Part 1. 1. What is the critical value when the variance is known, the sample is 40, and with 10 percent level of significance if two tailed test will be employed? 2. What is the critical value when the variance is unknown, the sample is 20 and with 5 percent level of significance if two tailed test will be employed? 3. If the variance is known, the sample is 800, and the level of significance is 0.01, What is the critical value if one tailed test be used? 4. If the variance is unknown and the sample is 15, what is the critical value if one-tailed test will be used at 0.01 significance level? 5. If the variance is unknown, the sample is 27, at 0.10 significance level, what is the critical value if two-tailed test will be used?Part 2. Direction: Solve the following problems. Problem 1: One of the manufacturing company produces an average of 8% defective batteries each day. Due to the high demand in the market, their machines were upgraded. Out of the 500 batteries randomly selected only 10 batteries were found defective. Using a 0.10 significance level, answer the following. a. State the null and alternative hypothesis b. What type of tests is applicable, is it one-tailed test or two-tailed test? c. Compute the critical value d. Illustrate using the normal curve Problem 2: Last year the average number of students per section in grade 11 academic strand in PNHS-Main SHS is 40. This year the guidance office claims that there is an increase of enrollees. A student researcher wants statistical evidence on the claim that is why he conducted her own study. His study resulted to a mean of 50. Using a 0.10 significance level. a. State the null and alternative hypothesis b. What type of tests is applicable, is it one-tailed test or two-tailed test? c. Compute the critical value d. Illustrate using the normal curveProblem 3. One of the activities conducted by the PE faculty members of Paranaque National High School-Main Senior High School Program is getting the Body Mass Index (BMI) of the students. After collecting the weight of the students, they claim that the average weight of Grade II students is 50 kgs. The mean weight of 25 randomly selected STEM students is 45 kgs. Use 0.05 significance level. a. State the null and alternative hypothesis b. What type of tests is applicable, is it one-tailed test or two-tailed test? c. Compute the critical value d. Illustrate using the normal curve