Parents are frequently concerned when their child seems slow to begin walking (although when the child finally walks, the resulting havoc sometimes has the parents wishing they could turn back the clock!). An article on this topic reported on an experiment in which the effects of several different treatments on the age at which a child first walks were compared. Children in the first group were given special walking exercises for 12 minutes per day beginning at age 1 week and lasting 7 weeks. The second group of children received daily exercises but not the walking exercises administered to the first group. The third and fourth groups were control groups. They received no special treatment and differed only in that the third group's progress was checked weekly, whereas the fourth group's progress was checked just once at the end of the study. Observations on age (in months) when the children first walked are shown in the accompanying table. Age n Total Treatment 1 9.00 9.50 9.75 6 61.50 10.00 13.75 9.50 Treatment 2 11.00 10.00 10.00 6 69.00 12.50 10.50 15.00 Treatment 3 11.50 12.50 9.00 6 70.75 11.50 13.25 13.00 Treatment 4 13.25 11.50 12.00 5 61.75 13.50 11.50 (a) Find the missing entries in the ANOVA table. (Use technology. Round your answers to three decimal places.) Source of variation Degrees of freedom Sum of squares Mean squares F Ratio F Prob Between Groups Within Group Total 22 (b) State and test the relevant hypotheses using a significance level of 0.05. State the appropriate null and alternative hypotheses. (Let ?1, ?2, ?3, and ?4 be the true means for the four different treatments.) H0 : all four of the ?i's are different Ha : ?1 = ?2 = ?3 = ?4H0 : ?1 = ?2 = ?3 = ?4 Ha : at least three of the four ?i's are different H0 : ?1 = ?2 = ?3 = ?4 Ha : at least two of the four ?i's are differentH0 : ?1 = ?2 = ?3 = ?4 Ha : all four of the ?i's are differentH0 : at least two of the four ?i's are different Ha : ?1 = ?2 = ?3 = ?4 State the test statistic and P-value. (Use technology. Round your answers to three decimal places.) F=P-value=

Parents are frequently concerned when their child seems slow to begin walking (although when the child finally walks, the resulting havoc sometimes has the parents wishing they could turn back the clock!). An article on this topic reported on an experiment in which the effects of several different treatments on the age at which a child first walks were compared. Children in the first group were given special walking exercises for 12 minutes per day beginning at age 1 week and lasting 7 weeks. The second group of children received daily exercises but not the walking exercises administered to the first group. The third and fourth groups were control groups. They received no special treatment and differed only in that the third group's progress was checked weekly, whereas the fourth group's progress was checked just once at the end of the study. Observations on age (in months) when the children first walked are shown in the accompanying table. Age n Total Treatment 1 9.00 9.50 9.75 6 61.50 10.00 13.75 9.50 Treatment 2 11.00 10.00 10.00 6 69.00 12.50 10.50 15.00 Treatment 3 11.50 12.50 9.00 6 70.75 11.50 13.25 13.00 Treatment 4 13.25 11.50 12.00 5 61.75 13.50 11.50 (a) Find the missing entries in the ANOVA table. (Use technology. Round your answers to three decimal places.) Source of variation Degrees of freedom Sum of squares Mean squares F Ratio F Prob Between Groups Within Group Total 22 (b) State and test the relevant hypotheses using a significance level of 0.05. State the appropriate null and alternative hypotheses. (Let ?1, ?2, ?3, and ?4 be the true means for the four different treatments.) H0 : all four of the ?i's are different Ha : ?1 = ?2 = ?3 = ?4H0 : ?1 = ?2 = ?3 = ?4 Ha : at least three of the four ?i's are different H0 : ?1 = ?2 = ?3 = ?4 Ha : at least two of the four ?i's are differentH0 : ?1 = ?2 = ?3 = ?4 Ha : all four of the ?i's are differentH0 : at least two of the four ?i's are different Ha : ?1 = ?2 = ?3 = ?4 State the test statistic and P-value. (Use technology. Round your answers to three decimal places.) F=P-value=

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 31EQ

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	Age			n	Total
Treatment 1	9.00	9.50	9.75	6	61.50
10.00	13.75	9.50
Treatment 2	11.00	10.00	10.00	6	69.00
12.50	10.50	15.00
Treatment 3	11.50	12.50	9.00	6	70.75
11.50	13.25	13.00
Treatment 4	13.25	11.50	12.00	5	61.75
13.50	11.50

(a)

Find the missing entries in the ANOVA table. (Use technology. Round your answers to three decimal places.)

Source of variation	Degrees of freedom	Sum of squares	Mean squares	F Ratio	F Prob
Between Groups
Within Group
Total	22

(b)

State and test the relevant hypotheses using a significance level of 0.05.

State the appropriate null and alternative hypotheses. (Let ?₁, ?₂, ?₃, and ?₄ be the true means for the four different treatments.)

H₀ : all four of the ?_i's are different
H_a : ?₁ = ?₂ = ?₃ = ?₄H₀ : ?₁ = ?₂ = ?₃ = ?₄
H_a : at least three of the four ?_i's are different H₀ : ?₁ = ?₂ = ?₃ = ?₄
H_a : at least two of the four ?_i's are differentH₀ : ?₁ = ?₂ = ?₃ = ?₄
H_a : all four of the ?_i's are differentH₀ : at least two of the four ?_i's are different
H_a : ?₁ = ?₂ = ?₃ = ?₄

State the test statistic and P-value. (Use technology. Round your answers to three decimal places.)

F=P-value=

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