10c6_3247
| Face | Observed | Expected |
|---|---|---|
| 1 | 32 | 29 |
| 2 | 36 | 29 |
| 3 | 22 | 29 |
| 4 | 21 | 29 |
| 5 | 24 | 29 |
| 6 | 39 | 29 |
You roll a six-sided die 174 times. The null hypothesis (H0) is that each face has probability 1⁄6 on every roll.
Which calculation gives the contribution of face 1 to the chi-square statistic (χ2)?
(32 − 29)2⁄292 = 9⁄841 ≈ 0.01 Incorrect (32 − 29)2⁄29 = 9⁄29 ≈ 0.31 Correct (24 − 29)2⁄29 = 25⁄29 ≈ 0.86 Incorrect (21 − 29)2⁄29 = 64⁄29 ≈ 2.21 Incorrect (39 − 29)2⁄29 = 100⁄29 ≈ 3.45 Incorrect MCdb84_c096
| Face | Observed | Expected |
|---|---|---|
| 1 | 8 | 10 |
| 2 | 10 | 10 |
| 3 | 12 | 10 |
| 4 | 6 | 10 |
| 5 | 9 | 10 |
| 6 | 15 | 10 |
You roll a six-sided die 60 times. The null hypothesis (H0) is that each face has probability 1⁄6 on every roll.
Which calculation gives the contribution of face 6 to the chi-square statistic (χ2)?
(10 − 10)2⁄10 = 0⁄10 = 0.00 Incorrect (9 − 10)2⁄10 = 1⁄10 = 0.10 Incorrect (15 − 10)2⁄102 = 25⁄100 = 0.25 Incorrect (15 − 10)2⁄15 = 25⁄15 ≈ 1.67 Incorrect (15 − 10)2⁄10 = 25⁄10 = 2.50 Correct MC88b0_d788
| Face | Observed | Expected |
|---|---|---|
| 1 | 25 | 15 |
| 2 | 12 | 15 |
| 3 | 12 | 15 |
| 4 | 14 | 15 |
| 5 | 14 | 15 |
| 6 | 13 | 15 |
You roll a six-sided die 90 times. The null hypothesis (H0) is that each face has probability 1⁄6 on every roll.
Which calculation gives the contribution of face 2 to the chi-square statistic (χ2)?
122 − 152⁄15 = -81⁄15 = -5.40 Incorrect (12 − 15)⁄15 = -3⁄15 = -0.20 Incorrect (12 − 15)2⁄90 = 9⁄90 = 0.10 Incorrect (12 − 15)2⁄15 = 9⁄15 = 0.60 Correct (25 − 15)2⁄15 = 100⁄15 ≈ 6.67 Incorrect MC4d68_8f0c
| Face | Observed | Expected |
|---|---|---|
| 1 | 7 | 13 |
| 2 | 10 | 13 |
| 3 | 32 | 13 |
| 4 | 9 | 13 |
| 5 | 10 | 13 |
| 6 | 10 | 13 |
You roll a six-sided die 78 times. The null hypothesis (H0) is that each face has probability 1⁄6 on every roll.
Which calculation gives the contribution of face 6 to the chi-square statistic (χ2)?
(10 − 13)⁄13 = -3⁄13 ≈ -0.23 Incorrect (10 − 13)2⁄132 = 9⁄169 ≈ 0.05 Incorrect (10 − 13)2⁄78 = 9⁄78 ≈ 0.12 Incorrect (10 − 13)2⁄13 = 9⁄13 ≈ 0.69 Correct (9 − 13)2⁄13 = 16⁄13 ≈ 1.23 Incorrect MCfe3a_a9b4
| Face | Observed | Expected |
|---|---|---|
| 1 | 16 | 21 |
| 2 | 18 | 21 |
| 3 | 19 | 21 |
| 4 | 12 | 21 |
| 5 | 20 | 21 |
| 6 | 41 | 21 |
You roll a six-sided die 126 times. The null hypothesis (H0) is that each face has probability 1⁄6 on every roll.
Which calculation gives the contribution of face 6 to the chi-square statistic (χ2)?
(18 − 21)2⁄21 = 9⁄21 ≈ 0.43 Incorrect (41 − 21)2⁄126 = 400⁄126 ≈ 3.17 Incorrect (41 − 21)2⁄21 = 400⁄21 ≈ 19.05 Correct 412 − 212⁄21 = 1240⁄21 ≈ 59.05 Incorrect (41 − 21)2⁄6 = 400⁄6 ≈ 66.67 Incorrect MCcae1_89ee
| Face | Observed | Expected |
|---|---|---|
| 1 | 17 | 18 |
| 2 | 20 | 18 |
| 3 | 18 | 18 |
| 4 | 19 | 18 |
| 5 | 15 | 18 |
| 6 | 19 | 18 |
You roll a six-sided die 108 times. The null hypothesis (H0) is that each face has probability 1⁄6 on every roll.
Which calculation gives the contribution of face 2 to the chi-square statistic (χ2)?
