{"id":16210,"date":"2021-11-16T08:30:02","date_gmt":"2021-11-16T08:30:02","guid":{"rendered":"https:\/\/assignmenttutors.net\/blog\/help-mathematics-homework-help\/"},"modified":"2021-11-16T08:30:02","modified_gmt":"2021-11-16T08:30:02","slug":"help-mathematics-homework-help","status":"publish","type":"post","link":"https:\/\/assignmenttutors.net\/blog\/help-mathematics-homework-help\/","title":{"rendered":"Help!! | Mathematics homework help"},"content":{"rendered":"<div>\n<h3>LESSON\u00a0<\/h3>\n<h4>Lesson Objectives:<\/h4>\n<p>\u00a0<\/p>\n<table width=\"85%\" align=\"center\">\n<tbody>\n<tr>\n<td width=\"100%\">\n<p>\u00a0<\/p>\n<ul>\n<li><span>Student will write null and alternative hypotheses.<\/span><\/li>\n<li><span>Student will find critical values for testing a mean or proportion against the population mean or proportion using the appropriate test, based on the sample size.<\/span><\/li>\n<li><span>Student will find critical values for testing the difference between two means or two proportions using the appropriate test, based on the sample size.<\/span><\/li>\n<\/ul>\n<p>\u00a0<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h4>What is a hypothesis?<\/h4>\n<p><span>In science, you may have learned that the hypothesis is an educated guess.\u00a0 In statistics, the same definition carries over but has some different applications.\u00a0 A statistical study is similar to the scientific method.\u00a0 From science you have learned that the scientific method includes the following steps:\u00a0 1) Ask a question 2) Do background research 3) Construct a hypothesis 4) Test your hypothesis by doing an experiment 5) Analyze the data and draw a conclusion 6) Communicate the results.\u00a0 In statistics, there are two hypotheses that need to be formed once you have defined the problem and completed background research.\u00a0 One is called the &#8220;null&#8221; hypothesis and the other is called the &#8220;alternative&#8221; hypothesis.\u00a0 Once the study is conducted, we can reject or fail to reject either of the hypothesis based on the results of the study.<\/span><\/p>\n<p><span><span>The Null Hypothesis<\/span><\/span><br \/><span><br \/><span>The null hypothesis is composed of the fact that there is no effect of the treatment on the subjects in the study.\u00a0\u00a0<span>For example if we were trying to investigate the relationship between two variables our null hypothesis may state that &#8220;there is no relationship between the two variables&#8221; or if we are trying to see if a new drug has an effect on weight gain the null hypothesis may state that &#8220;the drug has no effect on the weight gain of the subjects&#8221;<\/span>.\u00a0 The null hypothesis is the one that we will fail to reject (accept) unless the data provides convincing evidence that it is false.<\/span><\/span><\/p>\n<p><span><span>The Alternative Hypothesis<\/span><\/span><\/p>\n<p><span>The alternative hypothesis may be referred to as the opposite of the null hypothesis.\u00a0<\/span><span>\u00a0For example, if the null hypothesis states that there is no relationship between two variables, then the alternative hypothesis should state that<\/span><span>\u00a0<\/span><span>&#8220;there is a relationship between the two variables that can be measured<\/span><span>.\u00a0\u00a0<\/span><span>If the null hypothesis states that there is no effect on the subject then the alternative hypothesis should state that &#8220;there is an effect on the subject&#8221;.<\/span><span>\u00a0 We will fail to reject (accept) the alternative hypothesis if and only if the data provides convincing evidence that it is true.\u00a0\u00a0<\/span><\/p>\n<h4>Practice Writing Null and Alternative Hypotheses<\/h4>\n<p><span>The hypotheses can be written out in words or we may use mathematical symbols to express the hypothesis.\u00a0 Here a few examples of how to write the null and alternative hypothesis.\u00a0 The most common symbol for the null hypothesis is\u00a0<\/span><span>H<\/span><sub>0<\/sub><span>\u00a0and the most common symbol for the alternative hypothesis is\u00a0<\/span><span>H<\/span><sub>1<span>.