Directions: Consider the Four-Step process in determining the confidence interval. Problem: An admission officer of an educational institution wants to know the mean age of all entering Mathematics Majors. He computed a mean age of 18 years and a standard deviation of 1.2 years on a random sample of 25 entering Math majors, coming from a normally distributed population. With 99% confidence, find the point estimate and the interval estimate of the population mean.Andrei wants to know if cooperative grouping is an effective strategy in improving the Mathematics performance of Grade 7 students. Twenty students were included in the experimental group, while another 20 students were included in the control group. Mean Student Group Achievement Standard Deviation Score Experimental 82.5 W Control 80 The two groups came from a normally distributed population. The confidence level adopted was 95%. Solution: STEPS SOLUTION . The first parameter of interest is the mean /1, of the population where Step1: Describe the the experimental population Parameter group belongs. of interest. . The second parameter of interest is the mean /2 of the population where the control group belongs.. The samples of size 20 for each group come from normally distributed parent population and Step 2: Specify the the ofor each confidence interval group are criteria. unknown. . The test statistic . Check the is the t using assumptions. $1 = 3 and $2 = 6 . Determine the , respectively. test statistic to be . For a 95% used to calculate confidence, the interval. a = 1 - 0.95 = 0.05 . State the level of . From the t-table, confidence. with a df=n-1=20- 1=19 for each group, the confidence coefficient is 2.093for each group. . The sample consists of 20 raw scores for each group. From the Step 3: Collect and experimental group, present sample evidence. n=20; df = 19; X = 82.5, and s= 3 . Collect the From the control sample group: information. n=20; df=19; X =80, and s= 6 . The point estimate for the population means . Find the point are the sample estimate means. Thus, the point estimate for /1 = 82.5 and the point estimate for H2 = 80.. Since 20, then df=19. The confidence coefficients in the t-table for 95% is 2.093. . For the experimental group, Step 4:Determine the E =() - (2.093) () = 1.4 confidence interval For the controlled group, . Determine the E = 2.093 = 2.8 confidence coefficient. . For the . Find the experimental Maximum Error E. group, 82.5 -1.4= 81.1 and 82.5 +1.4=83.9 For the control group, 80- 2.8=77.2 and . Find the lower 80 +2.8= 82.8 and the upper . Interpretation: confidence limits. We can say with 95% confidence that the interval 81.1 and 83.9 . Describe the contains the true results. mean of the experimental population, while the interval 77.2 and 82.8 contains the true mean of the control population based on the given sample data