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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 expressive vocabularies than babies who travel in away-facing strollers. You randomly assign 12 newborns to parent-facing strollers and 12 newborns to away-facing strollers. You then test the babies' expressive vocabularies at age 18 months using the Expressive Vocabulary Test (EVT), which is designed primarily to assess children's expressive vocabulary. The sample means and sums of squares of the scores for each of the groups are presented in the following table. Group Away-facing Parent-facing Sample Mean Sum of Squares 98.1 2,064.59 106.2 1,404.59 You decide to use an ANOVA at a = 0.01 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. Source of Variation Between Treatments Within Treatments Total Sum of Squares 393.66 3,469.18 3,862.84 F Distribution Use the Distributions tool that follows to find Fertical at a significance level of a = 0.01, the value of F that bounds the critical region for the F-ratio test statistic. Numerator Degrees of Freedom-20 Denominator Degrees of Freedom-20 ANOVA Table Degrees of Freedom Mean Square F 1 22 23 0.00 5000 5000 1.00 1.000 2.00 393.66 157.69 3.00 4.00 5.00 6.00 7.00 8.00

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 expressive vocabularies than babies who travel in away-facing strollers. You randomly assign 12 newborns to parent-facing strollers and 12 newborns to away-facing strollers. You then test the babies' expressive vocabularies at age 18 months using the Expressive Vocabulary Test (EVT), which is designed primarily to assess children's expressive vocabulary. The sample means and sums of squares of the scores for each of the groups are presented in the following table. Group Away-facing Parent-facing Sample Mean Sum of Squares 98.1 2,064.59 106.2 1,404.59 You decide to use an ANOVA at a = 0.01 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. Source of Variation Between Treatments Within Treatments Total Sum of Squares 393.66 3,469.18 3,862.84 F Distribution Use the Distributions tool that follows to find Fertical at a significance level of a = 0.01, the value of F that bounds the critical region for the F-ratio test statistic. Numerator Degrees of Freedom-20 Denominator Degrees of Freedom-20 ANOVA Table Degrees of Freedom Mean Square F 1 22 23 0.00 5000 5000 1.00 1.000 2.00 393.66 157.69 3.00 4.00 5.00 6.00 7.00 8.00

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 27PPS
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Fertical at a = 0.01 is Now evaluate the null hypothesis that the population means for all treatments are equal. At a significance level of a = 0.01, the null hypothesis is You find that you conclude that the direction that the stroller faces influences a child's expressive vocabulary at 18 months. Now you decide to use a t test to test the hypothesis that there is no difference between the groups. The estimated standard error (SM1 M2) is 5.13, so the t test statistic is Use the following tool to find the critical regions for a = 0.01. t Distribution Degrees of Freedom - 21 -3.0 -2.0 2500 -1.0 5000 5000 5000 0.0 -0.686 0.000 0.686 2500 1.0 2.0 3.0 Now use the tool to evaluate the null hypothesis. At a significance level of a = 0.01, the null hypothesis is conclude that the direction the stroller faces influences a child's expressive vocabulary at 18 months. 1 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 You find that you When you evaluated the mean difference from the independent-measures study comparing only two samples, the ANOVA and the t test resulted in conclusion.
Transcribed Image Text:Fertical at a = 0.01 is Now evaluate the null hypothesis that the population means for all treatments are equal. At a significance level of a = 0.01, the null hypothesis is You find that you conclude that the direction that the stroller faces influences a child's expressive vocabulary at 18 months. Now you decide to use a t test to test the hypothesis that there is no difference between the groups. The estimated standard error (SM1 M2) is 5.13, so the t test statistic is Use the following tool to find the critical regions for a = 0.01. t Distribution Degrees of Freedom - 21 -3.0 -2.0 2500 -1.0 5000 5000 5000 0.0 -0.686 0.000 0.686 2500 1.0 2.0 3.0 Now use the tool to evaluate the null hypothesis. At a significance level of a = 0.01, the null hypothesis is conclude that the direction the stroller faces influences a child's expressive vocabulary at 18 months. 1 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 You find that you When you evaluated the mean difference from the independent-measures study comparing only two samples, the ANOVA and the t test resulted in conclusion.
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 expressive vocabularies than babies who travel in away-facing strollers. You randomly assign 12 newborns to parent-facing strollers and 12 newborns to away-facing strollers. You then test the babies' expressive vocabularies at age 18 months using the Expressive Vocabulary Test (EVT), which is designed primarily to assess children's expressive vocabulary. The sample means and sums of squares of the scores for each of the groups are presented in the following table. Group Away-facing Parent-facing Sample Mean Sum of Squares 2,064.59 1,404.59 You decide to use an ANOVA at a = 0.01 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. Source of Variation Between Treatments Within Treatments Total 98.1 106.2 F Distribution Sum of Squares 393.66 3,469.18 3,862.84 Use the Distributions tool that follows to find Feritical at a significance level of a = 0.01, the value of F that bounds the critical region for the F-ratio test statistic. Numerator Degrees of Freedom-20 0 Denominator Degrees of Freedom-20 0 ANOVA Table Degrees of Freedom 1 22 23 0.00 5000 1.00 1.000 5000 2.00 Mean Square F 393.66 157.69 3.00 4.00 5.00 6.00 7.00 8.00 F
Transcribed Image Text: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 expressive vocabularies than babies who travel in away-facing strollers. You randomly assign 12 newborns to parent-facing strollers and 12 newborns to away-facing strollers. You then test the babies' expressive vocabularies at age 18 months using the Expressive Vocabulary Test (EVT), which is designed primarily to assess children's expressive vocabulary. The sample means and sums of squares of the scores for each of the groups are presented in the following table. Group Away-facing Parent-facing Sample Mean Sum of Squares 2,064.59 1,404.59 You decide to use an ANOVA at a = 0.01 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. Source of Variation Between Treatments Within Treatments Total 98.1 106.2 F Distribution Sum of Squares 393.66 3,469.18 3,862.84 Use the Distributions tool that follows to find Feritical at a significance level of a = 0.01, the value of F that bounds the critical region for the F-ratio test statistic. Numerator Degrees of Freedom-20 0 Denominator Degrees of Freedom-20 0 ANOVA Table Degrees of Freedom 1 22 23 0.00 5000 1.00 1.000 5000 2.00 Mean Square F 393.66 157.69 3.00 4.00 5.00 6.00 7.00 8.00 F
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