<\/span><\/sub><\/p>\n<p><span>Let&#8217;s Practice:<\/span><sub><span>\u00a0\u00a0\u00a0<\/span><\/sub><sub><span\/><\/sub><\/p>\n<p><span><span>Case I<\/span><\/span><span><span>:<\/span><\/span><span><span>\u00a0<\/span><\/span><span><span><span>An agriculturist is doing a study to determine if a fertilizer has any effect on the average height of 100 apple trees.\u00a0 He knows that the average height of unfertilized apple trees is 10ft.\u00a0 The average height of the 100 apple trees that were treated with fertilizer is 10.8 feet with a standard deviation of .5 ft<\/span>.\u00a0\u00a0<\/span><\/span><span><span\/><\/span><\/p>\n<p><span><span>1)\u00a0 Do you think that the fertilizer has an effect on the height of the apple trees?<\/span><\/span><span><span><br \/><span>H<\/span><sub>0<\/sub><span>\u00a0= The fertilizer has no effect on the height of the apple trees\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Sample mean = Population mean<\/span><br \/><span>H<\/span><sub>1<\/sub><span>\u00a0= The fertilizer does have an effect on the height of the apple trees.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Sample mean\u00a0\u00a0<\/span><\/span><\/span><span>\u2260\u00a0<\/span><span>Population mean<\/span><br \/><span><span><br \/>2)\u00a0\u00a0<\/span><\/span><span><span><span>Does the fertilizer make the apple trees taller?<\/span><\/span><\/span><span><span><br \/>H<sub>0\u00a0<\/sub>= The fertilizer does not make the apple trees taller.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Sample mean = Population mean<br \/>H<sub>1<\/sub>\u00a0= The fertilizer does make the apple trees taller.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Sample mean &gt; Population mean<\/span><\/span><\/p>\n<p><span>Remember that when writing and testing hypotheses it is very important that you consider the question that want to answer with your study because this fact helps to shape the correct hypotheses.<\/span><span><span><br \/><\/span><\/span><\/p>\n<h4>Choosing the Appropriate Test<\/h4>\n<p><span>Choosing the appropriate test for any statistical research is very important to obtaining the most accurate results.\u00a0 We discussed in a previous lesson when to use a z-score or z-test and when to use a t-score or a t-test.\u00a0 Recall that we use a z-test when the sample size is fairly large (greater than 100) and a t-test when the sample size is small (less than 100).\u00a0 Another question that we need to consider is when to use a two- tailed test or a one- tailed test.\u00a0 This choice is made based upon the statement of the alternative hypothesis.\u00a0 We would use a two-tailed test if our alternative hypothesis is the exact opposite of the null hypothesis.\u00a0 We would use a one-tailed test if our alternative hypothesis suggests a certain direction for the results.\u00a0\u00a0<\/span><\/p>\n<p><span>If\u00a0\u00a0<\/span><span>H<\/span><sub>0<\/sub><sub>\u00a0=<\/sub><span>\u00a0There is no effect on the variable , then\u00a0<\/span><span>H<\/span><sub>1<\/sub><span>\u00a0= There is an effect on the variable.<\/span><\/p>\n<p><span>In this case we would use a two tailed test.<\/span><\/p>\n<p><span>If\u00a0<\/span><span>H<\/span><sub>0<\/sub><sub>\u00a0=<\/sub><span>\u00a0The mean sample mean is equal to the population mean , then\u00a0<\/span><span>H<\/span><sub>1<\/sub><span>\u00a0= The sample mean is greater than the population mean.<\/span><\/p>\n<p><span>In this case we would use the one-tailed test since we are concerned with only the right side of the probability distribution where the values are that are greater than the mean.<\/span><\/p>\n<p><span>Click\u00a0<\/span><a rel=\"nofollow noopener\" target=\"_blank\" style=\"font-family: verdana, sans-serif; font-size: 15.0544px;\" href=\"http:\/\/www.khanacademy.org\/video\/one-tailed-and-two-tailed-tests?playlist=Statistics\">here<\/a><span>\u00a0for a video explaining when to use a one-tailed test and when to use a two tailed test.<\/span><\/p>\n<h4>Critical Values &amp; Testing a Hypothesis<\/h4>\n<p><span>Testing a hypothesis includes finding the appropriate z or t score and finding critical values to compare it to the probability of an event and its position on the normal distribution curve given a confidence interval or p-value.\u00a0\u00a0<\/span><span>A critical value is the value of the dependent variable at a given point of a function that helps us to decide to reject or fail to reject the null hypothesis.