Two separate marketing teams, Team A and Team B, have each designed a 30 second advertisement for the new Cloak soft dlink. The manager of marketing is interested to see if there is any difference between the effectiveness of the two ads. A random sample of 150 people are shown the ad from Team A and asked if they would denitely buy the new drink. In this sample, a proportion of 0.680 people said that they would (to 3 decimal places). A second random sample of 150 people are shown the ad from Team B and asked if they would denitely buy the drink. In this sample, a proportion of 0.300 people said that they would [to 3 decimal places). Let in denote the population proportion of people that would denitely buy the drink ifthey saw the ad from Team A. Let it; denote the population proportion of people that would denito buy the drink if they saw the ad from Team B. A hypothesis test is conducted with thefollowing hypotheses: Ho: 1T1 = 1T2 HA: 111 e TI: 2 The level of signicance used in this test is 0.05. You may nd this standard normal table useful. a) Calculate the test statistic [2) for this test. Give your answer to 2 decimal places. IJ) In this test the null hypothesis rejected. Due to various socio economic factors, residents of a particular city have an unusually high level of attendance at private schools. A study is con ducted to detem'line whether there is any difference between the rate at which males and females choose private schools over public schools in this city. A random sample of 125 males from the city are contacted and asked if they attend or ever attended a private school. The proportion that did {to 2 decimal places) is 0.48. Similarly, a random sample of 25 females from the city are contacted and asked the same question. The proportion that attended a private school {to 2 decimal places) is 0.40. Let in denote the population proportion of males that attended a private school. Similariy, let 'J'Ez denote the population proportion of females that attended a private school. Construct a 90% condence interval for the difference between these two proportions [Til 1T2). Give your answers to 3 decimal places. You may nd this standard normal table useful