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Hypothesis Testing & Cohen's d

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Problem Set 1: Chapter 9, problems 4, 12, 14, 22

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

12. Last fall, a sample of n = 36 freshmen was selected to participate in a new 4-hour training program: µ = 74; M = 79.4, 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 ? = .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 ? = .05

14. In the Preview for this chapter, we discussed a study that examined the effect of eye spot patterns on the behaviour of moth eating birds: µ = 30; M = 37, SS = 288, n = 9.

a. Is this sample sufficient to conclude that the eye-spots have a significant influence on the birds' behaviour? Use a two-tailed test with ? = .05.

b. Compute the estimated Cohen's d to measure the size of the treatment effect.

22. A researcher would like to examine the effects of humidity on eating behaviours. It is known that laboratory rats normally eat an average of µ = 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 behaviour? Use a two tailed test with a alpha value = .05

b. Compute the estimated d and r2 to measure the size of the treatment effect.

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The solution provides step by step method for the calculation of testing of hypothesis and Cohen's d. Formula for the calculation and Interpretations of the results are also included. 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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Hypothesis Testing, Power of Hypothesis Testing & Cohen's d

2. The value of the z-score in a hypothesis test is influenced by a variety of factors. Assuming that all other variables are held constant, explain how the value of z is influenced by each of the following.

a. Increasing the difference between the sample mean and the original population mean.

b. Increasing the population standard deviation.

c. Increasing the number of scores of the sample.

4. If the alpha level is changed from ? = .05 to ? = .01.

a. What happens to the boundaries for the critical region?

b. What happens to the probability of a Type 1 error?

6. A researcher is investigating the effectiveness of a new study skills training program for elementary school children. A sample of n = 25 third grade children is selected to participate in the program and each child is given a standardized achievement test at the end the year. For the regular population of third grade children, scores on the test form a normal distribution with a mean of µ= 150 and standard deviation of Ï? = 25. The mean for the sample is M = 158.

a. Indenify the independent and the dependent variables for this study.

b. Assuming a two-tailed test, state the null hypothesis in a sentence that includes the independent variable and the dependent variable.

c. Using symbols, state the hypothesis (Ho and H1) for the two-tailed test.

d. Sketch the appropriate distribution, and locate the critical region for ? = .05

e. Calculate the test statistic (z-score) for the sample.

f. What decision should be made about the null hypothesis, and what decision should be about the effect of the program?

10. State College is evaluating a new English composition course for freshmen. A random sample of n = 25 freshmen. A random sample of n =25 freshmen is obtained and the students are placed in the course during their first semester. One year later, writing samples are graded using a standardized evaluation technique. The average score for the sample is M = 76. For the general population of college students, writing scores form a normal distribution with a mean of µ =70.

a. If the writing scores of the population have a standard deviation of Ï? =20, does the sample provide enough evidence to conclude that the new composition course has a significant effect? Assume a two-tailed test with ? = .05.

b. If the population standard deviation is Ï? = 10, is the sample sufficient to demonstrate a significant effect. Again, assume a two-tailed test with ? = .05.

c. Briefly, explain why reached different conclusion for part (a) and part (b).

18. A sample of n = 16 individuals is selected from a normal population with the mean of µ = 48 and the standard deviation of Ï? = 12. After receiving a treatment, the sample mean is found to be M = 52.

a. Compute Cohen's d to evaluate the size of the treatment plan.

b. If the sample size were n = 36, what value would be obtained for Cohen's d? How does sample size influence the measure of effect size?

c. If population standard deviation were Ï? =24 what value would be obtained for Cohen's d? How does the standard deviation influence the measure of effect size?

d. If the sample mean were M =56, what value would be obtained for Cohen's d? How does the size of the mean difference influence the measure of effect size?

22. Explain how the power of a hypothesis test is influenced by each of the following. Assume that all other factors are held constant.

a. Increasing the alpha level from .0.1 to .05.

b. Changing from a one-tailed test to a two-tailed test.

24. A researcher is evaluating the influence of a treatment using a sample selected from a normally distributed population with a mean of µ =80 and a standard deviation of Ï? = 20. He researcher expects a 12- point treatment effect and plans to use a two-tailed hypothesis test with ? = .05.

a. Compute the power of test if the researcher uses a sample of n =16 individuals.

b. Compute the power of the test if the researcher uses a sample of n = 25 individuals.

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