Discuss the below:
1. For a sample selected from a population with a mean of u = 50 and a standard deviation of o = 10:
a. What is the expected value of M and the standard error of M and the standard error of M for a sample of n = 4 scores?
b. What is the expected value of M and the standard error of M for a sample of n = 25 scores?
2. IQ scores form a normal distribution with u = 100 and o = 15. If a random sample is selected from this population, on average, how much distance would you expect between the sample mean and the population mean for each of the following samples?
a. A sample of n = 9 scores
b. A sample of n = 25 scores
c. A sample of n= 100 scores
3. A population has a mean of u = 100 and a standard deviation of o=20. Find the z score corresponding to each of the following sample means obtained from this population.
a. M= 102 for a sample of n = 4 scores
b. M= 102 for a sample of n =100 scores
c. M= 95 for a sample of n = 16 scores
d. M = 95 for a sample of n = 25 scores
4. A random sample is obtained from a normal population with a mean of u = 80 and a standard deviation of o = 8. Which of the following outcomes is more likely?
a. A sample mean greater than M = 86 for a sample of n = 4 scores.
b. A sample mean greater than M = 84 for a sample of n =16 scores.
5. The value of the z score that is obtained for a hypothesis test is influences by several factors. Some factors influence the size of the numerator of the z score and other factors influence the size of the standard error in the denominator. For each of the following, indicated whether the factor influences the numerator of denominator of the z score and determine whether the effect would be to increase the value of z (farther from zero) or decrease the value of z (closer to zero). In each case, assume that all other components of the Z score remain constant.
a. Increase the sample size
b. Increase the population standard deviation
c. Increase the difference between the sample mean and the value of u specified in the null hypothesis.
6. The term errors that can be made in hypothesis testing.
a. What factor can a researcher control that will reduce the risk of a type I error?
b. What factor can a research control that will reduce the standard error?
7. Childhood participation in sports, cultural groups, and youth groups appears to be related to improved self-esteem adolescents. In a representative study, a sample of n = 100 adolescents with a history of group participation is given a standardized self-esteem questionnaire. For the general population of adolescents, scores on this questionnaire form a normal distribution with a mean of u = 40 and a standard deviation of o = 12. The sample of group participation adolescents is significantly different from those of the general population? Use a two-tailed test with x = .01
8. Test the effectiveness of a treatment, a sample of n = 25 people is selected from a normal population with a mean of u = 60. After the treatment is administered to the individuals in the sample, the sample mean is found to be M = 55.
a. If the population standard deviation is o = 10, can you conclude that the treatment has a significant effect? Use a two-tailed test with x = .05.
b. If the population standard deviations is o = 20, can you conclude that the treatment has a significant effect? Use a two-tailed test with x =. 05.
c. Compute Cohen's d to measure effect size for both tests (o = 20 and o = 10).