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Direction: As part of the Five-step Procedure for Testing a Hypothesis, The Test Statistic plays a vital role in this procedure. Enumerate at least 5 types of test statistic and give their formula. PAGE 9Directions: Read and analyze each item carefully. Write TRUE if the statement is correct and FALSE if states otherwise. Write your answer on a separate sheet of paper. 1. There are two types of statistical inferences; estimation of population parameters and hypothesis testing. 2. Estimation theory deals with estimating the values of parameters based on measured or empirical data that has a random component. In other words, an estimator attempts to approximate the unknown parameters using the measurements. 3. Hypothesis testing is one of the most important tools of application of statistics to real-life problems. It is a form of statistical inference that uses a sample data to draw conclusions about a population parameter. 4. Confidence coefficient is the set of values of the test statistic for which the null hypothesis is rejected. PAGE 10Directions: Read and analyze each item carefully. Choose the letter of the best answer. Write the chosen letter on a separate sheet of paper. 1. Is a proposition, statement, or assumption based on some previous observations about the value of a population parameter for testing purposes. A. Alternative hypothesis C. Hypothesis B. Null hypothesis D. Hypothesis testing 2. Is a statement about the value of a population parameter. A. Alternative hypothesis C. Hypothesis B. Null hypothesis D. Hypothesis testing 3. It is a statement that is accepted if the sample data provide us with statistically significant evidence that the null hypothesis is false. A. Alternative hypothesis C. Hypothesis B. Null hypothesis D. Hypothesis testing 4. This is the risk the researcher is willing to take in rejecting a true null hypothesis. PAGE 1Direction: Read and analyze the sample problem below. Steps 1-5 will be elaborated as you complete your hypothesis testing procedure. Take note that for step number 5 you will be the one who will make a decision based on your decision rule. For a random sample of 100 students who have passed a statistics course, the average score was 71.8. Assuming that the population standard deviation is 8.9, with a significance level of 0.05, does it seem to signify that the average score is more than 70? 1. Null and alternative hypothesis: Ho: # = 70 versus Ha: # > 70. 2. Level of significance: a = 0.05. X-Ho - 71.8-70 3. Test statistic: =/ 7 89/ 100 = 2.02 z 4. Decision rule: Critical region: z > 1.645, i.e. reject H, if z > 1.645. 5. Decision: P 2.02 PAGE 5Activity 2. Write that Test Statistic. Direction: Give the three test statistic in testing for population mean. 1. Testing for Population Mean: Population Variance Known Test Statistic: 2. Testing for Population Mean: Large Sample, Population Variance Unknown PAGE 132. Is a statement about the value of a population parameter. A. Alternative hypothesis C. Hypothesis B. Null hypothesis D. Hypothesis testing 3. It is a statement that is accepted if the sample data provide us with statistically significant evidence that the null hypothesis is false. A. Alternative hypothesis C. Hypothesis B. Null hypothesis D. Hypothesis testing 4. This is the risk the researcher is willing to take in rejecting a true null hypothesis. A. Level of significance C. Rejection region B. Type I error D. Type II error 5. What happens if we reject the null hypothesis when it is actually true? A. we commit a Type III error C. we commit a Type IV error B. we commit a Type I error D. we commit a Type II error 6. What happens if we accept the null hypothesis when it is actually false? A. we commit a Type III error C. we commit a Type IV error B. we commit a Type I error D. we commit a Type II error 7. This describes the location of all those values that are so small or large that the probability of their occurrence under a true null hypothesis is slim. A. Level of significance C. Rejection region B. Type I error D. Type II error 8. This refers to the value used to determine whether or not to reject the null hypothesis. A. Test statistic C. Decision rule B. p-value D. t-value 9. Is a declaration of the situations under which the null hypothesis is rejected or not rejected. A. Test statistic C. Decision rule B. p-value D. t-value 10. This is the smallest level of significance for which the observed data indicated that the null hypothesis should be rejected. A. Test statistic C. Decision rule B. p-value D. t-value PAGE 88. Having a smaller sample size will give you a larger margin of error. 9. To have a higher level of confidence you will need a larger sample size. 10. The confidence interval obtained will always be equal to the population parameter. PAGE 42. Estimation theory deals with estimating the values of parameters based on measured or empirical data that has a random component. In other words, an estimator attempts to approximate the unknown parameters using the measurements. 3. Hypothesis testing is one of the most important tools of application of statistics to real-life problems. It is a form of statistical inference that uses a sample data to draw conclusions about a population parameter. 4. Confidence coefficient is the set of values of the test statistic for which the null hypothesis is rejected. 5. An estimator is not expected to estimate the population parameter without error. 6. Hypothesis testing is a process based on probability theory to conclude whether the hypothesis is reasonable and should not be rejected otherwise. 7. A hypothesis testing begins with a proposition or statement about a parameter referred to as a decision rule. 8. The p-value is the smallest level of significance for which the observed data indicate that the null hypothesis should be rejected. 9. Confidence interval is an interval estimate of a population parameter and is used to indicate the reliability of an estimate. 10. Degrees of freedom is the number of independent pieces of data being used to make a calculation. PAGE 15Direction: Read and analyze the statements below. Write TRUE if the statement is correct or FALSE if it states otherwise. 1. The mean of the population is equal to the sample mean. 2. The median for the population is equal to the sample median. 3. Low variation means narrow confidence interval. 4. Large sample size means narrow confidence interval. 5. t-distribution is a normal distribution with mean zero and standard deviation 1. 6. Sample size is the proportion of the population chosen for a survey or experiment. 7. If we have small standard deviation or smaller variation you will only need a small sample size. PAGE 3Activity 1. Don't You Recognize Me? Direction: Tell whether each statement is a Null Hypothesis or Alternative Hypothesis. 1. Ha: H = 70 kg 2. Ha: ( > 70 kg 3. p = 130 ml _4. p