Please help answer this 4 question and with detail

Problem 1 (2 points) In a hypothesis test about an unknown parameter, the test statistic... Select the best response a. measures the compatibility between the null and alternative hypotheses b. is the value of the unknown parameter under the null hypothesis c. measures the compatibility between the null hypothesis and data d. is the value of the unknown parameter under the alternative hypothesis e. None of the above REPLACE THIS TEXT WITH YOUR RESPONSE Problem 2 (3 points) A particle randomly moves along a line. That is, the particle starts at the origin (position 0) and moves either right or left in independent steps of length 0, 1, or 2 (where length 0 means the particle stays in its current location). The distribution of the particle's movement at step i is listed in the table below called x_distribution . X; is the random variable with the distribution below, and x, are the possible values X, can take. The probability of each x; is listed below under P(X; = x;). x_distribution ## 1 -2 0 .5 ## 2 -1 0.2 ## 3 0. 1 # # 4 0.2 The position of the particle after & steps is the sum of these random movements Y = X1 + X2+... +Xx. The probability distribution of Y (with computed values rounded to the nearest 0.01) is a. Exactly Normal with mean = 0 and variance = 1.67/k . Exactly Normal with mean = -0.5 and variance = 1.67/k C. Exactly Normal with mean = -1 and variance = 1.4/k d. Approximately Normal with mean = 0 and variance = 1.3/k e. Approximately Normal with mean = -0.5 and variance = 1.4/k f. Approximately Normal with mean = -1 and variance = 1.67/k J. None of the above. REPLACE THIS TEXT WITH YOUR RESPONSE Problem 3 (3 points) The weight, X, of cherry tomatoes selected at random from a very large bin at the local supermarket follows a Normal distribution with mean 3 oz. and standard deviation 2 oz. Suppose we pick 8 cherry tomatoes from the bin at random (independently) and put them in our bag. What is the probability that exactly 5 of the 8 cherry tomatoes weigh less than 4 oz (rounded to the nearest 0.01)? REPLACE THIS TEXT WITH YOUR RESPONSE Problem 4 (3 points) Suppose a confidence interval for the mean weight increase of pregnant women in their first 5 months of pregnancy is found to be 16 +/- 0.134 Ibs based on a random sample of size n = 400. Assuming the population standard deviation is known to be 2 lbs, what confidence level was used to calculate this confidence interval (rounded to the nearest %)? REPLACE THIS TEXT WITH YOUR RESPONSE