It is known that in the UK, 63% of households own at least one car. David, who lives in a big city, believes that in his neighbourhood car ownership is lower than this. He uses a hypothesis test, based on the binomial distribution, to confirm this. a State suitable null and alternative hypotheses for his test. David surveys a random sample of 50 households in his neighbourhood and finds that 29 of them own at least one car. b Use this data to test David's hypothesis at the 10% significance level. State your conclusion clearly. Angela is playing a board game with her friends, but thinks the dice is biased and that a 6 is rolled too infrequently. In the subsequent 40 rolls of the dice she got only three 6s. Test Angela's belief at the 10% significance level.The 2011 census found that 63% of 16- to 19-year-olds in a particular town attended a sixth form college. In 2015 a sample of 60 teenagers in this age range was surveyed and it was found that 46 of them attended a sixth form college. Is there evidence, at the 5% signicance Bevel, that the proportion of 16- to 19-year-olds attending a sixth form college has increased? In a certain local authority, the proportion of workers who drive to work is known to be 33%. In a sample of 18 teachers from a particular college, 12 drive to work. Is there evidence, at the 5% signicance level, that the teachers at this college are more likely to drive to work than the average for the local authority? An established treatment for a particular disease is known to be effective in 82% of the cases. A doctor devises a new treatment that she believes Is even more effective. She uses the treatment on a random sample of all patients and nds that the new treatment is effective in 4.1 cases. Does this data support the doctor's belief at the 2% significance level? A teacher knows that in his old school, a third of all sixth-formers had a younger sibling at the school. He moves to a new school and wants to find out whether this proportion is different. He asks a sample of 60 sixth-formers, and finds that 27 of them have a younger sibling at the school. Conduct a hypothesis test at the 5% significance level to decide whether there is evidence that the proportion of sixth- formers with a younger sibling at the new school is different from the old school. A large athletics club had the same running coach for several years. Records show that 28% of his athletes could run 100 metres in under 12 seconds. The club brings in a new coach and over the following year, 26 out of a sample of 75 athletes recorded 100-metre times under 12 seconds. Do these data support the hypothesis that the proportion of athletes who can run 100 metres in under 12 seconds has changed? Use the 5% significance level for your test.A student tests the hypothesis Ho : p = 0.4 against H1 : p > 0.4, where p is the proportion of brown cats of a particular breed. In a sample of 80 cats of this breed 40 were brown, and this leads him to reject the null hypothesis. What can you say about the significance level he used for his test