Question

To evaluate the effect of a treatment, a sample of n-8 is obtained from a population with a mean of ?-50, and the treatment is administered to the individuals in the sample. After treatment, the sample mean is found to be M 55. a) If the sample variance is s-32, use a two-tailed test with ?-0.05 to determine whether the treatment effect is significant and compute Cohen's d b) If the sample variance is s- 72, repeat the test and compute Cohen's d. c) Comparing your answers for parts a and b, how does the variability of the scores in the sample influence the outcome of a hypothesis test and the effect size? Research has shown that IQ scores have been increasing for years (Flynn, 1984, 1999). The phenomenon is called the Flynn effect and the data indicate that the increase appears to average about 7 points per decade. To examine this effect, a researcher obtains an IQ test with instructions for scoring from 10 years ago and plans to administer the test to a sample of n-25 of today's high school students. Ten years ago, the scores on this IQ test produced a standardized distribution with a mean of ? =100 and a standard deviation-15. If there actually has been a 7-point increase in the average IQ during the past ten years, then find the power of the hypothesis test for each of the following The researcher uses a two-tailed hypothesis test with ?-005 to determine the data indicate a significant change in IQ over the past 10 years. The researcher uses a one-tailed hypothesis test with ?-0.05 to determine the data indicate a significant increase in IQ over the past 10 years 1· 2.

Answer 1

Step1 The null and alternative hypotheses are ersus Step2 The level of significance is α= 0.05 Step3 The estim ated standard erroris 32 Step4 The t-test statistic is 55-50 2.5 2.5 Step5 Since, the t- test statistic is t2.5>os3 - 2.364624. We reject the null hypothesis Ho Make a decision The t value we obtained falls in the critical region The researcher rejects the null hypothesis H0 Hence, we conclude that the treatment is stati stically significant. The formula for calculating the Cohen's d is 5.656854 5.656854 0.883883 Interpretation The value of cohen'sd to measure the size of the treatm ent effect is d0.8 There is significant difference between the two treatm ent means based on the cohen's d, the measure of the effect size

Stepl The nul an d alternati ve hypotheses are ersus Step2 The level of significance is a 0.05 Step3 The estimated stan dard erroris Step4 The t test stati stic is 55-50 -1.666667 1.666667 Step5 Since, thet-test statistic is t1.666667 os, -2. 364624. We do not reject the null hypothesis Ho Make a decision: The t- value we obtained is not in the critical region. The researcher does not reject the null hypothesis Ho. Hence, we conclude that the treatment is not statistically significant The formula for calculating the Cohen's d is 8.485281 0.589256 Interpretation The value of cohen's d to measure the size of the treatment effect is 0.6 There is no significant difference between the two treatment means based on the cohen's d, the measure of the effect size Explanatiorn: As the variability in the sample increases, the hypothesis test and the effect size is not found to be stati stically significant. Where as the variability in the sample scores decreases influence the outcome of the hypothesis test and the effect size is stati cally si gnificant.