\u00a0 If the test statistic is this number or more then we will reject the null hypothesis but if the test statistic is less than this number then we will fail to reject or accept the null hypothesis.\u00a0\u00a0<\/span><\/p>\n<p><span>Consider these examples:<\/span><\/p>\n<p><span>Testing the mean against the population mean<\/span><br \/><span>\u00a0\u00a0<\/span><br \/><span><span><span>An agriculturist is doing a study to determine if a fertilizer has any effect on the average height of 100 apple trees.\u00a0 He knows that the average height of unfertilized apple trees is 10ft.\u00a0 The average height of the 100 apple trees that were treated with fertilizer is 10.1 feet with a standard deviation of 0.5 ft<\/span>.\u00a0\u00a0<\/span><\/span><span><span>Do you think that the fertilizer has an effect on the height of the apple trees?<br \/><\/span><\/span><br \/><span>Step 1<\/span><span>:\u00a0\u00a0<\/span><span>Write the null and alternative hypotheses<\/span><br \/><span><span><span>H<\/span><sub>0<\/sub><span>\u00a0= The fertilizer has no effect on the height of the apple trees\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Sample mean = Population mean<\/span><br \/><span>H<\/span><sub>1<\/sub><span>\u00a0= The fertilizer does have an effect on the height of the apple trees.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Sample mean\u00a0\u00a0<\/span><\/span><\/span><span>\u2260\u00a0<\/span><span>Population mean<\/span><br \/><span><span><br \/><\/span><\/span><span>Step 2<\/span><span>:\u00a0\u00a0<\/span><span>We will assume that the null hypothesis is true and find the z-score (since we have a large sample).<\/span><span>\u00a0\u00a0<\/span><\/p>\n<p><span>z = 10 &#8211; 10.1\/(.5\/\u221a100) = -2<\/span><span>\u00a0\u00a0<\/span><\/p>\n<p><span>Step 3<\/span><span>:\u00a0\u00a0<\/span><span>Find the critical value by applying the subtracting (since the z-score is negative) the product of the z-score and the standard deviation from the population mean.<\/span><\/p>\n<p><span>10 &#8211; 2(.5) = 9 so the critical value is 9<\/span><span\/><\/p>\n<p>Since the mean of the sample is greater than this critical value we must reject the null hypothesis.<\/p>\n<p><span>Testing a proportion against the population proportion<\/span><\/p>\n<p><span>A company found that in a sample of 100 of its products that 25 were defective after retraining the employees.\u00a0 If there is an overall 60% chance that the company will produce a defective product, did the training help employees minimize the number of defective products?<\/span><\/p>\n<p><span>Step 1:<\/span>\u00a0\u00a0<br \/><span>Write the null and alternative hypothesis.<\/span><\/p>\n<p><span>H<\/span><sub><span>0<\/span>\u00a0=<\/sub><span>\u00a0p = 60% or .6\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 The training had no effect on the proportion of defective products<\/span><br \/><span>H<\/span><sub>1\u00a0<\/sub><span>= p &lt; 60% or .6\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 The training helped to decrease the proportion of defective products.<\/span><\/p>\n<p><span>Remember that these types of problems are binomial experiments so we have to be sure that we can use the normal approximation by confirming that (n)(p) and (n)(q) are both greater than 5.\u00a0 So (100)(.6) = 60 and (100)(.4) = 40, we may proceed.<\/span><\/p>\n<p><span>Step 2<\/span><span>:\u00a0\u00a0<\/span><\/p>\n<p><span>Assume that the null hypothesis is true and find the standard deviation ( standard deviation = \u221a(n)(p(q)) so that we can find the z-score.<\/span><\/p>\n<p><span>standard deviation = 4.33<\/span><\/p>\n<p><span>z = .25 &#8211; .6\/ 4.33 = -.08<\/span><\/p>\n<p><span>Step 3<\/span><span>:\u00a0 Find the critical value by subtracting (since the z-score is negative) the product of the z-score and the standard deviation from the mean.<\/span><\/p>\n<p><span>.6 &#8211; .3464 = .2536 or 25.36 %\u00a0 since our test statistic is .6 or 60% and it is more than the critical value then we must reject the null hypothesis and conclude that training did decrease the number of defective products.