/"; book_segment.books.forEach((elem) => { prevbooks.find('#prevbooks-options'+nsegments.toString()).append(`

    ${elem.title} ${ordinal(elem.edition)} ${elem.author}

    `); }); } $('#search-pretype-options').append(prevbooks); }); } function anon_pretype() { let prebooks = null; try { prebooks = JSON.parse(localStorage.getItem('PRETYPE_BOOKS_ANON')); }catch(e) {} if ('previous_books' in prebooks && 'recommended_books' in prebooks) { previous_books = prebooks.previous_books; recommended_books = prebooks.recommended_books; if (typeof PREVBOOKS !== 'undefined' && Array.isArray(PREVBOOKS)) { new_prevbooks = PREVBOOKS; previous_books.forEach(elem => { for (let i = 0; i < new_prevbooks.length; i++) { if (elem.id == new_prevbooks[i].id) { return; } } new_prevbooks.push(elem); }); new_prevbooks = new_prevbooks.slice(0,3); previous_books = new_prevbooks; } if (typeof RECBOOKS !== 'undefined' && Array.isArray(RECBOOKS)) { new_recbooks = RECBOOKS; for (let j = 0; j < new_recbooks.length; j++) { new_recbooks[j].viewed_at = new Date(); } let insert = true; for (let i=0; i < recommended_books.length; i++){ for (let j = 0; j < new_recbooks.length; j++) { if (recommended_books[i].id == new_recbooks[j].id) { insert = false; } } if (insert){ new_recbooks.push(recommended_books[i]); } } new_recbooks.sort((a,b)=>{ adate = new Date(2000, 0, 1); bdate = new Date(2000, 0, 1); if ('viewed_at' in a) {adate = new Date(a.viewed_at);} if ('viewed_at' in b) {bdate = new Date(b.viewed_at);} // 100000000: instead of just erasing the suggestions from previous week, // we just move them to the back of the queue acurweek = ((new Date()).getDate()-adate.getDate()>7)?0:100000000; bcurweek = ((new Date()).getDate()-bdate.getDate()>7)?0:100000000; aviews = 0; bviews = 0; if ('views' in a) {aviews = acurweek+a.views;} if ('views' in b) {bviews = bcurweek+b.views;} return bviews - aviews; }); new_recbooks = new_recbooks.slice(0,3); recommended_books = new_recbooks; } localStorage.setItem('PRETYPE_BOOKS_ANON', JSON.stringify({ previous_books: previous_books, recommended_books: recommended_books })); build_popup(); } } var whiletyping_search_object = null; var whiletyping_search = { books: [], curriculum: [], topics: [] } var single_whiletyping_ajax_promise = null; var whiletyping_database_initial_burst = 0; //number of consecutive calls, after 3 we start the 1 per 5 min calls function get_whiletyping_database() { //gets the database from the server. // 1. by validating against a local database value we confirm that the framework is working and // reduce the ammount of continuous calls produced by errors to 1 per 5 minutes. return