4. ACE appliance manufacturing company claims that the proportion of defectives in their brand is lower than that of PREMIER's, their next door competitor. The manager of ACE wants to demonstrate the validity of this claim. For this purpose, he selects a random sample of 36 appliances from each company and find that 3 ACE and 5 PREMIER's appliances are defective. Should we believe ACE's claim based on this data? (a) (2 points) Let ACE be population 1 and PREMIER be population 2. State the null hypothesis and alternative hypothesis (b) (4 points) Find the test statistic (c) (2 points) If the type-I error a = 0.05, find the critical value(s) and shade the rejection region(s) (d) (2 points) Base on the type-I error a and rejection region(s), given above, what is your conclu sion?(Do not use p-value to support your conclusion)3. An official of the state department of social services claims that the proportion of 16-year old girls in Passaic County who are unwed mothers has gone down below 20%. A social researcher randomly selected 200 girls of the age group and found that 35 of them were unwed mothers. (a) (2 points) State the null hypothesis and alternative hypothesis (b) (4 points) Find the test statistic (c) (2 points) If the type-I error a = 0.05, find the critical value(s) and shade the rejection region(s) (d) (2 points) Base on the type-I error a and rejection region(s), given above, what is your conclu sion?(Do not use p-value to support your conclusion)