Suppose that between their first and second years in college, 400 students are randomly selected and given a university grant to purchase a new computer. For student i, y; denotes the change in GPA from the first year to the second year. If the average change is ỹ = .132 with standard deviation s = 1.27, is the average change in GPAS statistically greater than zero?

Suppose that you wish to estimate the difference between mean pH measurements of rainfalls in two different locations, one in relatively unpolluted area and the other in an area subject to heavy air pollution. You want to be 95% confident that the margin of error for the difference between mean pH of rainfalls in relatively unpolluted area and mean pH of rainfalls in an area subject to heavy air pollution will not exceed 0.1 pH. How many rainfalls (pH measurements) must be included in each sample? Assume that the variance of pH measurements in a relatively unpolluted area is equal to 2 = 20, and the variance of pH measurements in an area subject to heavy pollution is equal to 2 = 0.25, and samples will be of equal size (n = n₂ = n). 2 It is supposed that values of pH in rainfalls are normally distributed in polluted and unpolluted areas. The number of rainfalls (pH measurements) that must be included in each sample is

In a recent year, grade 6 Ohio State public school students taking a mathematics assessment test had a mean score of 303.1 with a standard deviation of 36.  Possible test scores could range from 0 to 1000. Assume that the scores were normally distributed.  This is not a normal approximation, so do not correct for continuity. Find the probability that a student had a score higher than 295. Find the probability that a student had a score between 230 and 305. What is the highest score that would still place a student in the bottom 16% of the scores? If 4000 students are randomly selected, how many will have a test score that is less than 300? A random sample of 40 students is drawn from this population. What is the probability that the mean test score is greater than 290?

Student Satisfaction sent from average to the 60th percentile (z score = .2533). Dr. Reed wants to know the projected impact on test scores.  All she knows is that Student Satisfaction and Student Test scores are correlated at .43 and the current average test score is 81% with a standard deviation of 5%.  Show your work

Assume that IQ scores are normally distributed with μ = 100 and σ = 15 What IQ score would be needed to score in the top 2% of IQ scores?

Suppose the mean and standard deviation of the GPAs at school are Xbar = 1.654; and s = -0.562Adam's GPA has a z-score of -1.460. What is Adam's GPA?(Leave your answer to 2 decimals: ex: 1.23)