Solve the following questions below

1. Which of the following choices best classifies the ODE y'' + 4ty' - 7y = sin t ? Assume that y' = dy/dt.Question 4 options:

A) linear, homogeneous, constant coefficient

B) linear, non-homogeneous, constant coefficient

C) non-linear, homogeneous, constant coefficient

D) non-linear, non-homogeneous, constant coefficient

E) linear, homogeneous, variable coefficient

F) linear, non-homogeneous, variable coefficient

G) non-linear, homogeneous, variable coefficient

H) non-linear, non-homogeneous, variable coefficient

100 d Q34: As you decrease the number of subjects in your sample, the calculated value of a t-test will A. increase B. decrease C. remain the same Q35: As you increase the true distance between the null and alternative hypotheses (un - up), the likelihood of rejecting the null hypothesis A. increases B. decreases C. remains the same Q36: Keeping everything else the same, if you were to increase your alpha level from .01 to .05, the likelihood of rejecting the null hypothesis A. increases B. decreases C. remains the same The following 4 questions (037 to (40) are either "True" or "False" Q37: Predicting the characteristics of an entire group, after having measured a small group, is the major goal of inferential statistics, Q38: The single-most critical component of deciding whether you are to conduct a t-test versus a z-test for hypothesis testing is whether there is a 'N'. Q39: Degrees of freedom for a single sample t-test is/are 'n-1'. Q40: Degrees of freedom for a single sample z-test is/are 'n-1',4. Problem 9.29 (1.5 points) Be sure to set up your hypotheses first. Ho always contains equal sign and the alternative never does. Data is in the Insurance $13 file in your Problem Set folder. Use PHSTAT - One sample test - for a mean (Need to fill in the hypothesized mean in the top window, then level of significance (.05), then highlight the data, and last pick 2 tailed, upper or lower depending upon what you have in your H1. Make sure you state hypotheses and write up a conclusion stating how confident you are in Hi. t Test for Hypothesis of the Mean Data Null Hypothesis Level of Significance 0.05 Sample Size 27 Sample Mean 43.88888889 Sample Standard Deviation 25.28352053 Intermediate Calculations Standard Error of the Mean 4.8658 Degrees of Freedom 26 Test Statistic 9.0198 Two-Tall Test Lower Critical Value -2.0555 Upper Critical Value 2.0555 p-Value 0.0000000017358 Reject the null hypothesis5. Corrupted by their power, the judges running the popular game show America's Next Top Mathematician have been taking bribes from many of the contestants. Each episode, a given contestant is either allowed to stay on the show or is kicked off. If the contestant has been bribing the judges she will be allowed to stay with probability 1. If the contestant has not been bribing the judges, she will be allowed to stay with probability 1/3. Suppose that 1/4 of the contestants have been bribing the judges. The same contestants bribe the judges in both rounds, i.e., if a contestant bribes them in the first round, she bribes them in the second round too (and vice versa). (a) If you pick a random contestant who was allowed to stay during the first episode, what is the probability that she was bribing the judges? (b) If you pick a random contestant, what is the probability that she is allowed to stay during both of the first two episodes? (c) If you pick random contestant who was allowed to stay during the first episode, what is the probability that she gets kicked off during the second episode