Please answer all parts of the attached question. The probability that a train is behind schedule is 0.3. A new engine with better acceleration is to betried on the route to see if the arrival time can be improved. To test the effectiveness of the engineimprovements, 10 trials along the route are conducted. The train was behind schedule once.a. State the hypothesis to be considered.b. Identify the test statistic and state the null distribution.c. The test is to be conducted at a significance level of 5%. Find the critical region for this test.d. Is there convincing evidence to support the claim that the engine is better?

Since you have posted a question with multiple sub-parts , we will solve the first three complete sub parts and request you to repost this remaining unsolved parts separately. In case you want a specific part to be solved , please mention at the time of posting the question Let n be the no. of trials = 10 p be the population mean =0.3 q =1-0.3 =0.7 p⏞ is the proportion of trains late with new engine = 110=0.1 q⏞is the proportion of train on time with new engine =910=0.9 The hypothesis considered : Ho : μ = 0.3H1 : μ <0. 3 Since the distribution is binomial we can perform the test with normal approximation with N(p , pqn) Z test =p-p⏞pqn=0.1-0.30.3×0.710=-1.3801 The null distribution is Standard normal distribution if the null hypothesis is true The critical region in this case is the region below the value of -1.6449 when the test is conducted at 0.05 significance level