12 Comparing ANOVA and the t test for an independent-measures hypothesis test As
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12 Comparing ANOVA and the t test for an independent-measures hypothesis test As Aa Suzanne Zeedyk, a developmental psychologist at Dundee University's School of Psychology, conducted a pilot study in which parents started 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 interested in testing the hypothesis that babies who travel in parent-facing strollers have different receptive vocabularies than babies who travel in away-facing strollers. You randomly assign 18 newborns to parent-facing strollers and 18 newborns to away-facing strollers. You then test the babies' receptive vocabularies at age 36 months using the Peabody Picture Vocabulary Test- Revised (PPVT-R), which is designed primarily to assess children's receptive vocabulary The sample means and sums of squares of the soores for each of the groups are presented in the following table. Group Sample Mean Sum of Squares 2,828.97 2,530.28 Away-facing92.7 Parent facing104.3 You decide to use an ANOVA at -.01 to test the nul hypothesis that there is no difference between the groups. The ANOVA table follows. Calculate the F-ratio and enter it into the table. ANOVA Table Degrees of Source of Variation Between Treatments Within Treatments Total Sum of Squares: FreedomMean SquareF 1211.04 1,211.04 5,359.25 6,570.29 34 157.63 35 Use the Distributions tool that fotows to find Fattat at a significance tevet of .01, the value of F that bounds the critical region for the F-ratio test statisticExplanation / Answer
Answer:
Calculated F =1211.04/157.63 = 7.68
Critical F=7.44
At 0.01 level, null hypothesis is rejected. You can conclude that the direction that the stroller faces influences a child receptive vocabulary at 36 months.
t statistic = (92.7-104.3)/4.19 = -2.7684
critical values are (-2.728, 2.728)
At 0.01 level, null hypothesis is rejected. You can conclude that the direction that the stroller faces influences a child receptive vocabulary at 36 months.
ANOVA and t test resulted in same conclusion.
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