Stats-Prob-Week-5 PDF

Lesson 12.1 The Null and Alternative Hypotheses 1 Chronicles 16:34 Oh give thanks to the Lord, for he is good; for his steadfast love endures forever!  James 1:3 When your faith is tested, you learn to be patient.  Objectives At the end of this lesson, the learners...

Lesson 12.1 The Null and Alternative Hypotheses 1 Chronicles 16:34 Oh give thanks to the Lord, for he is good; for his steadfast love endures forever!  James 1:3 When your faith is tested, you learn to be patient.  Objectives At the end of this lesson, the learners should be able to do the following: Define hypothesis testing Differentiate a right-tailed, left-tailed, and two- tailed test State the null and alternative hypotheses in words and symbols  ACTIVITY: Advertising Claims Duration: 20 minutes Methodology: 1. In a group of 5 members, think about a certain advertisement, re-enact. 2. One person from the group will explain the advertisement claims about the product or service and ways on how you can test these claims. 5 We have always been interested in answering different types of questions, whether they be related to a specific discipline or just anything under the sun. In education, for instance, a teacher may want to determine the effectiveness of a particular teaching method in science. Scores in a science test may be obtained from a sample of students exposed to the old and new teaching methods. Gathering information or data needed in the study has obvious importance. You learned from the previous lessons how data are gathered, organized, and presented. But these do not constitute the primary goal of research and statistics— decision-making. In this lesson, you will learn about null and alternate hypotheses.  Learn about It! Hypothesis Testing This is a statistical method of using sample data to determine the probability that a given hypothesis about the population is true  Learn about It! Hypothesis Testing Steps in Hypothesis Testing a. Formulate the null and alternative hypotheses b. Determine the level of significance c. Calculate the test statistic and identify the rejection region. d. Make a decision e. Draw a conclusion  Learn about It! Statistical Hypothesis This is a statement about a population parameter Example: The daily mean number of patients in an emergency room is 74.  Learn about It! Null Hypothesis This is the hypothesis that is assumed to be true. It uses a relation symbol with a statement of equality, such as and , and is denoted by. Example: The average life expectancy of females is the same as the average life expectancy of males. ()  Learn about It! Alternative Hypothesis This is the hypothesis that is contrary to the null hypothesis. It uses a relation symbol with no statement of equality, such as and , and is denoted by or Example: The average life expectancy of females is different from the average life expectancy of males. (  Learn about It! Directional Test of Hypothesis or One- tailed Test This is a type of hypothesis test that uses only one side or tail of the distribution. It can either be a right-tailed or left-tailed test.  Learn about It! Right-tailed Test This is a type of directional test of hypothesis or one- tailed test used when it is hypothesized that the parameter falls within the positive end of the distribution. In a right-tailed test, the alternative hypothesis uses comparatives such as greater than, higher than, better than, superior to, exceeds, above, increased, etc.  Learn about It! Right-tailed Test Example: A department head wants to test the claim that the daily mean water intake of each employee is greater than 1.3 liters. State the null and alternative hypotheses. The daily mean water intake of each employee is less than or equal to 1.3 liters. () The daily mean water intake of each employee is more than 1.3 liters. ()  Learn about It! Left-tailed Test This is a type of directional test of hypothesis or one- tailed test that is used when it is hypothesized that the parameter falls within the negative end of the distribution. In a left-tailed test, the alternative hypothesis uses comparatives such as less than, smaller than, inferior to, lower than, below, decreased, etc.  Learn about It! Left-tailed Test Example: A bariatric physician believes that one side effect of a new vitamin pill for women is weight loss. The average weight of women in the population is 54 kg. State the null and alternative hypotheses. The mean weight of women who takes the new vitamin pill is not less than 54 kg. () The mean weight of women who takes the new vitamin pill  Learn about It! Non-directional Test of Hypothesis or Two- tailed Test This is a type of hypothesis test that makes use of two opposite sides or tails of the distribution. It is used when no assertion is made on whether the parameter falls within the positive or negative end of the distribution.  Learn about It! Non-directional Test of Hypothesis or Two- tailed Test In a two-tailed test, the alternative hypothesis uses comparatives such as not equal to, different from, not the same as, etc.  Learn about It! Non-directional Test of Hypothesis or Two- tailed Test Example: Researcher A claims that an average professional typist has a mean typing speed of 75 words per minute. Researcher B wants to test whether this claim is true. State the null and alternative hypotheses. The population mean typing speed of an average professional typist is 75 words per minute. () The population mean typing speed of an average professional  INDIVIDUAL SEATWORK I. Identify the term being described by the following statements. Write your answer on the blank before each number. 1. It is a method of using sample data to decide between two competing claims about a population. 2. It is the hypothesis to be tested. 3. It is the hypothesis that has no statement of equality. 4. It is a type of test that is used when there is a hypothesis that the parameter falls within the positive end of the distribution. 5. It is a type of test that is used when no assertion is made on whether the parameter falls within the positive or negative 23  INDIVIDUAL SEATWORK II. Determine the type of test needed for each statement. For each item, write two-tailed, left-tailed, or right-tailed on the blank before each number. 