localforage.getItem('whiletyping_last_attempt').then(function(value) { if ( value==null || (new Date()) - (new Date(value)) > 1000*60*5 || (whiletyping_database_initial_burst < 3) ) { localforage.setItem('whiletyping_last_attempt', (new Date()).getTime()); // 2. Make an ajax call to the server and get the search database. let databaseUrl = `/search/whiletype_database/`; let resp = single_whiletyping_ajax_promise; if (resp === null) { whiletyping_database_initial_burst = whiletyping_database_initial_burst + 1; single_whiletyping_ajax_promise = resp = new Promise((resolve, reject) => { $.ajax({ url: databaseUrl, type: 'POST', data:{csrfmiddlewaretoken: "LImhRfyNzIsyaucH9xiM25dAkdpvQGOkxARQPG5ECOccUf5JT57ktYkHTwCb3rbp"}, success: function (data) { // 3. verify that the elements of the database exist and are arrays if ( ('books' in data) && ('curriculum' in data) && ('topics' in data) && Array.isArray(data.books) && Array.isArray(data.curriculum) && Array.isArray(data.topics)) { localforage.setItem('whiletyping_last_success', (new Date()).getTime()); localforage.setItem('whiletyping_database', data); resolve(data); } }, error: function (error) { console.log(error); resolve(null); }, complete: function (data) { single_whiletyping_ajax_promise = null; } }) }); } return resp; } return Promise.resolve(null); }).catch(function(err) { console.log(err); return Promise.resolve(null); }); } function get_whiletyping_search_object() { // gets the fuse objects that will be in charge of the search if (whiletyping_search_object){ return Promise.resolve(whiletyping_search_object); } database_promise = localforage.getItem('whiletyping_database').then(function(database) { return localforage.getItem('whiletyping_last_success').then(function(last_success) { if (database==null || (new Date()) - (new Date(last_success)) > 1000*60*60*24*30 || (new Date('2023-04-25T00:00:00')) - (new Date(last_success)) > 0) { // New database update return get_whiletyping_database().then(function(new_database) { if (new_database) { database = new_database; } return database; }); } else { return Promise.resolve(database); } }); }); return database_promise.then(function(database) { if (database) { const options = { isCaseSensitive: false, includeScore: true, shouldSort: true, // includeMatches: false, // findAllMatches: false, // minMatchCharLength: 1, // location: 0, threshold: 0.2, // distance: 100, // useExtendedSearch: false, ignoreLocation: true, // ignoreFieldNorm: false, // fieldNormWeight: 1, keys: [ "title" ] }; let curriculum_index={}; let topics_index={}; database.curriculum.forEach(c => curriculum_index[c.id]=c); database.topics.forEach(t => topics_index[t.id]=t); for (j=0; j

