1. The manager of a construction supply claims that their store has been selling cement in 20kg bags for several months. It has been known that the population standard deviation of the weights is 0.4kg. A customer then claims that he has been sold underweight bags and is thinking of reporting the manager to the authorities. He brought 10 bags of cement and found out that the average weight is 19.45kg. (level of significance = 0.05)State the null and alternative hypothesis.

• what is the critical value?
• What is the rejection and non rejection region?
• What is the (z or t) value?
• What is the decision?
• Based on the decision, write the conclusion.

2. Teacher A believes that the students in their school have an IQ of above average. The mean scores of 30 randomly selected students are is 112.5. Is there a significant evidence to prove the claim of the teacher? The mean IQ is 100 with a standard deviation of 15. Level of significance = 0.05State the null and alternative hypothesis.

• what is the critical value?
• What is the rejection and non rejection region?
• What is the (z or t) value?
• What is the decision?
• Based on the decision, write the conclusion.