Researchers investigating characteristics of gifted children collected data from schools in a large city on a random sample of 36 children who were identified as gifted children soon after they reached the age of four years old. one recorded characteristic was the age in months that each child was first able to count to ten. the sample mean was 30.69 months with a standard deviation of 4.31 months. suppose you read online that children first count to ten successfully when they are 32 months old, on average. you decide test the hypothesis that the average age at which gifted children first count to ten is different from 32 months. what would the test statistic (i. e., z-score) be for the null hypothesis in this case?

I've been working on this for a few days and i just don't understand, it's due in a few hours. you. the direction of a vector is defined as the angle of the vector in relation to a horizontal line. as a standard, this angle is measured counterclockwise from the positive x-axis. the direction or angle of v in the diagram is α. part a: how can you use trigonometric ratios to calculate the direction α of a general vector v = < x, y> similar to the diagram? part b suppose that vector v lies in quadrant ii, quadrant iii, or quadrant iv. how can you use trigonometric ratios to calculate the direction (i.e., angle) of the vector in each of these quadrants with respect to the positive x-axis? the angle between the vector and the positive x-axis will be greater than 90 degrees in each case. part c now try a numerical problem. what is the direction of the vector w = < -1, 6 > ?