Question

8. Two independent random samples drawn from normal distributions have equal variances and means pli and M2. You are given • The sample mean from the first sample is 16.9. • The sample mean from the second sample is 22.1. • The number of observations from both samples combined is 17. • The upper bound of the 90% confidence interval for H1 - H2 is 1.44. Let tay be the critical value of a t random variable with v degrees of freedom. The following table lists values of tay for specific combinations of a and v: v = 15 v= 16 v = 17 a=0.1 1.341 1.337 1.333 a = 0.05 1.753 1.746 1.740 a= 0.025 2.131 2.120 2.11 Determine the lower bound of the 95% confidence interval for u1 - 42.

Answer 1

Sol n = = 17 zu = 16.9 ; Ę = 22.11 - (1-2) lowl. Confidence Internal for lli - M₂ is - Bu -5,) + tarlayabi tutti • confidence Inter val of Given, upper bound of 90% of Merla is 1.44 - - = (st -Tz) + ta 12, Meth-2 Spf + t = 1.44 =>(16.9-224) +1.694.spot - 1.44

» SP = (-Чч +5.2 ) 1.04 Ч sp= 1). Ч28 of 95% confidence Interval lower bound Сол ц" и, 3 -5% ) - Rap, m, no. - - (16, 9 -22-/) - 2.03 64 x |]. Ч28 +1 2 13. 1842