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# Description of Hypothesis Testing, Cohen's d & Effect size

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4. Explain why a t distribution tends to be flatter and more spread out than the normal distribution.

12. Last fall a sample of n = 36 freshman was selected to participate in a new four hour training program designed to improve study skills. To evaluate the effectiveness of the new program, the sample was compared with the rest of the freshman class. All freshman must take the same English Language skills course, and the mean score of the final exam for the entire freshman class population mean = 74. The students in the new program has a mean score of M = 79.4 with a standard deviation of s = 18.

A. On the basis of these data, can the college conclude that the students in the new program performed significantly better than the rest of the freshman class? Use a one tailed test with alpha value = .05

B. Can the college conclude that the students in the new program are significantly different from the rest of the freshman class? Use a two-tailed test with alpha value = .05

22. A researcher would like to examine the effects of humidity on eating behaviors. It is known that laboratory rats normally eat an average of population mean = 21 grams of food each day. The researcher selects a random sample of n = 16 rats and places them in a controlled atmosphere room in which the relative humidity is maintained to 90%. The daily food consumption scores for the rats are as follows:

14, 18, 21, 15, 18, 18, 21, 18
16, 20, 17, 19, 20, 17, 17, 19

A. Can the researcher conclude that humidity has a significant effect on eating behavior? Use a two tailed test with alpha value = .05

B. Compute the estimated d and percentage of variance accounted for by the treatment (r squared) to measure the size of the treatment effect.

18. Other research examining the effects of preschool childcare has found that children who spent time in day care, especially high quality day care, perform better on math and language tests than children who stay home with their mother. Typical results, for example, show that a sample of n= 25 children who attended day care before starting school had and average score of M= 87 with SS= 1536 on a standardize math test for which the population mean u=81 . Is the sample sufficient to conclude that children with a history of preschool day care are significantly different from the general population? Use a two tailed test with a = .01

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#### Solution Summary

The solution provides a step by step method for the calculation of testing of hypothesis, Cohen's d and effect size. Formula for the calculation and interpretations of the results are also included. An interactive excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data.

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## Statistics problem

Hello. I am doing my regular homework assignment and I cannot figure out and understand how to solve some of the problems. The book that I have does not explain or show how to solve the specific problems below. I have answered the questions that I am able to, but I cannot answer the other ones no matter how hard I have tried. Can you PLEASE include step-bt-step instructions on how to solve the problems. If I get behind with this, I won't be able to figure out next week's assignments. Because the course is online, it is impossible to really get any help or questions answered from the instructor, so I'm stuck.

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. 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).

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