DIRECTION: For each of the given problems, conduct a hypothesis test (assume that the underlying population is normally distributed). 1. ATMs must be stocked with enough cash to satisfy customers making withdrawals over an entire weekend. But if too much cash is unnecessarily kept in the ATMs, the bank is forgoing the opportunity of investing the money and earning interest. Suppose that at a particular branch, the population mean amount of money withdrawn from ATMs per customer transaction over the weekend is Php8,000, with a population standard deviation of Php1,500. a. If a random sample of 36 customer transactions indicates that the sample mean withdrawal amount is Php8,600, is there evidence to believe that the population mean withdrawal amount is no longer Php8,000? (Use a 0.05 level of significance.) 2. A research done by a graduating student reports that the average score of University students in statistics course is less than 80. To test this claim, a random sample of 10 students was taken and their scores in the course are recorded as: 65, 70, 80, 85, 60, 90, 80, 75, 85, 90. At 0.05 level of significance, test the validity of this claim. 3. A research study was conducted to compare two methods of teaching statistics in graduate school. One method, called the traditional method, presented the course without the use of statistical software. The other method, referred to as experimental method, taught the course and utilized statistical software extensively. The scores made on a common comprehensive final exam by the students in both classes are shown in the table below. Traditional 82 85 82 73 82 73 79 71 86 90 98 86 77 81 Experimental 78 83 96 89 83 68 84 83 76 83 89 90 85 77 At 5% significance level, determine whether there is a sufficient statistical evidence to indicate that the experimental method is more effective than the traditional method