To evaluate the effect of a treatment, a sample is obtained from a population with a mean of  = 20, and the treatment is administered to the individuals in the sample. After treatment, the sample mean is found to be M = 21.3 with a variance of s2 = 9.

a. Assuming that the sample consists of n = 16 individuals, use a two-tailed hypothesis test with  = .05 to determine whether the treatment effect is significant and compute both Cohen’s d and r2 to measure effect size. Are the data sufficient to conclude that the treatment has a significant effect using a two-tailed test with  =.05?

b. Assuming that the sample consists of n = 36 individuals, repeat the test and compute both measures of effect size. c. Comparing your answers for parts a and b, how does the size of sample influence the outcome of a hypothesis test and measure of effect size?

After a dreary day of rain, the sun peeks through the clouds and a rainbow forms. you notice the rainbow is the shape of a parabola. the equation for this parabola is y = -x2 + 36. graph of a parabola opening down at the vertex 0 comma 36 crossing the x–axis at negative 6 comma 0 and 6 comma 0. in the distance, an airplane is taking off. as it ascends during take-off, it makes a slanted line that cuts through the rainbow at two points. create a table of at least four values for the function that includes two points of intersection between the airplane and the rainbow. analyze the two functions. answer the following reflection questions in complete sentences. what is the domain and range of the rainbow? explain what the domain and range represent. do all of the values make sense in this situation? why or why not? what are the x- and y-intercepts of the rainbow? explain what each intercept represents. is the linear function you created with your table positive or negative? explain. what are the solutions or solution to the system of equations created? explain what it or they represent. create your own piecewise function with at least two functions. explain, using complete sentences, the steps for graphing the function. graph the function by hand or using a graphing software of your choice (remember to submit the graph).