Comparing ANOVA and the t test for an independent-measures hypothesis test Suzan

Question

Comparing ANOVA and the t test for an independent-measures hypothesis test Suzanne Zeedyk, a developmental psychologist at Dundee University's School of Psychology, conducted a pilot study in which parents start d a half-hour walk with their infants in a parent-facing or an away-facing stroller and then switched to the other type of stroller midway. Her results suggest that parents talked less to the babies, the babies had higher heart rates, and they were less likely to fall asleep in away-facing strollers than in parent-facing strollers. You are interest in testing the hypothesis that babies who travel in parent-facing strollers have different expressive vocabularies than babies who travel in away-facing strollers. You randomly assign 15 newborns to parent-facing strollers and to 15 newborns to away-facing strollers. You then test the babies expressive vocabularies at age 36 months using the Expressive Vocabulary Test (EVT), which is designed primarily to assess children's expressive vocabulary. The sample mea and sums of squares of the scores for each of the groups are presented in the following table. You decide to use an ANOVA at alpha = .05 to test the null hypothesis that there is no difference between the groups. The ANOVA table follows. Calculate the F-ratio and enter it into the table. Use the Distributions tool that follows to find F_ at a significance level of alpha = .05, the value of F that bounds the critical region for the F-ratio test statist. F_ at alpha = .05 is _____. Now evaluate the null hypothesis that the population means for all treatments are equal. At a significance level of alpha = .05, the null hypothesis is _____. You find that you _______ conclude that the direction that the stroller faces influences a child's expressive vocabulary at 35 months. Now you decide to use at test to test the hypothesis that there is no difference between the groups. The estimated standard error (S_M1 -M2) is 4.53, so the t test statistic is ____. Use the following tool to find the critical regions for alpha = .05. The critical t-scores (the values for t-scores that separate the tails from the main body of the distribution, forming the critical regions) are _____. Now use the tool to evaluate the null hypothesis. At a significance level of alpha = .05, the null hypothesis is _____. You find that you _____ conclude that the direction the stroller faces influences a child's expressive vocabulary 36 months. When you evaluated the mean difference from the independent-measures study comparing only two samples, the ANOVA and the t test resulted in _____ conclusion.

Explanation / Answer

Sol:

F critical at 0.05 is 4.196

Fcal =4.31

Fcal > F crit

Reject Null hypothesis

you can conclude that the direction that the stroller faces influences a childs expression vocab at 36 months

T critical for -2.048 and +2.048

Reject Null Hypothesis

you can conclude that the direction that the stroller faces influences a childs expression vocab at 36 months

Both resulted in same conclusion

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