    Solutions
  • Textbooks
  • `); } function build_solutions() { if (Array.isArray(solution_search_result)) { const viewAllHTML = userSubscribed ? `View All` : ''; var solutions_section = $(`
  • Solutions ${viewAllHTML}
  • `); let questionUrl = "/questions/xxx/"; let askUrl = "/ask/question/xxx/"; solution_search_result.forEach((elem) => { let url = ('course' in elem)?askUrl:questionUrl; let solution_type = ('course' in elem)?'ask':'question'; let subtitle = ('course' in elem)?(elem.course??""):(elem.book ?? "")+"    "+(elem.chapter?"Chapter "+elem.chapter:""); solutions_section.find('#whiletyping-solutions').append(` ${elem.text} ${subtitle} `); }); $('#search-solution-options').empty(); if (Array.isArray(solution_search_result) && solution_search_result.length>0){ $('#search-solution-options').append(solutions_section); } MathJax.typesetPromise([document.getElementById('search-solution-options')]); } } function build_textbooks() { $('#search-pretype-options').empty(); $('#search-pretype-options').append($('#search-solution-options').html()); if (Array.isArray(textbook_search_result)) { var books_section = $(`
  • Textbooks View All
  • `); let searchUrl = "/books/xxx/"; textbook_search_result.forEach((elem) => { books_section.find('#whiletyping-books').append(` ${elem.title} ${ordinal(elem.edition)} ${elem.author} `); }); } if (Array.isArray(textbook_search_result) && textbook_search_result.length>0){ $('#search-pretype-options').append(books_section); } } function build_popup(first_time = false) { if ($('#search-text').val()=='') { build_pretype(); } else { solution_and_textbook_search(); } } var search_text_out = true; var search_popup_out = true; const is_login = false; function pretype_setup() { $('#search-text').focusin(function() { $('#search-popup').addClass('show'); resize_popup(); search_text_out = false; }); $( window ).resize(function() { resize_popup(); }); $('#search-text').focusout(() => { search_text_out = true; if (search_text_out && search_popup_out) { $('#search-popup').removeClass('show'); } }); $('#search-popup').mouseenter(() => { search_popup_out = false; }); $('#search-popup').mouseleave(() => { search_popup_out = true; if (search_text_out && search_popup_out) { $('#search-popup').removeClass('show'); } }); $('#search-text').on("keyup", delay(() => { build_popup(); }, 200)); build_popup(true); let prevbookUrl = `/search/pretype_books/`; if (is_login) { $.ajax({ url: prevbookUrl, method: 'POST', data:{csrfmiddlewaretoken: "LImhRfyNzIsyaucH9xiM25dAkdpvQGOkxARQPG5ECOccUf5JT57ktYkHTwCb3rbp"}, success: function(response){ previous_books = response.previous_books; recommended_books = response.recommended_books; build_popup(); }, error: function(response){ console.log(response); } }); } else { let prebooks = null; try { prebooks = JSON.parse(localStorage.getItem('PRETYPE_BOOKS_ANON')); }catch(e) {} if (prebooks && 'previous_books' in prebooks && 'recommended_books' in prebooks) { anon_pretype(); } else { $.ajax({ url: prevbookUrl, method: 'POST', data:{csrfmiddlewaretoken: "LImhRfyNzIsyaucH9xiM25dAkdpvQGOkxARQPG5ECOccUf5JT57ktYkHTwCb3rbp"}, success: function(response){ previous_books = response.previous_books; recommended_books = response.recommended_books; build_popup(); }, error: function(response){ console.log(response); } }); } } } $( document ).ready(pretype_setup); $( document ).ready(function(){ $('#search-popup').on('click', '.search-view-item', function(e) { e.preventDefault(); let autoCompleteSearchViewUrl = `/search/autocomplete_search_view/`; let objectUrl = $(this).attr('href'); let selectedId = $(this).data('objid'); let searchResults = []; $("#whiletyping-solutions").find("a").each(function() { let is_selected = selectedId === $(this).data('objid'); searchResults.push({ objectId: $(this).data('objid'), contentType: $(this).data('contenttype'), category: $(this).data('category'), selected: is_selected }); }); $("#whiletyping-books").find("a").each(function() { let is_selected = selectedId === $(this).data('objid'); searchResults.push({ objectId: $(this).data('objid'), contentType: $(this).data('contenttype'), category: $(this).data('category'), selected: is_selected }); }); $.ajax({ url: autoCompleteSearchViewUrl, method: 'POST', data:{ csrfmiddlewaretoken: "LImhRfyNzIsyaucH9xiM25dAkdpvQGOkxARQPG5ECOccUf5JT57ktYkHTwCb3rbp", query: $('#search-text').val(), searchObjects: JSON.stringify(searchResults) }, dataType: 'json', complete: function(data){ window.location.href = objectUrl; } }); }); });
    SOLVED: The following hypotheses are given. H0 : π ≤ 0.81 H1 : π >
0.81 A sample of 80 observations revealed that p = 0.95. At the
0.01 significance level, can the null hypothesis be rejected? a.
State the decision rule. (Round your answer to 2 decimal pl (2024)

