This is Statistics. Answer what is required. Provide clean and clear Solutions

Directions: Complete the solution in each of the following problem. 1. The average score in the entrance examination in Mathematics at Sto. Rosario National High School is 80 with a standard deviation of 10. A random of 40 students was taken from this year's examinees and it was found to have a mean score of 84. a. Is there a significant difference between the known mean and the sample mean? Test at a= 0.05 Solution : Step 1. Ho : p = 80 : There is no significant difference between the hypothesized and the sample mean. Ha : H x 80 : Step 2. Level of significance, a = 0.05, Step 3. two tailed test, find the critical value, Zt = Step 4. Compute the test-statistic value: Zc - Step 5. Decision Rule : Step 6. Conclusion: b. Does this indicate that this year's batch is better in mathematics than the previous batches? Solution Step 1. Ho: u This year's batch is as good as the previous batches in mathematics. Ha : Step 2. Level of significance, a = Step 3. Find the critical value, Zt = Step 4. Compute the test statistic: Zc. Step 5. Decision Rule Step 6. Conclusion