Hypothesis Testing, Cohen's d & Effect size

See attached file.

Questions 6,16,18 for Chp 8
4, 10, 14 for Chp 9
4, 6, 8 for Chp 10

Chapter 8

#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 of 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 a standard deviation of σ = 25. The mean for the sample is M = 158.

a. Identify the independent and the dependent variables for this study.
Independent variable:
Dependant variable:

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, identify the hypothesis (H0 and H1) for the two-tailed test.
Ho: &#956;1 = &#956;2 Ho: &#956;1 > &#956;2 Ho: &#956;1 < &#956;2 Ho: &#956;1 &#8800; &#956;2
H1: &#956;1 = &#956;2 H1: &#956;1 > &#956;2 H1: &#956;1 < &#956;2 H1: &#956;1 &#8800; &#956;2

e. Calculate the test statistic (z-score) for the sample. Z= ???
f. What decision should be made about the null hypothesis, (decision = ???)
and what decision should be made about the effect of the program? (decision = ???)
# 16 A researcher is testing the hypothesis that consuming a sports drink during exercise improves endurance. A sample of n = 50 male college students is obtained and each student is given a series of three endurance tasks and asked to consume 4 ounces of the drink during each break between tasks. The overall endurance score for this sample is M = 53. For the general population, without any sports drink, the scores for this task average &#956; = 50 with a standard deviation of &#963; = 12.
a. Can the researcher conclude that endurance scores with the sports drink are significantly higher than scores without the drink? Use a one-tailed test with &#945; = 0.05.
Z= ???, Z critical = ??? , Conclusion = ???
b. Can the researcher conclude that endurance scores with the sports drink are significantly different than scores without the drink? Use a two-tailed test with &#945; = 0.05.
Z= ???, Z critical = ??? , Conclusion = ???
c. You should find that the two tests lead to different conclusions. Explain why.
#18 Researchers have often noted increases in violent crimes when it is very hot. In fact, Reifman, Larrick, and Fein (1991) noted that this relationship even extends to baseball. That is, there is a much greater chance of a better being hit by a pitch when the temperature increases. Consider the following hypothetical data. Suppose that over the past 30 years, during any given week of the major-league season, an average of &#956; = 12 players are hit by wild pitches. Assume that the distribution is nearly normal with &#963; = 3. For a sample if n = 4 weeks in which the daily temperature was extremely hot, the weekly average of hit-by-pitch players was M = 15.5. Are players more likely to get hit by pitches during hot weeks? Set alpha to 0.05 for a one-tailed test.
Z= ???, Z critical = ??? , Conclusion = ???
Chapter 9

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

#10 To evaluate the effect of a treatment, a sample of n = 9 is obtained from a population with a mean of &#956; = 40, and the treatment is administered to the individuals in the sample. After treatment, the sample mean is found to be M = 33.
a. If the sample has a standard deviation of s = 9, are the data sufficient to conclude that the treatment has a significant effect using a two-tailed test with &#945; = 0.05?

Df = ??? S2 = ??? Sm = ??? T= ??? z critical = ??? Conclusion: ???

b. If the sample has a standard deviation of s = 15, are the data sufficient to conclude that the treatment has a significant effect using a two-tailed test with &#945; = 0.05?

Df = ??? S2 = ??? Sm = ??? T= ??? z critical = ??? Conclusion: ???

c. Comparing your answer for parts a and b, how does the variability of the scores in the sample influence the outcome of a hypothesis test?

#14 Many animals, including humans, tend to avoid direct eye contact and even patters that look like eyes. Some insects, including moths, have evolved eye-spot patterns on their wings to help ward off predators. Scaife (1976) reports a study examining how eye-spot patterns affect the behavior of birds. In the study, the birds were tested in a box with two chambers and were free to move from one chamber to another. In one chamber, two large eye-spots were painted on one wall. The other chamber had plain walls. The researcher recorded the amount of time each bird spent in the plain chamber during a 60 minute session. Suppose the study produced a mean of M = 37 minutes on the plain chamber with SS = 288 for a sample of n = 9 birds. (Note: If the eye spots have no effect, then the birds should spend an average of &#956; = 30 minutes in each chamber.)
a. Is this sample sufficient to conclude that the eye-spots have a significant influence on the birds' behavior? Use a two-tailed test with &#945; = 0.05.

Df = ??? S2 = ??? Sm = ??? T= ??? z critical = ??? Conclusion: ???
b. Compute the estimated Cohen's to measure the size of the treatment effect.

D = ???

c. Write a sentence that demonstrates how the outcome of the hypothesis test and the measure of effect size would appear in a research report.

Chapter 10

#4 If other factors are held constant, how does increasing the sample variance affect the value of the independent-measures statistic and the likelihood of rejecting the null hypothesis?

#6 One sample has SS = 48 and a second sample has SS = 32.
a. Assuming that n = 5 for both samples, find each of the sample variances and compute the pooled variance. Because the samples are the same size, you should find that the pooled variance is exactly halfway between the two sample variances.

S1²= ??? S2²= ??? Sp²= ???

b. Now assume that n = 5 for the first sample and n = 9 for the second. Again, calculate the two sample variances and the pooled variance. You should find that the poled variance is closer to the variance for the larger sample.

S1²= ??? S2²= ??? Sp²= ???

#8 As noted on page 281, when the two population means are equal, the estimated standard error for the independent-measures t test provides a measure of how much difference to expect between two sample means. For each of the following situations, assume that &#956;1 = &#956;2 and calculate how much difference should be expected between the two sample means.
a. One sample has n = 8 scores with SS = 45 and the second sample has n = 4 scores with SS = 15.

S1²= ??? S2²= ??? s(M1 - M2) = ???

b. One sample has n = 8 scores with SS = 150 and the second sample has n = 4 scores with SS = 90.

S1²= ??? S2²= ??? s(M1 - M2) = ???

c. In part b, the samples a have larger variability (bigger SS values) than in part a, but the sample sizes are unchanged. How does larger variability affect the size of the standard error for the sample mean difference?

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