Question

Assuming that both populations are normally? distributed, construct a 90?% confidence interval about mu 1 - mu 2. ?(mu 1 represents the mean of the experimental group and mu 2 represents the mean of the control? group.)

Experimental n = 23 x = 48.4 s =4.7

Control n = 17 x = 46.6 s = 14.1

Answer 1

Step 1: Find ?/2
Level of Confidence = 90%
? = 100% - (Level of Confidence) = 10%
?/2 = 5% = 0.05


Step 2: Find degrees of freedom and t_?/2
Degrees of freedom = smaller of (n₁ - 1 , n₂ - 1 ) = smaller of (22 , 16) = 16

Calculate t_?/2 by using t-distribution with degrees of freedom (DF) = 16 and ?/2 = 0.05 as right-tailed area and left-tailed area.

Step 3: Calculate Confidence Interval

t_?/2 = 1.74586

Standard Error = ? (s?)²/n? + (s?)²/n? = ?1.9492583120204605 = 1.3961584122227895

Lower Bound = (x?? - x??) - t_?/2•(? (s?)²/n? + (s?)²/n? ) = (48.4 - 46.6) - (1.7458)(1.3961) = -0.6374

Upper Bound = (x?? + x??) + t_?/2•(? (s?)²/n? + (s?)²/n? ) = (48.4 - 46.6) + (1.7458)(1.39615) = 4.2374

Confidence Interval = (-0.6374, 4.2374)