Question

This problem is going to use the data set in R called "ChickWeight" that has 4 variables, as described below.

ChickWeight:
A data frame with 578 observations on 4 variables.
1) weight: a numeric vector giving the body weight of the chick (gm).
2) Time: a numeric vector giving the number of days since birth when the measurement was made.
3) Chick: an ordered factor with levels 18 < ... < 48 giving a unique identifier for the chick. The ordering of the levels groups chicks on the same diet together and orders them according to their final weight (lightest to heaviest) within diet.
4) Diet: a factor with levels 1, ..., 4 indicating which experimental diet the chick received.

Using a significance level of 0.05, is there evidence to support that the weight can be determined by the Time (treatment) and Diet (block)?

Fill in the R code below.

dat.aov=aov( ~ factor( ) +  ,data= )
summary( )

Fill in the ANOVA table below.
Type the values into the table EXACTLY as they appear in your output in R.

	df	SS	MS	F	Pr(>F)
factor(Time)					2e-16
Diet					2e-16
Residuals

Is there evidence to support that the treatment variable Time is significant?
1. ?0:?1=?2=...=?12H0:μ1=μ2=...=μ12 vs ??:????Ha:ALOI
2. ?=0.01α=0.01
3. F =  
4. ??Fα =  
5. Conclusion:
Reject H0
Fail to reject H0
Interpretation:
There is sufficient evidence to support that the variable Time is significant.
There is not sufficient evidence to support that the variable Time is significant.

Is there evidence to support that the block variable Diet is significant?
1. ?0:H0: No block effect vs ??:Ha: There is a block effect
2. ?=0.01α=0.01
3. F =  
4. ??Fα =  
5. Conclusion:
Reject H0
Fail to reject H0
Interpretation:
There is sufficient evidence to support that the variable Diet is significant.
There is not sufficient evidence to support that the variable Diet is significant.

Answer 1

This problem is going to use the data set in R called "ChickWeight" that has 4 variables, as described below.

ChickWeight:
A data frame with 578 observations on 4 variables.
1) weight: a numeric vector giving the body weight of the chick (gm).
2) Time: a numeric vector giving the number of days since birth when the measurement was made.
3) Chick: an ordered factor with levels 18 < ... < 48 giving a unique identifier for the chick. The ordering of the levels groups chicks on the same diet together and orders them according to their final weight (lightest to heaviest) within diet.
4) Diet: a factor with levels 1, ..., 4 indicating which experimental diet the chick received.

Using a significance level of 0.05, is there evidence to support that the weight can be determined by the Time (treatment) and Diet (block)?

Fill in the R code below.

dat.aov = aov(weight~factor(Diet)+factor(Time),data=ChickWeight)

summary( dat.aov)

Fill in the ANOVA table below.
Type the values into the table EXACTLY as they appear in your output in R.

	df	SS	MS	F	Pr(>F)
factor(Time)					2e-16
Diet					2e-16
Residuals

summary(dat.aov)

                   Df Sum Sq    Mean Sq F value Pr(>F)   

factor(Diet)   3 155863     51954     40.75     <2e-16 ***

factor(Time) 11 2040908 185537 145.53    <2e-16 ***

Residuals      563 717785    1275                  

---

Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Is there evidence to support that the treatment variable Time is significant?
1. H0:μ1=μ2=...=μ12 vs ??:????
2. ?=0.01
3. F =  145.53
4. ?? =  2.279
5. Conclusion:
Reject H0
Interpretation:
There is sufficient evidence to support that the variable Time is significant.

Is there evidence to support that the block variable Diet is significant?
1. H0: No block effect vs Ha: There is a block effect
2. ?=0.01
3. F =  40.75
4. ?? =  3.817
5. Conclusion:
Reject H0
Interpretation:
There is sufficient evidence to support that the variable Diet is significant.