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It was recently reported that in the United States, 40.3 percent of all births are to unmarried mothers. A county health administrator is investigating whether births to unmarried women is higher in her county than in the national average. If so, she will propose additional funding to counsel unmarried mothers. A random sample of 100 births in the county will be looked at. Let p represent the proportion of all women giving birth in the county who are unmarried Consider the following hypotheses. Ho : p = 0,403, H. : p > 0.403 (a) Describe a Type II error in context and a possible consequence. (b) What values of the sample proportion p would represent sufficient evidence to reject the null hypothesis at a significance level of a = 0.057 Suppose the actual proportion of all women giving birth in the county who are unmarried is 0.045. (c) Using the actual proportion of 0.045 and the answer from (b), find the probability that the null hypothesis will be rejected. Show your work. (d) What statistical term describes the probability calculated in (c)? (e) Suppose the size of the sample was greater than 100. How would that effect the probability of rejecting the null hypothesis calculated in (c)? Explain.Aggregated logit model. Consider a binary logit model for car and bus, where the following representative utility functions have been estimated with a sample of 750 individuals belonging to a particular O-D pair of an urban area: Vc = 3.5 - 0.25tc - 0.42ec - 0.1cc vb =-0.251b - 0.42es - 0.1cb where f is in-vehicle time (minutes), e is access time (minute) and c is travel cost (cents). The subscripts b denotes bus and c denotes car. Assume the following average data is known: variable Mode C Car 25 140 Bus 40 50 If this O-D pair has 8,600 person-trips/day (a) Calculate the probabilities that a person will take bus and car. (b) Calculate the expected number of persons taking bus and car. (c) If the cost of travel by car increases by 10% (i.e., c. is now 154) while other attributes remain unchanged, calculate the expected number of trip using each mode,. Perform your calculations by means of the conventional logit model as well as the incremental logit model