Review on module 7
- 1. STATISITCAL HYPOTHESES 1. NULL HYPOTHESES, denoted by 𝐻𝑜, is a statement saying that there is no significant difference between the population parameter and the value that is being claimed. It is the hypotheses to be tested. CLUE : It always used equal sign (=) 2. ALTERNATIVE HYPOTHESES, denoted by 𝐻𝑎, is a statement saying that there is a significant difference between the population parameter and the value that is being claimed. This is a statement that will be true once the null hypotheses is rejected. CLUE : It always used inequality symbol (≠, <, >, ≤, ≥) : Non-directional (two-tailed test) ≠ : Directional (one-tailed test) <, > EXAMPLE 1: The head of the PE department of a certain high school claims that the mean height of grade 7 students is 163 cm. The mean height of 45 randomly selected grade 7 students is 161 cm. Using the significance level, can it be concluded that the mean height if grade 7 students is different from 163 cm as claimed by the Head of PE Department? Identify the null hypotheses and alternative hypotheses. 𝑯𝒐: 𝝁 = 𝟏𝟔𝟑 𝑯𝒂: 𝝁 ≠ 𝟏𝟔𝟑 EXAMPLE 2: The LB Company produces an average if 4% defective bulbs each day. Recently, some of the machines were upgraded. Out of the 400 bulbs randomly selected only 14 bulbs were found defective. Does this suggest that there is a decrease in the number of defective bulbs produced each day? Use 0.05 significance level. Identify the null hypotheses and alternative hypotheses. 𝑯𝒐:𝒑 = 𝟒% 𝒐𝒓 𝟎. 𝟎𝟒 𝑯𝒂: 𝒑 < 𝟒% 𝒐𝒓 𝟎. 𝟎𝟒 REJECTION REGION, CRITICAL VALUE, AND LEVEL OF SIGNIFICANCE After identifying the null and alternative hypotheses, the researchers should follow the steps and rules to help them decide whether or not to reject the null hypotheses or accept the alternative hypotheses. The researcher needs to convert the sample mean to a value called TEST STATISTIC. This value would help the researchers make a decision and draw a conclusion. The researcher also should establish a rejection region.
- 2. Separating the two regions is appoint called the CRITICAL VALUE (𝜶) which is derived from the level of significance. The most commonly used values for the level of significance are 0.01, 0.05, and 0.010.