Fail to reject the null hypothesis however errors

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fail to reject the null hypothesis. However, errors could be made in some decisions, which we can divide in two. 1. A type I error occurs if the null hypothesis is rejected when it is true. 2. A type II error occurs if the null hypothesis is not rejected when it is false. Note : No matter which hypothesis represents the claim, always begin the hypothesis test assuming that the null hypothesis is true . Example 4 FEU Institute of Education claims that 89% of their graduates find employment within six months of graduation. What will a type I or type II error be? A type I error is rejecting the null when it is true. The population proportion is actually 0.89, but is rejected. (We believe it is not 0.89.) A type II error is failing to reject the null when it is false. The population proportion is not 0.89, but is not rejected. (We believe it is 0.89.) 2. A laptop manufacturer claims that the mean life of the battery for a certain model of laptop is more than 5 hours. 3. An amusement park claims that the mean daily attendance at the park is at least 17,450 people. 4. The standard deviation of the base price of a certain type of all-terrain vehicle is no more than Php 28,300. Learning Activity 2 In reference to Learning Activity 1, construct a sentence of what could be a type I and type II error for each of the given scenario.
Science, Technology, Engineering and Mathematics Statistics and Probability SY 2020 2021 Page 4 of 11 Lesson 13.3 Level of Significance In a hypothesis test, the level of significance is your maximum allowable probability of making a type I error. It is denoted by , the lowercase Greek letter alpha . By setting the level of significance at a small value, you are saying that you want the probability of rejecting a true null hypothesis to be small. Commonly used levels of significance: = 0.10 = 0.05 = 0.01 Meanwhile, the probability of making a type II error is denoted by 1 - , where is the lowercase Greek letter beta . Lesson 13.4 Statistical Tests After stating the null and alternative hypotheses and specifying the level of significance, a random sample is taken from the population and sample statistics are calculated. The statistic that is compared with the parameter in the null hypothesis is called the test statistic . Population parameter Test statistic Standardized test statistic μ (mean) 𝑥̅ z (n 30) t (n < 30) p (proportion) ˆ p z 2 (variance) s 2 X 2 (chi-square) Lesson 13.5 P-Value Another way of expressing the level of statistical significance is using P-values, which is based on the normal distribution. A P-value (or probability value ) of a hypothesis test is the probability of obtaining a sample statistic with a value as extreme or more extreme than the one determined from the sample data. The smaller the p-value, the stronger the evidence that you should reject the null hypothesis.
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