<\/span><\/p>\n<h4>Testing the Difference of Means and Difference of Proportions<\/h4>\n<p><span>The difference of means or difference of proportions is used to find out whether there is a significance between the controlled group and the uncontrolled group.\u00a0 We can also use critical values to determine the significance for the difference of means as well as the difference of proportions.<\/span><\/p>\n<p><span>Difference of Means<\/span><span>:<\/span><\/p>\n<p><span>A teacher gave 100 students a study guide in preparation for a major test.\u00a0 The average score for these students was 88 with standard deviation of 2.\u00a0 She did not give study guides to another group of 100 students and the average score for these students was 80 with a standard deviation of 3.\u00a0 Determine whether the study guide had an effect on student scores.<\/span><\/p>\n<p><span>Step 1<\/span><span>:\u00a0 Find the difference in the sample mean scores.\u00a0\u00a0<\/span><span>88-80 = 8\u00a0<\/span><\/p>\n<p><span>Step 2<\/span><span>:\u00a0 Write the null and alternative hypotheses.<\/span><br \/><span>H<\/span><sub>0<\/sub><span>\u00a0= The study guide has no effect on student test scores<\/span><span>\u00a0or\u00a0<\/span><span>population mean<\/span><sub>1<\/sub><span>\u00a0= population mean<\/span><sub>2<\/sub><span>\u00a0or\u00a0<\/span><span>population mean<\/span><sub>1<\/sub><span>\u00a0&#8211; population mean<\/span><sub>2<\/sub><span>\u00a0= 0<\/span><sub>\u00a0<br \/><\/sub><span>H<\/span><sub>1<\/sub><span>\u00a0= The study guide has an effect on student test scores\u00a0<span>or<\/span>\u00a0population mean<\/span><sub>1<\/sub><span>\u00a0\u2260 population mean<\/span><sub>2<\/sub><span>\u00a0or\u00a0<\/span><span>population mean<\/span><sub>1<\/sub><span>\u00a0&#8211; population mean<\/span><sub>2<\/sub><span>\u00a0\u2260 0<\/span><br \/><sub><br \/><\/sub><span>Step 3<\/span><span>:\u00a0 Calculate the standard deviation for the difference of the sample means.\u00a0\u00a0<\/span><br \/><span>To do this we need to find the variance (square the standard deviation for each sample) and divide it by n for each sample then add the two values together and take the square root.<\/span><\/p>\n<p><span>\u221a[(2<\/span><sup>2<\/sup><span>\u00a0)\/100 + (3<\/span><sup>2<\/sup><span>\u00a0)\/100] = \u221a4\/100 + 3\/100 = \u221a7\/100 = \u221a.07 = .26<\/span><\/p>\n<p><span>Step 4<\/span><span>:\u00a0 Assume that the null hypothesis is true and find the z-score using the difference of the means.<\/span><br \/><span>z = 0-8\/.26 = -30.76<\/span><span>\u00a0 find the critical value by adding (since the z-score is positive) the product of the z-score and the standard deviation to the test statistic.\u00a0\u00a0<\/span><\/p>\n<p><span>0 &#8211; 8 =<\/span><span>\u00a0-8<\/span><span>\u00a0This is the critical value and since the test statistic 0 is must than this value we must reject the null hypothesis and conclude that the study guide has an effect on student test scores<\/span><span>.<\/span><\/p>\n<p><center><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/www.sc.whitmoreschool.org\/images\/livechatoff.gif\" alt=\"Chat Off\" width=\"211\" height=\"56\"\/><br \/>NEXT TEACHER OFFICE HOURS ARE:\u00a0<\/center><\/p>\n<h4>Grading Rubric:<\/h4>\n<table border=\"1\" align=\"center\">\n<tbody>\n<tr>\n<td width=\"700\">\n<p>\u00a0<\/p>\n<p><span><span><strong>Grading for this lesson:<\/strong><\/span><\/span><\/p>\n<p><span><span\/><\/span><\/p>\n<p><strong><span>To get a 10<\/span><\/strong><span>: All answers are correct the first time, or within first revision.\u00a0<\/span><br \/><strong><span>To get a 9<\/span><\/strong><span>: You can have 1 incorrect answer after your\u00a0original submission.<\/span><br \/><strong><span>To get an 8<\/span><\/strong><span>: You can have 2 incorrect answers after your\u00a0original submission.<\/span><br \/><strong><span>To get a 7<\/span><\/strong><span>: You can have 3\u00a0 incorrect answers after your\u00a0original submission.\u00a0<\/span><br \/><strong><span>To get a 6<\/span><\/strong><span>: You can have 4 incorrect answers after your\u00a0original submission.<\/span><br \/><strong><span>To get a 5<\/span><\/strong><span>:\u00a0Cheating- Plagiarism &#8211; purposeful or mistaken, which will lower your final grade for the course (so be very careful when posting your work!); lack of effort, disrespect, or attitude (we are here to communicate with you if you don&#8217;t understand something);\u00a0<\/span>lesson requirements have not been met.