Answer these questions. Binomial Hypothesis Tests

1. Naomi loves granola. Normally, the probability of an almond being in a random spoon is 0.25. However, Naomi thinks her favourite brand has reduced the amount of almond in the granola. In a sample of 50 spoons only 2 have an almond. Test Naomi's suspicion at a 5% significance level. [3] 2. Rose is in charge of sparkling water production. Her machine fails to fully sparkle 1 in 10 bottles. Rose invests in a new machine and wants to test if it is better, using a 10% significance level. In a sample of 100 bottles from the new machine, 6 aren't fully sparkled. [3] 3. Boone is on time to his Maths lessons 70% of the time. His Maths Teacher wants to improve this so bans eating cake in class. Over the next 30 lessons, Boone is on time to 28 of them. Test at a 5% significance level if Boone's punctuality has improved. [3] 4. Mr. Eko is testing the strength of wood grown in his forest. The wood meet his requirements 30% of the time. He wants to improve this so changes the feed given to the plantation. Following this, 24 of the 50 tested samples met his criteria. Test at a 2.5% significance level to identify if changing the feed improved the strength of the wood. [3] 5. X ~ B(25, P) Ho : p = 0.4 H1 : p + 0.4 In a sample of 25, X = 7. Test this value at a 10% significance level. [4]