Question

Independent random samples were selected from two quantitative populations, with sample sizes, means, and standard deviations given below. n = n2 = 90, x1 = 125.3, %2 = 123.8, s, = 5.7, s, = 6.9 Construct a 95% confidence interval for the difference in the population means ( M M ) (Round your answers to two decimal places.) Find a point estimate for the difference in the population means, Calculate the margin of error. (Round your answer to two decimal places.) Compare your results. Can you conclude that there is a difference in the two population means (4, - H2)? The confidence interval and the point estimate together with the margin of error suggest C. Since the value u -ul, = 0 is --Select-- the interval, the confidence interval suggests it isu-Select- The range of values given by the point estimate the margin of error --Select.. 0. This suggests that the two population means are ---Select- You may need to use the appropriate appendix table or tecnology to answer this question.

Answer 1

ANSWER:

Solution : - Given Dola Sample mean (X.) =125.3 Sample slorded Devotion (s) + 5-7 Sample size cno).90 E Sample mean (F2) = 123.8 Sample standard divroton (52) = 629 - sample size (N2) = 90 Based on the infomation provided : we assume that population valiency are Equal, so, then the number of degrees of freedom are if en, the-2 -90+90 - 2 2180-2 Af = 178 The critical value for 2: 0.05 and dB = 178 degrees of freedom is test,-d/an-l a4,-0.98/20 2cdon

Segniteace. 0.025 Degree of freedom : 178 calculate on critical values 1ts-o/2n-14) = 1,973) Since the population variance are assume de to be squel, we need to compule the Standard deviation, as follows. Sps ((ni-1),"+(12-1) 522 v nit m2 -2. = 120-1) (5:7)+(90-1) (6.972 V 9.0+90--2 . : 789)(5.7777189366.913 y 90 +90:- 2 (89)82.49)+ (89)47.60] 178 s 2,891061+4,237.29 W 178 7,128.9. ✓ 178

3140.05 Sp261327 .. we assume that the population Variance are equal, the standard Euro is computed as follows. se sr%. - 6.32 x P 5 26-32% 10.022 -Ġ-32.X0:148 Be = 0.937) Now, we finally compute the confidence interval CI -(«, -7e-tex Sex, -8 + texse) : (195.3 - 123-8 -1.973X0:937, 125.3 -123.8 +)1973 x0.937 ) :(-0.443, 3-254)

. Based on the data provided the 95.1 confidence interval for the difference bli the population means M, -d2 (-0.443<u, uh <3-254) which indicates that we are 95.1 Confident that the true difference between population means is conferred by internal (-0.443, 3.254) ..Point Estimale for difference in population mlar x; -82= 125.3. - 12318 = 1.5 - - Y2 -1.5 margin of Erro. Este se -1.973 * 0.937 . !.848 : Es 11848)