Consider random samples of size 100 drawn from population A with proportion 0.24 and random samples of size 50 drawn from population B with proportion 0.43.  FIND THE STANDARD ERROR OF THE DISTRIBUTION OF DIFFERENCES IN SAMPLE P HAT a - P HAT b dot . round your answer for the standard error to three decimal places.   ARE THE SAMPLES SIZES LARGE ENOUGH FOR THE CENTRAL LIMIT THEOREM TO APPLY?

2. Compute the mean absolute deviation (MAD) and mean square error (MSE) for the following errors: Period (t) 1 2 3 6 4 5 7 Forecast (F;) 6.5 3.8 9.2 1.2 2.3 8.3 6.5 Error (e,) -2.3 | 1.3 -0.9 | 2.1 0.5 | -3.8 | 2.9 Calculate the actual values also.

The time (in minutes) it takes Greg to complete a homework problem is uniformly distributed (continuously) on the interval (15, 28). What is the standard deviation of the time it takes to complete a homework problem?

Central High School believes their students have unusually high SAT scores on average. The school has 165 students.Based on national data, the average SAT score is 1067 with a population standard deviation of 207. Assume SAT scores are normally distributed. Let X be the random variable representing the mean SAT scores for groups of 165 randomly selected students.a. Fill in the blank, rounding your answers to 2 decimal places if needed. According to the Central Limit Theorem, X is approximately normal with a mean of  and a standard error of the mean  .b. Find the z-score associated to a sample with a mean of 1109, using the sampling distribution. Round your answer to two decimal places. c. Find the probability that a randomly selected sample of 165 students has a mean SAT score higher than 1109. Round your answer to 4 decimal places. d. Central High School finds that for their students, the average SAT score is 1109. Are they justified in saying their students perform unusually well on…