<br \/>\u00a0<\/p>\n<p><span><span\/><\/span><\/p>\n<p><span>Note:\u00a0 For this class it is necessary to post the questions over each answer. Failure to do so will result in asking for a revision.\u00a0\u00a0\u00a0<\/span><strong><span>No grade will be given for incomplete work<\/span><\/strong><span>.<\/span><\/p>\n<p><span><span\/><\/span><\/p>\n<p>\u00a0<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h4><strong>Assignment:<\/strong><\/h4>\n<p><span>For questions 1-5, write the null and alternative hypothesis.<\/span><\/p>\n<p><span>1.\u00a0 Does the water temperature have an effect on the number of people in the pool?<\/span><\/p>\n<p><span>2.\u00a0 Does the weather have an effect on the number of people at the beach?<\/span><\/p>\n<p><span>3.\u00a0 A fitness center is running a discounted membership fee.\u00a0 Did the discount increase the membership sales? Write your hypotheses mathematically.<\/span><\/p>\n<p><span>4.\u00a0 A medical researcher gave 100 patients a new drug to see if it reduces their blood pressure?\u00a0 Did the new drug reduce the patients&#8217; blood pressure?\u00a0 Write your hypothesis mathematically.<\/span><\/p>\n<p><span>5.\u00a0 Some students took a conflict resolution class?\u00a0 Did this class help to reduce the number of conflicts that the students were involved in?\u00a0 Write your hypothesis mathematically.<\/span><\/p>\n<p><span>For questions 6-10, find the critical value.<\/span><\/p>\n<p><span>6.\u00a0 There is an annual hot dog eating contest in Plattsburg, MS and the average number of hot dogs eaten by one person is 36 with a standard deviation of 6.\u00a0 Find the critical value for a person who can eat more than 2 deviations above the mean.<\/span><\/p>\n<p><span>7.\u00a0 Female high school seniors at a particular school have an average height of 65 inches with a standard deviation of 5 inches.\u00a0 Find the critical value for a female high senior who is less than 1 deviation from the mean.<\/span><\/p>\n<p><span>8.\u00a0 The average weight of a newborn at a particular hospital is 96 ounces with a standard deviation of 3 ounces.\u00a0 Find the critical value for a newborn who is 2 standard deviations below the average weight.<\/span><\/p>\n<p><span>9.\u00a0 A company found that 27 out of 150 of its products were defective after retraining its employees.\u00a0 If the company normally has a 40% defective product rate, find the critical value to determine if retraining the employees helped to minimize the number of defective products.<\/span><\/p>\n<p><span>10.\u00a0 A teacher gives 200 students a study guide for a test and the average score was 90 with a standard deviation of 6.\u00a0 She did not give the other 200 students a study guide and their average score was 70 with a standard deviation of 8.\u00a0 Find the critical value to determine whether or not the study guide helped students to increase their test score.<\/span><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>LESSON\u00a0 Lesson Objectives: \u00a0 \u00a0 Student will write null and alternative hypotheses. Student will find critical values for testing a mean or proportion against the population mean or proportion using the appropriate test, based on the sample size. Student will find critical values for testing the difference between two means or two proportions using the [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[31],"tags":[],"class_list":["post-16210","post","type-post","status-publish","format-standard","hentry","category-homework-help"],"_links":{"self":[{"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/posts\/16210","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/comments?post=16210"}],"version-history":[{"count":0,"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/posts\/16210\/revisions"}],"wp:attachment":[{"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/media?parent=16210"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/categories?post=16210"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/tags?post=16210"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}