1. For a population that has a standard deviation of 24, figure the standard deviation of the sampling distribution of samples of sizes a) 3, b)4, and d)12. Type all formulas and steps in calculation in order to receive full credits (parts (a) through (c).2. For a population that has a known standard deviation of 22, figure the 95% confidence interval (that is, the lower and upper confidence limits for part(a) through (b). Assume that in each case the researcher’s sample has a mean of 98 and the population is known to follow a normal curve. (parts (a) through (b).One can be 95% confident that for a sample size of 6, the true population mean is between ………… and ………..One can be 95% confident that for a sample size of 14, the true population mean is between ………… and ………..3. For each of the following samples that were given an experimental treatment, test whether the sample represents populations that score significantly higher than the general population. Make sure to indicate your conclusion. It is known that the general population of individuals has a mean of 78, a standard deviation of 6, and follows a normal distribution. Type all formulas and steps in calculation.A sample of 102 with a mean of 80.A sample of 9 with a mean of 83.4. 22 Women between ages of 70 and 80 were randomly selected from general population of women in this age group to take part in a study that examined the simple reaction time. The sample of women selected for the study had an average reaction time of 1.4 seconds. It is known that the mean reaction time of the population of women in this age group is 1.8 with a standard deviation of 0.4 seconds. Was the mean reaction time of the women participated in the study was significantly lower than the general population? Type all formulas, critical values, and steps in calculation.5. In a completed study, there is a known population with a normal distribution, μ=30, and σ=11. What is the estimated effect size if a sample given an experimental procedure that has a mean of 223040For each part also indicate whether the effect is approximately small, medium, or large. Type all formulas and steps in calculation Parts (a) through (c).6. On an intelligent test, the mean number of raw items correct is 240 and standard deviation is 38. What are the raw scores on the test for people with standardized IQ scores of a)115, b) 85, and c) 130. To solve this problem, first figure the Z score for the particular IQ score, then use that Z score to find the raw score. Note that IQ scores have a mean of 100 and a standard deviation of 15. Type all formulas and steps in calculation.