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Perform the following test of hypothesis: 1. We have a random sample of 25 new recruits who can do 15 pushups on the average, with a standard deviation of 9, after completing a special physical education program. Does this value of 15 differ significantly from the population value of 12? (a=0.05) 2. New tires manufactured by a company are designed to provide a mean life expectancy of at least 40,000 km. The tire rating has a standard deviation of 1000 miles. A test using 35 tires showed a mean of 39,600 km. Using a 0.05 level of significance, test whether or not there is sufficient evidence to reject the claim of a mean of at least 40,000 km. 3. The average salary of bank tellers is more than PhP42,500. A sample of 30 bank tellers has a mean salary of PhP43,500 with a standard deviation of PhP 5,300. At a = 0.05, test the claim that bank tellers earn more than PhP42,000 per month. 4. A typing instructor wondered whether a new method of instruction would result in a change in the mean typing speed of students. The old method produced a mean of 65 words per minute. The results of 40 students using the new method were as follows: 56 60 60 76 60 59 41 66 67 33 55 43 61 71 73 60 56 77 43 58 65 67 71 56 48 90 82 46 68 36 27 52 64 54 49 69 46 68 62 68 At the 5% level, can the instructor conclude that the new mean is different from 64? 5. A special team of XYZ Telecom is proposing a new project of Internet Broadband Wireless Connectivity to their new clients in a rural town. The company will accept the proposal if the results of the survey conducted by the special team would have 75% or more favorable response indication regardless of additional fees and other surcharges. The results show that there are only 1, 950 out of 2, 600 customers who agreed on the said survey. Using the 1% level of significance. Would the company launch the project of the special team