EDUC602 Hypothesis Testing: Small and Large Sample Case Name: Pastorite Maria Liza Navaja Student Number: 1252525 Module7 Activity: Answer the following exercise following the steps in hypothesis testing. 1. .A stock of tilapia will only be harvested if the average body weight of the tilapia is greater than 20g. A sample of 50 pieces is drawn with an average weight of 22g and SD of 15. Using a test of hypothesis at the 1% level of significance, will you decide to harvest your stock? Assume that the body weight of tilapia, X is normally distributed. Null hypothesis : X 20 Alternate hypothesis: X > 20 Z score is calculated as : -X Z = ________ S N 22-20 Critical Z- score = ________ 15 50 = 0.943 Thus, p(X 20)= p(Z 0.943) = 0.827 Since p(X 20) > 0.01% at 1% significant level the null hypothesis is not true. Hence, I will not decide to harvest the stock. 2. Among 10,000 school children, 500 of them are randomly selected for a survey on nutritional status among school age children. Of these 500 school children, 91 are found to be moderately and severely underweight children. At 5% level of significance, is their evidence that the proportion of moderately and severely underweight children is 20%? Assume that the underweight children, X is normally distributed. Null hypothesis : X 20% Alternate hypothesis: X > 20% Z score is calculated as : -X Z = ________ S N 10000-500 Critical Z- score = ________ 91 500 = 2375 Thus, p(X > 20% )= p(Z 2375) = 2375 Since p(X > 20%) < 0.01% at 5% significant level the null hypothesis is not true. Hence, it is evident that the proportion of moderately and severely underweight children is more than 20% We want to compare fasting serum cholesterol levels of Filipino women to that of the American women. Assume the cholesterol levels in 20- to 39-years old women in the United States is normally distributed with mean = 190 mg/dl. Blood tests are preformed on 100 female Filipinos in this age range rendered a sample mean cholesterol level of 181.52 mg/dl and standard deviation of 40 mg/dl. Conduct a test of hypothesis to determine whether Filipino women have lower average cholesterol levels than their American counterparts. Show all hypothesis testing steps. A psychologist wanted to know whether there is a difference between the boys and girls in their persistence in learning a task. The number of times the task was resumed or continued was taken to account. For a class of 25 students, the data are as follows: GB Sample size 14 11 Sample Means 26.9 21.3 Sample SD (s) 12 13 Perform a hypothesis test at a 1% level of significance. 5. Mental measurements of young children are often made by giving them blocks and telling them to build a tower as tall as possible. One experiment of block building was repeated a month later, with the times (in seconds) listed in the accompanying table. Use a 0.01 level of significance to test the claim that there is no difference between the two times. Child A B C D E F G H I J K L M N O First 30 19 19 23 29 178 42 20 12 39 14 81 17 31 52 Trial Second Trial 30 6 14 8 14 52 14 22 17 8 11 30 14 17 15