Perform a statistical analysis / test of hypothesis
- A high school athletic director is asked if basketball players are doing as well academically as the other student athletes at his school. It was known from previous records that the average grade for the student athletes is 77.50%. after an initiative to help improve the GPA of student athletes, the athletic director samples 20 basketball players and obtains the following grades: 80, 82, 77, 79, 83, 75, 84, 80, 78, 79, 80, 82, 81, 79, 77, 80, 82, 79, 85, 76. Is there a significant improvement? Perform a hypothesis test at the 0.05 level of significance.
Extracted text: Perform a statistical analysis / test of hypothesis on each of the following problems. 1. The average length of time for students to register during the enrolment in the university has been 70 minutes. A new registration procedure using modern computing machines is being tried. If a random sample of 61 students had an average registration time of 58 minutes with a standard deviation of 15.9 minutes under the new system, test the hypothesis that the population mean is now less than 70, using a level of significance of 5%. 2. Past records showed that the average grade of students taking Filipino I is 85. A new method of teaching the subject is employed and a random sample of 24 students taking up the said subject is selected. The mean grade of the sample is 89 while the corresponding standard deviation is 16. Is there evidence that the new method of teaching has improved the student's grade? Perform an analysis at the 5% level of significance. 3. A random sample of 21 children from the same age group participated in a special language skills program designed to build vocabulary. Measurements at the end of the program showed the children's vocabularies had a mean of 1060.1 words with a standard deviation of 109.0 words. It is known that the mean vocabulary of children who have taken the special program is greater than 1000 words. Assume that the vocabulary size of children who have taken the program is approximately normally distributed. Conduct a test of hypothesis at the 5% level of significance. 4. A high school athletic director is asked if basketball players are doing as well academically as the other student athletes at his school. It was known from previous records that the average grade for the student athletes is 77.50%. after an initiative to help improve the GPA of student athletes, the athletic director samples 20 basketball players and obtains the following grades: 80, 82, 77, 79, 83, 75, 84, 80, 78, 79, 80, 82, 81, 79, 77, 80, 82, 79, 85, 76. Is there a significant improvement? Perform a hypothesis test at the 0.05 level of significance.
Extracted text: Perform a statistical analysis / test of hypothesis on each of the following problems. 1. The average length of time for students to register during the enrolment in the university has been 70 minutes. A new registration procedure using modern computing machines is being tried. If a random sample of 61 students had an average registration time of 58 minutes with a standard deviation of 15.9 minutes under the new system, test the hypothesis that the population mean is now less than 70, using a level of significance of 5%. 2. Past records showed that the average grade of students taking Filipino I is 85. A new method of teaching the subject is employed and a random sample of 24 students taking up the said subject is selected. The mean grade of the sample is 89 while the corresponding standard deviation is 16. Is there evidence that the new method of teaching has improved the student's grade? Perform an analysis at the 5% level of significance. 3. A random sample of 21 children from the same age group participated in a special language skills program designed to build vocabulary. Measurements at the end of the program showed the children's vocabularies had a mean of 1060.1 words with a standard deviation of 109.0 words. It is known that the mean vocabulary of children who have taken the special program is greater than 1000 words. Assume that the vocabulary size of children who have taken the program is approximately normally distributed. Conduct a test of hypothesis at the 5% level of significance. 4. A high school athletic director is asked if basketball players are doing as well academically as the other student athletes at his school. It was known from previous records that the average grade for the student athletes is 77.50%. after an initiative to help improve the GPA of student athletes, the athletic director samples 20 basketball players and obtains the following grades: 80, 82, 77, 79, 83, 75, 84, 80, 78, 79, 80, 82, 81, 79, 77, 80, 82, 79, 85, 76. Is there a significant improvement? Perform a hypothesis test at the 0.05 level of significance.