Solution: 2 3 J 3.05 3.10 5 Deer At time of Injection 2.76 5.18 2.68 4:10 30 Minutes after Injection 7.02 5:44 3.99 5621 Determine a 95% confidence interval for the mean level of androgens at time of captuve. Ans: confidence level = 959%. = 0.95 = 1 -0.95 a = 0.05 significance level 95% confidence Interval for mean level of androgens at time of capture is given by: 0 + toros s un
where 2 χ= Σχ n [{(x-769² (n-0) and s= رس ملح x={x D 2.76 + 5:18 + 2-68 +3.05 + 4.10 5 3.554 17.77 5 20 = 3.554 =(x-3)? = (2.76–3,554) +(5.18-3,554) + (2.68- 3.554)?+(3.05–3.554)+7(4.10– 3.554)? Elx-)? - 0.6304 + 2.6439 +0.7639+0.2540 +0.2981 E(2-)= 4.5903 Se 4.5903 4.5903 5-1 -F-147575 4 = 1.07125
Critical value of t at 0.05 level of stgnificance for (5-1)= 4 degree of freedom toros (4) 2.776 I from 2 tailed tables] we get same value if we divide 0.05 = 0.025 to.25(4)= 2.776 [ from 1 tai led table] 95% confidence Interval is : 3.554 + 2.776 x 1.07125 5 3. 554 I 2.776 X 0:4791 3.554 + 1:32 (3.554 - 1.33, 3.554 + 1.33) (1 = (2.224, 4.884)
Dale (b) Test at 1% level of significance whether the androgen concentrations are altered after 30 minutes Deerl At time of Injection 30 minutes after (X) Injection (Y) d=x-Y d? 2.76 7.02 -4.26 18.1476 2 5.18 3.10 2.08 4.3264 3 2.68 5.44 -2.76 716176 y 3.05 3.99 -0.94 5 4.10 -1011 1.2321 Ed=-6.99 22232.20 73 We get Ed= -6:99 and Ed2 320 2073 0.8836 5.21 Ed b -6.99 5 -1.398 T = -1.398 Ho: Ma=0 Hi : Md ²0 Androgen concentrations are altered after 30 minutes This is two tailed test. Under Ho, the test Statistic ta d slun with degree of freedom = n-1 where. Sa I Fed2 (5d27 2 n-1 n
S- 1 5-1 32.2073 - (-6099227 5. 5 [32-2073 – 48.86017 Vu [32-2013 – 9:27 202] 1 x 22. 43528 5. 60 882 = 2.3683 S= 2.3683 Now t= te d -10398 -1.396 slun 2.3683/5 1.0591 t = -1.32 Significance level = 0.01 degree of freedom = 5-1 = 4 Now, critical value of t at oool level of Significance for 4 degree of freedom for two tailed test tovar (4) = 4,604 [ from 2 tailed tables Our test is two tailed, so critical value is -4.604 ana +4.604
Date Test Criteria : Reject Ho if calculated t calculated t < -4.604 Reject Ho if calculated t >+4.604 In Our Resulte : Calulated t > -4.604 -1.32 > -4.604 -4.604 So, we fail to reject Ho at 1% level of significance and conclude that Androgen concentrations are not altered after 30 minutes.