1. There is no significant difference between the mean height of plants on normal soil and the mean height of plants on soil with commercial fertilizer. 2. The mean age of students in the contemporary dance class is significantly lower than the mean age of students in the tap dance class. 3. The mean number of children in each household in a barangay is below 4. 4. The average weight of the parcels exceeds one kilogram. 5. The mean temperature for the whole year is equal to 21 degrees Celsius. 24  Learn about It! Level of Significance This is the probability of rejecting the null hypothesis in favor of the alternative hypothesis when it is really true, denoted by.  Learn about It! Level of Significance In hypothesis testing, the researcher decides what level Conventional significance levels such as 0.05 and 0.01 of significance to use at the beginning of the test. are frequently used in hypothesis testing because of the desire to maintain a low probability of rejecting the null hypothesis when it is actually true.  Learn about It! Level of Significance Example: A significance level of means that there is a 5% chance of rejecting a true null hypothesis. In other words, we are 95% confident that a right decision is made.  Try Let’s it!Practice Example 1: A researcher wants to test whether there is a significant difference between the mean frequency of exercise between young and old people. State the null and alternative hypotheses.  Solution to Let’s Practice Example 1: A researcher wants to test whether there is a significant difference between the mean frequency of exercise between young and old people. State the null and alternative hypotheses. Solution Let and be the population mean frequency of exercise of young and old people, respectively. The hypotheses can be stated as:  Solution to Let’s Practice Example 1: A researcher wants to test whether there is a significant difference between the mean frequency of exercise between young and old people. State the null and alternative hypotheses. Solution There is no significant difference between the mean frequency of exercise of young and old people.  Solution to Let’s Practice Example 1: A researcher wants to test whether there is a significant difference between the mean frequency of exercise between young and old people. State the null and alternative hypotheses. Solution There is a significant difference between the mean frequency of exercise of young and old people.  Try Let’s it!Practice Example 2: A store owner wants to know if the daily average number of customers in the clothing shop is greater than 246. State the null and alternative hypotheses.  Solution to Let’s Practice Example 2: A store owner wants to know if the daily average number of customers in the clothing shop is greater than 246. State the null and alternative hypotheses. Solution Let be the population daily mean number of customers in the clothing shop. The hypotheses can be stated as:  Solution to Let’s Practice Example 2: A store owner wants to know if the daily average number of customers in the clothing shop is greater than 246. State the null and alternative hypotheses. Solution The daily mean number of customers in the clothing shop is less than or equal to 246. () The daily mean number of customers in the clothing shop is greater than 246. ()  Try Let’s it!Practice Example 3: A college professor wants to show that the mean score in the programming test of students taught using Method A is higher than the mean score in the same test of those students taught using Method B. State the null and alternative hypotheses.  Solution to Let’s Practice Example 3: A college professor wants to show that the mean score in the programming test of students taught using Method A is higher than the mean score in the same test of those students taught using Method B. State the null and alternative hypotheses. Solution Let and be the mean scores in the programming test of students taught using Method A and Method B, respectively. Thus, the hypotheses can be stated as:  Solution to Let’s Practice Example 3: A college professor wants to show that the mean score in the programming test of students taught using Method A is higher than the mean score in the same test of those students taught using Method B. State the null and alternative hypotheses. Solution The mean score in the programming test of students taught using Method A is not higher than that of students taught using Method B. () The mean score in the programming test of students taught using Method A is higher than that of students taught using Method B. ()  ACTIVITY 2: BY GROUP 1. The owner of a coffee shop believes that an average of 500 customers per day visit their shop. Earlier in the month, a competitor opened another coffee shop nearby. The owner would like to test whether there is a decrease in the number of customers visiting their shop daily. State the null and alternative hypotheses. 38  ACTIVITY 2: BY GROUP 2. A researcher wants to know if there is a significant difference between the mean number of math anxiety cases for females and males. State the null and alternative hypotheses. 39  ACTIVITY 2: BY GROUP 3. A psychologist thinks that playing soft music during a Statistics test can improve scores of students. It is known that the mean score in statistics tests of students was 82. State the null and alternative hypotheses. 40  ACTIVITY 2: BY GROUP 4. A teacher wants to know if there is a significant difference between the mean score in the Statistics test of students in his morning and afternoon classes. State the null and alternative hypotheses. 41  ACTIVITY 2: BY GROUP 5. A mathematics teacher wants to prove that male students outperform female students in mathematics in terms of mean final grade. State the null and Alternative hypotheses. 42  Bibliography Berman, Harvey. “What is Hypothesis Testing?” Stat Trek. Retrieved 20 August 2019 from https://bit.ly/2J02pbP. “Examples of null and alternative hypotheses.” Khan Academy. Retrieved 20 August 2019 from https://bit.ly/2IblYuw. Glen, Stephanie. “Hypothesis Testing.” Statistics How To. Retrieved 20 August 2019 from https://bit.ly/33MKr4U. “Writing null and alternative hypotheses.” Khan Academy. Retrieved 20 August 2019 from https://bit.ly/2DZ34Vb.