    FAQs

    Does a small p-value mean that we will likely fail to reject ho? ›

    No. The p-value only tells you how likely the data you have observed is to have occurred under the null hypothesis. If the p-value is below your threshold of significance (typically p < 0.05), then you can reject the null hypothesis, but this does not necessarily mean that your alternative hypothesis is true.

    Which of the following p values would be stronger evidence against the null hypothesis? ›

    A p-value less than 0.05 is typically considered to be statistically significant, in which case the null hypothesis should be rejected. A p-value greater than 0.05 means that deviation from the null hypothesis is not statistically significant, and the null hypothesis is not rejected.

    What is the probability you reject the null hypothesis when in fact the null hypothesis is true called? ›

    The probability of committing a type I error (rejecting the null hypothesis when it is actually true) is called α (alpha) the other name for this is the level of statistical significance.

    Which of the following would lead you to reject the null hypothesis? ›

    If our statistical analysis shows that the significance level is below the cut-off value we have set (e.g., either 0.05 or 0.01), we reject the null hypothesis and accept the alternative hypothesis.

    What causes a low p-value? ›

    Spread of the data. The spread of observations in a data set is measured commonly with standard deviation. The bigger the standard deviation, the more the spread of observations and the lower the P value.

    Why is a low p-value bad? ›

    A small P-value signifies that the evidence in favour of the null hypothesis is weak and that the likelihood of the observed differences due to chance is so small that the null hypothesis is unlikely to be true.

    Is p-value of 0.05 significant? ›

    If the p-value is less than 0.05, it is judged as “significant,” and if the p-value is greater than 0.05, it is judged as “not significant.” However, since the significance probability is a value set by the researcher according to the circ*mstances of each study, it does not necessarily have to be 0.05.

    What if p is greater than 0.05 null hypothesis? ›

    What does p 0.05 mean? A P-value less than 0.05 is deemed to be statistically significant, meaning the null hypothesis should be rejected in such a case. A P-Value greater than 0.05 is not considered to be statistically significant, meaning the null hypothesis should not be rejected.

    What does p-value of 0.05 mean? ›

    These are as follows: if the P value is 0.05, the null hypothesis has a 5% chance of being true; a nonsignificant P value means that (for example) there is no difference between groups; a statistically significant finding (P is below a predetermined threshold) is clinically important; studies that yield P values on ...

    What is p-value in hypothesis testing? ›

    The p-value is defined as the probability of obtaining the result at least as extreme as the observed result of a statistical hypothesis test, assuming that the null hypothesis is true.

    Is the null hypothesis reject? ›

    We reject the null hypothesis when the data provide strong enough evidence to conclude that it is likely incorrect. This often occurs when the p-value (probability of observing the data given the null hypothesis is true) is below a predetermined significance level.

    What is the probability of rejecting h0 when h0 is true? ›

    The probability of rejecting the null hypothesis when it is true is the level of significance, denoted by alpha (α), which is typically set at 0.05 or 0.01. This means that there is a 5% or 1% chance of incorrectly rejecting the null hypothesis when it is actually true.

    What affects null hypothesis? ›

    Role of Sample Size and Relationship Strength

    Specifically, the stronger the sample relationship and the larger the sample, the less likely the result would be if the null hypothesis were true.

    How do you fail a null hypothesis? ›

    If the P-value is less than or equal to the significance level, we reject the null hypothesis and accept the alternative hypothesis instead. If the P-value is greater than the significance level, we say we “fail to reject” the null hypothesis.

    What is a null hypothesis example? ›

    Examples: Null Hypothesis: H0: There is no difference in the salary of factory workers based on gender. Alternative Hypothesis: Ha: Male factory workers have a higher salary than female factory workers.

    What does a small p-value indicate? ›

    The p-value is the probability that the null hypothesis is true. (1 – the p-value) is the probability that the alternative hypothesis is true. A low p-value shows that the results are replicable. A low p-value shows that the effect is large or that the result is of major theoretical, clinical or practical importance.

    What does it mean if p-value is very small? ›

    A very small P-value indicates that the null hypothesis is very incompatible with the data that have been collected. However, we cannot say with certainty that the null hypothesis is not true, or that the alternative hypothesis must be true [5].

    Why do we reject the null hypothesis if P is small? ›

    A low p value means that the sample result would be unlikely if the null hypothesis were true and leads to the rejection of the null hypothesis. A high p value means that the sample result would be likely if the null hypothesis were true and leads to the retention of the null hypothesis.

    What p-value fails to reject the null hypothesis? ›

    If your p-value is less than your selected alpha level (typically 0.05), you reject the null hypothesis in favor of the alternative hypothesis. If the p-value is above your alpha value, you fail to reject the null hypothesis.

    References

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