A sample of 300 orders for take-out at a local pizzeria found that the average cost of an order was $29 with S=$17.(a) Find the margin of error, if we use a 95% confidence interval, for the average cost of an order(b) Interpret for the management the margin of error(c) If we need to be 99% confident does the confident interval become wider or narrower?(d) Find the 99% confidence interval.4. An accounting firm is considering offering investment advice in addition to its current focus on tax planning. Its analysis of the costs and benefits of adding this service indicate that it will be profitable if 40% or more of its current customer base use it. The firm plans to survey its customers. Let p denote the proportion of its customers who will use this service if offered, and let (upper p) denote the proportion who say in a survey that they will use this service. The firm doesn't want to invest in this expansion unless data show that it will be profitable. Determine whether the following statement is true or false. If the statement is false, explain why it is false. If (upper p) is larger than 0.4, a test will reject the appropriate null hypothesis for this context. 5.Consider the following test of whether a coin is fairToss the coin four times. If the coin lands either all heads or all tails, reject null hypothesis; p=1/2 (the p denotes the chance for the coin to land on heads) complete a and b.(a) I have the answer to this= 1/8(b)if p=2/3, what is the probability of a type II error for this procedure?