Question

A survey of sik accounting firms in the Captal Region, Great Lakes, Mid-Atlantic, and Northeest regions included the number of partners in the frm. This informetion is included in the data table below. Complete (a) and (b) below. Click on the icon to view the data table. Click on the icon to view a partial table of critical values of the Studentized Range, Q. Critical values of the Studentized Range, Q a. At the 0.05 level of significance, is there evidence af a difference amang the Capital, Great Lakes, Mid-Atlantic, and Northeast Determine the hypotheses. Choose the correct answer below. n accounting frms with respect to the mean number af pariners? Number of partners in six accounting fims - Crtical Vaues of the Studenttd Range, O H1: Not all μί are equal where j- 1,2.., 6) H. Not all pi are equal (where i . 1.2, 4) Upper 5% Ponts '.or-005) Nunmerator Number of Partners Capital Great Mid-Atantic Northeast 19 2698 3282 17,4 4041 43.12 4540 4736 4907 47 89 84 85 114 Find the test statistic. FSATType an integer or decimal rounded to two decimal places as needed.) Determine the critical value. 4.5 591 83 70848 885 918 946 393 504 5.76 ă29 671 705 ?35 3.50 733 364 460 5.22 5.67 603 .33 658 650 00 46 434 490 5.313 5. 612 62 4 159 16 90 120 21 25 28 23 38 (Type an inleger or decimal rounded to two decimal places as needed.) 20 95 42 4 0 24 54 50 5.74 3.15 3 4.33 4.05 491 5.12 531 5.46 5.50 3.0 3.77 4.20 5 .75 4.95 5.12 527 540 03 330 411 441 464 4 513 $25 301 367 08 .37 4 . 49 e520 PrintDone Reach a decision ▼| H-There is evidence of a difference in the mean number of partners in the accounting b. If appropriate, determine which regians dfer in maan number of partnars. Use a table of critical values of the Studentized range to find Qa for α = 0.05. u0Type an integer or a decimal rounded to two decimal places as needed.) Is there significant evidence that the Capital and the Great Lakes differ? 2.97 301 4.00 .28 450 4T 482 9 307 96 3.9 398 425 447 4.6 4.79 492 504 295 3,58 96 4 445 4.7 490 50 292 353 3..Y 43 44. 492 28 344 3.29 4.04 423 4.3954 474 O A. No because the absolute diference in the sample means is less than the critical range. B. Yes because the absolute difTerence in the sample means is less than the critical range. OC. No because the absolune derance in the sample means is greater than the critical range. O D. Yes because the absolute difference in the sample means is greater than the critical range. OE. tis not appropriale to test wtich brands differ in mean strength. 2.80 336 3.69 3.24.10 4.24 436 447 456 331 33 3,643 .17 429 9 44 Print Done Is there significant evidence that the Capital and the Great Lakes differ? A. O B. No because the absolute difference in the sample means is less than the critical range. Yes because the absolute difference in the sample means is less than the critical range. C. O D. ( E. No because the absolute difference in the sample means is greater than the critical range. Yes because the absolute difference in the sample means is greater than the critical range. It is not appropriate to test which brands difer in mean strength. ls there significant evidence that the Capital and the Mid-Atlantic differ? OA. No because the absolute difference in the sample means is greater than the critical range O B. Yes because the absolute difference in the sample moans is greater than the critical range. O C. No because the absolute difference in the sample means is less than the critical range. O D. Yes because the absolute difference in the sample means is less than the critical range. E. It is not appropriate to test which brands differ in mean strength. Is there significant evidence that the Capital and the Northeast differ? O A. No because the absolute difference in the sample means is less than the critical range. O B. Yes because the absolute difference in the sample means is less than the critical range. ○ C. No because the absolute difference in the sample moans is greater than the critical range. O D. Yes because the absolute difference in the sample means is greater than the critical range. O E. It is not appropriate to test which brands differ in mean strength. Is there significant evidence that the Great Lakes and the Mid-Atiantic differ? O A. No because the absolute difference in the sample means is less than the critical range. B. Yes because the absolute difference in the sample means is greater than the critical range. O C. No because the absolute difference in the sample means is greater than the critical range. O D. Yes bocause the absolute difference in the sample means is less than the critical range. O E. Itis not appropriate to test which brands differ in mean strength. Is there significant evidence that the Great Lakes and the Northeast differ? 0 A. No because the absolute difference in the sample means is greater than the critical range. B. Yes because the absolute difference in the sample means is less than the critical range. C. Yes because the absolute difference in the sample means is greater than the critical range D. No because the absolute difference in the sample means is less than the critical range. O E. It is not appropriate to test which brands differ in mean strength. Is there significant evidence that the Mid-Atlantic and the Northeast differ? O A. No because the absolute difference in the sample means is greater than the critical range. Yes because the absolute difference in the sample means is greater than the critical range Yes because the absolute difference in the sample means is less than the critical range No because the absolute difference in the sample means is less than the critical range It is not appropriate to test which brands differ in mean strength. O B. C. O D. E.

Answer 1

	Capital Region	Great Lakes	Mid-Atlantic	Northeast	Total
Sum	134	435	558	130	1257
Count, n	6	6	6	6	24
Mean, sum/n	22.3333	72.5	93	21.6667
Sum of square, Ʃ(xᵢ-x̅)²	457.333	4165.5	12308	97.3333

Number of treatment, k =        4
Total sample Size, N =        24
      
df(between) = k-1 =       3
df(within) = k(n-1) =       20
df(total) = N-1 =       23
      
SS(between) = (Sum1)²/n1 + (Sum2)²/n2 + (Sum3)²/n3 + (Sum4)²/n4 - (Grand Sum)²/ N = 23405.4583
SS(within) = SS1 + SS2 + SS3 + SS4 = 17028.1667
SS(total) = SS(between) + SS(within) =  40433.625
      
MS(between) = SS(between)/df(between) =       7801.8194
MS(within) = SS(within)/df(within) =       851.4083
      
F_STAT = MS(between)/MS(within) =       9.1634

a)  Null and Alternative Hypothesis: Answer B
Ho:µ1 = µ2 = µ3 = µ4
H1: Not all µ_i are equal.

Test statisric:

F_STAT = 9.16

Critical Value:

At α = 0.05, df1 = 3, df2 =   20, F_α =F.INV.RT(0.05, 3, 20) =  3.10   

Decision:

Reject H0. There is enough evidence of a difference in the mean number of partners in the accounting firm.

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b) Q statistic at α = 0.05, k = 4, N-k = 20, Q_0.05 = 3.96

Comparison	Absolute Diff. = |xi - xj|	Critical Range = Q* √(MS(Within)/n)	Result
Capital - Great lakes	50.1667	47.1725	Means are different, Answer D
Capital - Mid-Atlantic	70.6667	47.1725	Means are different, Answer B
Capital - Northeast	0.6667	47.1725	Means are not different, Answer A
Great lakes - Mid-Atlantic	20.5	47.1725	Means are not different, Answer A
Great lakes - Northeast	50.8333	47.1725	Means are different, Answer C
Mid-Atlantic - Northeast	71.3333	47.1725	Means are different, Answer B