Question

The values listed below are waiting times in minutes) of customers at two different banks. Al Bank A. customers enter a single waiting line that feeds three teler windows. Al Bank B, customers may enter any one of three different lines that have formed at three toller windows. Answer the following questions Bank A 6.4 6.6 8.7 68 7.1 7.2 Bank B 7.5 42 79 5.4 79 79 68 10.0 Click the icon to view the table of Chi-Square critical values 72 7 Construct a 95% confidence interval for the population standard deviations at Bank 5 (Round to two decimal places as needed)

Answer 1

Standard Deviation, s: 0.5754225500544 Count, N: 10 Sum, Ex: 72 Mean, x: 7.2 Variance, s2:0.33111111111111 Steps N 1 S = Σ(αι – T)?, N-1 i=1 S2 = Elxi - x)2 N-1 - (6.4 - 7.2)2 + ... + (7.9 - 7.2)2 10-1 2.98 9 = 0.33111111111111 S = V0.33111111111111 = 0.5754225500544 =

Confidence Interval Formula for o is as follows: Square Root((n - 1)s/x?a/2) < 0<Square Root((n - 1)s2/x?1-a/2) where: (n-1) = Degrees of Freedom, s2 = sample variance and a = 1 - Confidence Percentage First find degrees of freedom: Degrees of Freedom = n - 1 Degrees of Freedom = 10 - 1 Degrees of Freedom = 9 Calculate a: a = 1 - confidence% a = 1-0.95 a = 0.05 Find low end confidence interval value: dlow end = a/2 dlow end = 0.05/2 dlow end = 0.025 Find low end x2 value for 0.025 x20.025 = 19.0228 <--- Value can be found on Excel using =CHIINV(0.025,9) Calculate low end confidence interval total: Low End = Square Root((n - 1)s2/x?a/2) Low End = (9)(0.3311)/19.0228) Low End = 12.9799/19.0228 Low End = V0.1566488634691 Low End = 0.3958 Find high end confidence interval value: Ahigh end = 1 -a/2 dhigh end 1 -0.05/2 Ahigh end = 0.975 Find high end x2 value for 0.975 x20.975 = 2.7004 <--- Value can be found on Excel using =CHIINV(0.975,9) Calculate high end confidence interval total: High End = Square Root((n - 1)s/x21 -a/2) High End = V(9)(0.3311)/2.7004) High End = 72.9799/2.7004 High End = V1.1035031847134 High End = 1.0505 Now we have everything, display our interval answer: 0.3958 < 0 < 1.0505 <---- This is our 95% confidence interval

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