Instruction: Answer the following problems:

Assessment: Answer the following problems. 1. A manufacturer of baby powder claims that 20 out of 56 mothers prefer brand A of baby powder. A random sample of 25 mothers are selected and asked what brand of baby powder they prefer. If 8 of the 25 mothers prefer Brand A, what is the conclusion? Use z-test at 1% level of significance. 2. In a certain university, it is claimed by the security guard that 30% of the 1,500 students in the campus have cars. A random sample of 100 students were asked if they have cars and 27 students answered yes. Test the validity of the claim of the security guard by using the z-test as test statistics at 5% level of significance