Question

Two samples each of size 20 are taken from independent populations assumed to be normally distributed with equal variances. The first sample has a mean of 43.5 and a standard deviation of 4.1 while the second sample has a mean of 40.1 and a standard deviation of 3.2. A researcher would like to test if there is a difference between the population means at the 0.05 significance level. What can the researcher conclude? There is not sufficient evidence to reject the null hypothesis: the population means and standard deviations are equal. The two population means are equal but the standard deviations are different There is sufficient evidence to reject the null hypothesis and conclude that the two population means are different

Answer 1

Given Sample 1 ni = 20 X1 = 43. 5 Si = 4.1 Sample 2 n2 = 20 X2 = 40.1 $2 = 3.2 Sample size Sample mean Standard deviation Test hypothesis are Null hypothesis Alternate hypothesis H. : i - u2 H: U1 - u2 = 0 Pooled Standard deviation Pooled variance S2 = (N121)$1+(12+)2 ni+n2-2 = ((20-1)*4.1^2)+((20-1)*3.242)/(20+20-2) = 13.52500 Pooled standard deviation Sp 3.67764 Test statistic Test statistic t= ({1-22)-(M1 – 42) = (43.5-40.1)-0)/(3.6776*(1/20+1/20) 2.923548 2.924 P-value P(|t>2.924) 0.0058 Two tailed Since p-value < 0.05 hence reject the null hypothesis There is suficient evidence to conclude that there is a diffrence between the population means