Question

4. The manager of Young Corporation, wants to determine whether or not the type of work schedule for her employees has any effect on their productivity. She has selected 15 production employees at random and then randomly assigned 5 employees to each of the 3 proposed work schedules. The data sheet table shows the units of production (per week) under each of the work schedules. State the null and alternative hypotheses. 1. At a 5% level of significance determine if there is a significant difference in the mean weekly units of production for the three types of work schedules.

Answer 1

Hypothesis to be tested is, Ho : There is significant difference in the mean of production for the three types of work schedules. no (ولا = ولا = ) s୧୧ Hi There is difference in the mean of production for the three types of work sh schedules. (Means are not equal) Here, ni =n2 = n3 = 5 That is Sample size is same for each type. N-nitna n3 = 15 K = number of groups = 3 degrees of freedom for numerator =K-1 = 3-1 = 2 degrees of freedom for denominator = N-K = 15-3= 12 Here, d= 0.05 .. We will table value as F2,12 in statistics table F2, 12 3.89 e critical value Test statistic is given by, F= MSTR MSE Now, we will find mean for each type of work schedule Let, , and my be mean for work schedule 1, 2 and 3 respectively ã, = 50+60+10+ 40 +45 265 255 = 53 5 22 = 60+ 65 +66+54 +57 5 302 5 60.4 13 70 +75 +55 + 40 +55 5 = 295 59 5

2 Now, grand mean no na 50 + 60 + 70 +40 +45 +60 +65 +66 + 54 +577 70 + 75+ 55 + 40 +55 15 ZG where, r;= grand mean 862 = 57.47 15 Between group variance is treatment sum of squares. ie. SSTR I 8; (Xj - TE² no. of rows in ith in jth treatment mean of jth treatment XG SSTR [5x5 - 57.47)2] + [5X(60.4 - 57.47)2]+ [5*(59-59.407] 99.9045 SSTR 245343. 5045 + 42.9245 + 11.7045 SSTR 246556.619 154.5335 Within group variance is proor sum of squares. SSE = II (Xi} - ;) :: 55€ = [ 50-53) +(60--63)2 +670-53)2 +(40-53)* +(45-53)] +60-60,42 + (65 - 60.4) +( 66-60.49€ + (54-60.49%+ (57-60.4933 +T60 - 59)2 +(75-59)2 + (55-59)2+(40-59)*+(55-59)) i.e :. SSE = 1455.2

Now, 3 MSTR = SSTR 77.267 154.53 35 3-1 MSE SSE N-K 1455.2 15-3 = 121.2667 :. F = MSTR ms = 0.667 0.6371 = 77, 267 121. 2667 F calculated 0.6371 Here, Fcalculated = 0.6371 < ftabulated = 3.89 Hence, we may accept Ho at 5% 1.0.S. That is, That is, there is no significant significant difference in the mean weekly units of production for the three types of work schedules.