Page 457 - Six Sigma Demystified

a n S w e r S To q u i z z e S a n D f i n a l e x a m 437

48. c.
49. a.
50. d.
51. a. Subgroups larger than one would include samples taken over too long a
period, increasing the chance of including special causes within the subgroup.
52. d.
53. b. Although increasing the subgroup size will increase the sensitivity of the chart
to small process shifts, it comes at the cost of increased sampling and
measurement.
54. d.
55. b.
56. d.
57. b.
58. d.
59. a.
60. a.
61. a.
62. b. In Excel, the 95% two-sided upper and lower confidence limits are
calculated as
upper: =121+TiNV(0.05,20-1)*15/SQRT(20)

Lower: =121-TiNV(0.05,20-1)*15/SQRT(20)

63. c. In Excel, the 95% one-sided upper confidence limit is calculated as
upper: =121+TiNV(0.05*2,20-1)*15/SQRT(20)

64. d. In Excel, the p value for the two-sided hypothesis that the mean equals 115 is
0.09, calculated as P=TDIST(ABS((121–115)/(15/SQRT(20))),20-1,2). When
the p value exceeds 0.05, we fail to reject the null hypothesis. Choice c is
incorrect because we cannot assert the alternative (because this is the weak

conclusion of failing to reject); we can only suggest that there are insufficient
data to reject the null hypothesis.
65. a. In Excel, the p value for the one-sided hypothesis that the mean is less than or
equal to 115 (case 2 in Part 3) is 0.045, calculated (for t > 0) as
P=TDIST(ABS((121-115)/(15/SQRT(20))),20-1,2). When the p value is less
than 0.05, we reject the null hypothesis and can assert the alternative hypothesis
(i.e., the strong conclusion).
66. d. In Excel, the p value for the two-sided hypothesis that the standard deviation
equals 21 is 0.08, calculated (for CHIDIST > 0.5) as P=2*(1-
CHIDIST((20-1)*(15^2)/(21^2),20-1)). When the p value exceeds 0.05, we fail
to reject the null hypothesis. Choice c is incorrect because we cannot assert the
alternative (because this is the weak conclusion of failing to reject); we can only
suggest that there are insufficient data to reject the null hypothesis.
67. a. In Excel, the p value for the one-sided hypothesis that the standard deviation
is greater than or equal to 21 (case 1 in Part 3) is 0.040, calculated as P=(1-