Please show the solution and explain the following questions:
\\/ In an anthropological study, 32 human skulls were found in a certain excavation site. The scientists wanted to know if these skulls might be a sample from a race known to have skulls with a mean width of 146 mm. The appropriate statistical test procedure to apply IS A. Test on the mean of a single C. Regression Analysis population D. Correlation Analysis B. Analysis of Variance F0r2 questions below. The energy intake of women aged 18 to 25 years is known to follow a normal distribution with mean 2000 and standard deviation of 100 calories. A random sample of 100 women in this age group yielded a mean energy intake of 2150 calories. J A 95% condence interval estimate for the true mean energy intake of women aged 18 to 25 years is given by A. [2148.040, 2151.960] C. [2148.355, 2151.645] B. [2130.400, 2169.600] D. [2133.550, 2166.450] J Which of the following is (are) TRUE regarding the constructed condence interval in (24)? I. Ninety ve out of a hundred women aged 18 to 25 years have energy intake falling within this condence interval. II. A decrease in the signicance level of this condence interval will lead to a larger tolerable error, holding other factors constant. A. I only C. Both 1 and II B. II only D. Neither I nor II I If V(t) pesos is the value of a certain equipment t years after its purchase, then V(t)=Be' 020' where B is a constant ,If the equipment was purchased for 8,000 pesos, what will be its value in 2 years? 5,363 pesos C. 4,363 pesos 3,565 pesos D. 4,565 pesos P\"? J If the probability that an annual rainfall of 3,000 mm will be equaled or exceeded is 4%, the return period is A. 10 years C. 20 years B. 15 years D. 25 years \\/ In a particular community, a certain epidemic spreads in such a way that x months after the start of the epidemic, P per cent of the population is infected, where P =30X2/ (1+x2)2. In how many months will the most people be infected? A. 1 C. 2 B. 1.5 D. 2.5 / If there are four judges and three contenders in a show choir competition, and each judge shall choose only one winner, in how many ways can the judges cast their votes? A. (4)(3) C. 43 B. 34 D. 4C3 For 2 questions below: Lenard and Sheldon are baseball battery. Lenard as catcher will send hand signals that will communicate his choice of pitch to Sheldon. Sheldon as pitcher will either veto or accept the pitch. The probability that Sheldon will veto a pitch is 0.11 and the probability that he will get a strike given he vetoed a pitch is 0.23. \\/ Which of the following is (are) TRUE? I. The event that Sheldon accepts Lenard's choice of pitch is independent of the event that he vetoes it. II. The event that Sheldon accepts Lenard's choice of pitch is complement to the event that he vetoes it. A. I only C. Both I and II B. II only D. Neither I nor II \\/ Which of the following is (are) TRUE? I. The probability that Sheldon will accept Lenard's choice of pitch is 0.89. II. The probability that Sheldon will veto a pitch and get a strike is 0.0253. A. I only C. Both I and II B. II only D. Neither I nor II \\/ The following infiltration capacity equation has been derived based on experimental data: f=8.1+4.1e'12-9"~ where f is in mm/hr and t is in hr. The cumulative inltration in mm after 30 minutes is: A. 4.0mm C. 4.6mm B. 4.4mm D. 5.0mm / A certain type of bacteria, given a favorable growth medium, doubles in population every 6.5 hours. Given that there were approximately 100 bacteria to start with, how many bacteria will there be in a day and a half? A. 4640 C. 4864 B 4648 D. 4684 / Which of the following is (are) TRUE about the correlation analysis? I. Interpreting the degree of linear relation between two variables is meaningful only when correlation is signicant. II. A value of the correlation coefcient equal to zero means there is no existing relationship between two variables. A. I only C. Both I and II B. II only D. Neither I nor II In a particular community, a certain epidemic spreads in such a way that P = 30X2 / (1+x2)2 where x is the months after the start of the epidemic and P is the per cent of the population infected. In how many months will the most people be infected? a) 1.0 b) 1.5 c) 2.0 d) 2.5 e) 3.0 A tetrahedron is rolled 50 times and the number of dots on the down-turned face was observed. The results are as follow: Outcome 1 2 3 4 Frequency 13 17 11 9 What is the probability of observing an odd number of dots on the down-turned face of the tetrahedron? a) 0.220 c) 0.480 b) 0.260 d) 0.820 e) none of the choices The same tetrahedron in Problem above is rolled. Assume that the tetrahedron is biased with the probabilities of observing each number of dots on the down-tu rned face given in Problem No.6. If the number of dots on the down-turned face of the tetrahedron is odd, then a marble is drawn from an urn containing 3 green and 2 white marbles. What is the probability of observing a white marble? a) 0.192 b) 0.250 c) 0.333 d) 0.400 e) 0.598 Store Next Door, an online dress shop is currently determining the average number of items ordered by its customers every month. Gail, its proprietor, randomly selected ve customers from a set of 50 students and seven buyers from a set of 60 professionals. The following data were observed: No. of Items Ordered Students 5 2 7 8 6 Professionals 4 5 9 3 8 7 7 The average number of items ordered by professionals and students are and respectively. a) 7 and 5.375 c) 6.1429 and 5.6 b) 5.6 and 6.1429 d) 5.375 and 7.5 e) none of the choices
