Question

2. In an effort to maximize egg size, Farmer Brown decided to test the effect of various feeds on
longitudinal egg length (in mm). He had three main breeds of chickens on his farm that were egg-layers:
Rhode Island Red, Brahma, and Golden Comet. Farmer Brown selected 3 different brands of feeds at
random from the 5 brands that he had available. The labels had fallen off the bags of feed, but he knew
that they were different. This was just a preliminary experiment to see if there were any differences
between breeds and feeds (or possibly interactions). Do the appropriate 2-way ANOVA to test this.
The data on 3 eggs per chicken breed-feed combination are given below.
		Egg Length (mm)
Chicken Breeds	Feed A	Feed B	Feed C
Rhode Island Red	53.66	57.46	56.59
	53.15	56.90	57.86
	55.66	55.94	54.75
Brahma	54.25	50.54	52.13
	52.05	55.66	52.35
	50.62	54.07	56.37
Golden Comet	60.64	58.58	56.14
	57.79	55.79	58.78
	57.30	61.47	55.52

Put your answers in column B using the standard format : hypotheses and conclusions relative to the hypotheses.

Hypotheses:

Ho

Ha

Ho

Ha

Ho

Ha

Conclusion relative to the hypothesis:

Answer 1

Hypothesis:

H₀: µ₁ = µ₂ = µ₃

H₁: At least one means is not equal

The SPSS output is:

Between-Subjects Factors Island 1 Category 1 N Descriptive Statistics Dependent Variable: Feed Island Category Mean Std. Deviation 54.16 1.327 2 56.77 .769 3 56.40 1.564 Total 55.77 1.642 1 52.31 1.829 2 53.42 2.621 53.62 2.387 Total 53.12 2.086 58.58 1.804 58.61 2.840 56.81 1.731 Total 58.00 2.091 Total 1 55.01 3.142 2 56.27 3.012 55.61 2.248 Total 55.63 2.767 2 3

Levene's Test of Equality of Error Variancesa, Sig. 621 971 .967 Levene Statistic df1 d f2 Feed Based on Mean 787 8 1 8 Based on Median 2628 18 Based on Median and .262 8 12.423 with adjusted df Based on trimmed mean .738 8 18 Tests the null hypothesis that the error variance of the dependent variable is equal across groups. a. Dependent variable: Feed b. Design: Intercept + Island + Category + Island * Category 658 Sig. .006 Partial Eta Squared .648 Tests of Between-Subjects Effects Dependent Variable: Feed Type III Sum Source of Squares df Mean Square F. Corrected Model 129.019a 16.127 4.145 Intercept 83557.929 83557.929 21 473.400 Island 107.689 53.845 13.837 Category 7.087 3.543 .911 Island * Category 14.243 3.561 .915 Error 70.042 18 3.891 Total 83756.990 Corrected Total 199.061 a. R Squared = .648 (Adjusted R Squared = .492) .000 .000 .420 .476 .999 .606 .092 .169 27

Estimated Marginal Means 1. Category * Island Dependent Variable: Feed 95% Confidence interval Category Island Mean Std. Error Lower Bound Upper Bound 1 1 54.157 1.139 51.764 56.549 52.307 1.139 49.914 54.699 58.577 1.139 56.184 60.969 56.767 1.139 54.374 59.159 53.423 1.139 51.031 55.816 58.613 1.139 56.221 61.006 56.400 1.139 54.007 58.793 53.617 1.139 51.224 56.009 56.813 1.139 54.421 59.206 2. Island Estimates Dependent Variable: Feed 95% Confidence Interval Island Mean Std. ErrorLower Bound Upper Bound 1 55.774 .658 54.393 57.156 53.116 .658 51.734 54.497 58.001 .658 56.620 59.383

Sig.b Pairwise Comparisons Dependent Variable: Feed 95% Confidence Interval for Mean Difference Difference (1- (1) Island (J) Island Std. Error Lower Bound Upper Bound 2.659 .930 .010 .705 4.613 -2.227" 930 .028 -4.180 - 273 -2.659 .010 -4.613 -705 -4.886 .930 .000 -6.839 -2.932 2.227 .028 .273 4.180 4.886 930 .000 2.932 6.839 Based on estimated marginal means *. The mean difference is significant at the .05 level. b. Adjustment for multiple comparisons: Least Significant Difference (equivalent to no adjustments). 930 930 w 2930 Univariate Tests Sig. Dependent Variable: Feed Sum of Partial Eta Squares df Mean Square F Squared Contrast 107.689 2 53.845 13.837 .000 .606 Error 70.042 183 .891 The F tests the effect of Island. This test is based on the linearly independent pairwise comparisons among the estimated marginal means. 3. Category Estimates Dependent Variable: Feed 95% Confidence interval Category Mean Std. Error Lower Bound Upper Bound 55.013 658 53.632 56.395 2 56.268 .658 54.886 57.649 3 55.610 .658 54.229 5 6.991

Pairwise Comparisons Dependent Variable: Feed 95% Confidence Interval for Mean Difference Difference (I- (1) Category (J) Category Std. Error Sig. Lower Bound Upper Bound -1.254 .930 .194 -3.208 .699 -597 .930 .529 -2.550 1.357 1.254 .930 .194 - 699 3.208 .658 .930 .488 -1.296 2.611 .597 .930 .529 -1.357 2.550 -.658 .930 .488 -2.611 1.296 Based on estimated marginal means a. Adjustment for multiple comparisons: Least Significant Difference (equivalent to no adjustments). Univariate Tests Dependent Variable: Feed Sum of Partial Eta Squares df Mean Square F Sig. Squared Contrast 7.087 2 3 .543 911 .420 .092 Error 70.042 18 3.891 The F tests the effect of Category. This test is based on the linearly independent pairwise comparisons among the estimated marginal means.

The p-value for interaction is 0.476.

Since the p-value (0.476) is greater than the significance level, we cannot reject the null hypothesis.

Therefore, we cannot conclude that there were any differences between breeds and feeds.

Please give me a thumbs-up if this helps you out. Thank you!