Explain why it would not be reasonable to use estimation after a hypothesis test for which the decision was fail to reject H0. 4. A researcher has constructed an 80% confidence interval of ????45 ??8, using a sample of n??25 scores. a. What would happen to the width of the interval if the researcher had used a larger sample size? (Assume other factors are held constant.) b. What would happen to the width of the interval if the researcher had used 90% confidence instead of 80%? c. What would happen to the width of the interval if the sample variance increased? (Assume other factors are held constant.) 10. . Standardized measures seem to indicate that the average level of anxiety has increased gradually over the past 50 years (Twenge, 2000). In the 1950s, the average score on the Child Manifest Anxiety Scale was ????15.1. A sample of n??16 of today s children produces a mean score of M??23.3 with SS??240. a. Based on the sample, make a point estimate of the population mean anxiety score for today s children. b. Make a 90% confidence interval estimate of today s population mean. 18. Problem 15 in Chapter 10 described a study by Laughlin, Zander, Knievel, and Tan (2003) showing that groups of three people consistently outperformed the best of the individuals working alone on a letters to numbers substitution problem. The following data describe the number of trials needed to solve each problem for a sample of n??15 groups and a sample of n??15 individuals. Groups Individuals n??15 n??15 M??3.8 M??4.7 SS??15.4 SS??18.2 a. Make a point estimate of how much better groups perform than individuals for the general population. (Estimate the mean difference in the number of trials needed for a solution.) b. Make an interval estimate of the mean difference so that you are 95% confident that the true mean difference is in your interval. c. Based on your answer to part b, what would be the decision from a hypothesis test evaluating the significance of the mean difference using a two tailed test with ????.05. Explain your answer. 4. Explain why you should use ANOVA instead of several t tests to evaluate mean differences when an experiment consists of three or more treatment conditions. 14. A researcher reports an F ratio with df??2, 24 for an independent measures research study. a. How many treatment conditions were compared in the study? b. How many subjects participated in the entire study? 16. Recent research indicates that the effectiveness of anti depressant medication is directly related to the severity of the depression (Khan, Brodhead, Kolts, & Brown, 2005). Based on pre treatment depression scores, patients were divided into four groups based on their level of depression. After receiving the antidepressant medication, depression scores were measured again and the amount of improvement was recorded for each patient. The following data are similar to the results of the study. a. Do the data indicate significant differences among the four levels of severity? Test with ????.05. b. Compute ??2, the percentage of variance explained by the group differences. Low High Moderately Moderate Moderate Severe Severe 0 1 4 5 N=16 2 3 6 6 G=48 2 2 2 6 X2=204 0 2 4 3 M=1 M=2 M=4 M=5 T=4 T=8 T=16 T=20 SS=4 SS=2 SS=8 SS=6 20. The following summary table presents the results from an ANOVA comparing three treatment conditions with n=12 participants in each condition. Complete all missing values. (Hint:Start with the dfcolumn.) Source SS df MS Between Treatments 9 F= Within Treatments Total 117 26. One possible explanation for why some birds migrate and others maintain year round residency in a single location is intelligence. Specifically, birds with small brains, relative to their body size, are simply not smart enough to find food during the winter and must migrate to warmer climates where food is easily available (Sol, Lefebvre, & Rodriguez Teijeiro, 2005). Birds with bigger brains, on the other hand, are more creative and can find food even when the weather turns harsh. Following are hypothetical data similar to the actual research results. The numbers represent relative brain size for the individual birds in each sample. Short Long Non Distance Distance Migrating Migrants Migrants Non Short Long Migrating Distance Migrants Distance Migrants 18 6 4 N=18 13 11 9 G=180 19 7 5 zX2=2150 12 9 6 16 8 5 12 13 7 M=15 M=9 M=6 T=90 T=54 T=36 SS=48 SS=34 SS=16
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