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7.02* It is conjectured that driver's training improves one's chances of pass- ing their driver's test. From a school where driver's training is offered, 89 of 100 students who took driver's training passed their test. From a group of 100 individuals who did not take driver's training, only 74 passed their test. (a) Write down the statistical model and relevant hypotheses. (b) Calculate the corresponding p-value and provide conclusions. (c) Is there any cause for worry in this experiment that assesses driver's training?7.04* An experiment was carried out to investigate the amount of reside ual chemicals in the soil due to two different treatments. Treatment 1 had six measurements: 28.5, 24.7, 26.2, 23.9, 29.6, 29.1. Treatment 2 had five measurements: 38.7, 41.6, 35.9, 41.8, 42.0. Assume normality of the mea- surements. (a) Write down an appropriate statistical model stating all as-sumptions and introducing relevant notation. (b) Write down the null and alternative hypotheses corresponding to the question "Is there a difference in the two treatments regarding the amount of residual chemicals?" (c) Obtain the corresponding p-value and give a concluding statement.7.07 A university is considering the proposal of a new policy. Not only is it important that the policy have widespread support, the university wants to have a good understanding of the difference in support between the teaching staff and the non-teaching staff. It is proposed that n teaching staff and n non-teaching staff are randomly selected and asked whether they support the new policy. Determine n so that the length of the 95% confidence interval for the difference in the percentage support between teaching staff and non- teaching staff is at most 5%.7.10\" A group of ill!) students are randomly assigned to classes of size 51] and 5D. Before a test, the students in the rst group are instructed to pull an all-nighter (i.e. no sleep the previous night} whereas the second group has their normal amount of sleep. Suppose we know that the population variance for test scores is 98.2 (likely an unrealistic assumption) and that the sample mean test scores from the two groups are 75.1 and 82.3 respectively. Assume further that test scores are normally distributed. (a) Write down an appropriate statistical model stating all assmnptions and introducing relevant notation. (b) Write down the null and alternative hypotheses corresponding to the question \"Does sleep deprivation hinder performance in test scores by more than 3%?" (c) Obtain the corresponding p-value and give a concluding statement. (d) Provide a 99% condence interval for the mean improvement in test scores based on normal sleep versus deprived sleep