Question

A poultry producer is interested in which feed type will yield the poultry weight. He has two types of feed; the first made from soybeans and the second made from sunflower seeds. He has 71 chickens and randomly selects 26 of these chickens to use in his experiment. 14 of these chickens are randomly assigned to receive only the soybean product and the remaining 12 are to receive only the sunflower product. Is there a difference in these weights at a ten percent error rate? Estimate the mean difference in the weights of these chickens using 90% confidence. The data are below.

Soybean Feed 199.86 237.32 335.21 203.80 166.66 340.68 234.31 254.03 296.78 289.57 246.15 247.51 125.27 296.90

Sunflower Feed 279.04 247.33 362.32 262.55 305.91 295.22 335.41 292.62 336.80 307.60 307.67 317.60

Soybean Feed

n1 = 10
x̄1 = 0.022

s1 = 0.159

Sunflower Feed

n2 = 13
x̄2 = 0.008

s2 = 0.008

Answer 1

	Soybean Feed ( X )		Sunflower Feed ( Y )
	199.86	2331.5764	279.04	631.6426
	237.32	117.2109	247.33	3231.0698
	335.21	7580.0704	362.32	3381.1318
	203.8	1966.6032	262.55	1732.4325
	166.66	6640.0334	305.91	3.0189
	340.68	8562.4671	295.22	80.1473
	234.31	191.446	335.41	975.7814
	254.03	34.6167	292.62	133.4603
	296.78	2365.227	336.8	1064.5538
	289.57	1715.9146	307.6	11.7478
	246.15	3.9856	307.67	12.2325
	247.51	0.405	317.6	180.2978
	125.3	15098.6097
	296.9	2376.9135
Total	3474.05	48985.0795	3650.07	11437.5165

Mean

Standard deviation

Mean

Standard deviation

To Test :-

H0 :-

H1 :-  

Test Statistic :-
t = (\bar{X_{1}} - \bar{X_{2}}) / \sqrt{ ( S_{1}^{2} / n1) + (S_{2}^{2} / n2)}
t = ( 248.1464 - 304.1725 ) / \sqrt{ ( 61.3847^{2} / 14) + ( 32.2455^{2} / 12)}
t = -2.9702

Test Criteria :-
Reject null hypothesis if

DF = 20

Result :- Reject Null Hypothesis

Decision based on P value
P - value = P ( t > 2.9702 ) = 0.0076
Reject null hypothesis if P value <    level of significance
P - value = 0.0076 < 0.1 ,hence we reject null hypothesis
Conclusion :- Reject null hypothesis

There is sufficient evidence to support the claim that there is difference in average  poultry weight at 10% level of significance.

Confidence interval :-



Lower Limit =
Lower Limit = -88.5587
Upper Limit =
Upper Limit = -23.4935
90% Confidence interval is ( -88.5587 , -23.4935 )