(18 − 18)2⁄18 = 0⁄18 = 0.00 Incorrect (20 − 18)2⁄182 = 4⁄324 ≈ 0.01 Incorrect (20 − 18)2⁄108 = 4⁄108 ≈ 0.04 Incorrect (20 − 18)2⁄20 = 4⁄20 = 0.20 Incorrect (20 − 18)2⁄18 = 4⁄18 ≈ 0.22 Correct MCdc59_bc44
| Face | Observed | Expected |
|---|---|---|
| 1 | 41 | 29 |
| 2 | 27 | 29 |
| 3 | 19 | 29 |
| 4 | 26 | 29 |
| 5 | 31 | 29 |
| 6 | 30 | 29 |
You roll a six-sided die 174 times. The null hypothesis (H0) is that each face has probability 1⁄6 on every roll.
Which calculation gives the contribution of face 1 to the chi-square statistic (χ2)?
(27 − 29)2⁄29 = 4⁄29 ≈ 0.14 Incorrect (41 − 29)⁄29 = 12⁄29 ≈ 0.41 Incorrect (41 − 29)2⁄174 = 144⁄174 ≈ 0.83 Incorrect (41 − 29)2⁄41 = 144⁄41 ≈ 3.51 Incorrect (41 − 29)2⁄29 = 144⁄29 ≈ 4.97 Correct MC3c47_01a4
| Face | Observed | Expected |
|---|---|---|
| 1 | 3 | 6 |
| 2 | 5 | 6 |
| 3 | 4 | 6 |
| 4 | 6 | 6 |
| 5 | 15 | 6 |
| 6 | 3 | 6 |
You roll a six-sided die 36 times. The null hypothesis (H0) is that each face has probability 1⁄6 on every roll.
Which calculation gives the contribution of face 5 to the chi-square statistic (χ2)?
(5 − 6)2⁄6 = 1⁄6 ≈ 0.17 Incorrect (4 − 6)2⁄6 = 4⁄6 ≈ 0.67 Incorrect (15 − 6)⁄6 = 9⁄6 = 1.50 Incorrect (15 − 6)2⁄15 = 81⁄15 = 5.40 Incorrect (15 − 6)2⁄6 = 81⁄6 = 13.50 Correct MC3c3d_77a1
| Face | Observed | Expected |
|---|---|---|
| 1 | 28 | 12 |
| 2 | 7 | 12 |
| 3 | 17 | 12 |
| 4 | 5 | 12 |
| 5 | 9 | 12 |
| 6 | 6 | 12 |
You roll a six-sided die 72 times. The null hypothesis (H0) is that each face has probability 1⁄6 on every roll.
Which calculation gives the contribution of face 6 to the chi-square statistic (χ2)?
62 − 122⁄12 = -108⁄12 = -9.00 Incorrect (6 − 12)2⁄12 = 36⁄12 = 3.00 Correct (5 − 12)2⁄12 = 49⁄12 ≈ 4.08 Incorrect (6 − 12)2⁄6 = 36⁄6 = 6.00 Incorrect (28 − 12)2⁄12 = 256⁄12 ≈ 21.33 Incorrect MCb835_03ad
| Face | Observed | Expected |
|---|---|---|
| 1 | 10 | 5 |
| 2 | 7 | 5 |
| 3 | 3 | 5 |
| 4 | 3 | 5 |
| 5 | 4 | 5 |
| 6 | 3 | 5 |
You roll a six-sided die 30 times. The null hypothesis (H0) is that each face has probability 1⁄6 on every roll.
Which calculation gives the contribution of face 6 to the chi-square statistic (χ2)?
32 − 52⁄5 = -16⁄5 = -3.20 Incorrect (3 − 5)⁄5 = -2⁄5 = -0.40 Incorrect (3 − 5)2⁄6 = 4⁄6 ≈ 0.67 Incorrect (3 − 5)2⁄5 = 4⁄5 = 0.80 Correct (10 − 5)2⁄5 = 25⁄5 = 5.00 Incorrect MC0f1b_9182
| Face | Observed | Expected |
|---|---|---|
| 1 | 25 | 24 |
| 2 | 26 | 24 |
| 3 | 24 | 24 |
| 4 | 28 | 24 |
| 5 | 23 | 24 |
| 6 | 18 | 24 |
You roll a six-sided die 144 times. The null hypothesis (H0) is that each face has probability 1⁄6 on every roll.
Which calculation gives the contribution of face 6 to the chi-square statistic (χ2)?
182 − 242⁄24 = -252⁄24 = -10.50 Incorrect (18 − 24)2⁄242 = 36⁄576 ≈ 0.06 Incorrect (18 − 24)2⁄24 = 36⁄24 = 1.50 Correct (18 − 24)2⁄18 = 36⁄18 = 2.00 Incorrect (18 − 24)2⁄6 = 36⁄6 = 6.00 Incorrect MC36bd_e4b9
| Face | Observed | Expected |
|---|---|---|
| 1 | 6 | 14 |
| 2 | 13 | 14 |
| 3 | 6 | 14 |
| 4 | 8 | 14 |
| 5 | 39 | 14 |
| 6 | 12 | 14 |
You roll a six-sided die 84 times. The null hypothesis (H0) is that each face has probability 1⁄6 on every roll.
Which calculation gives the contribution of face 3 to the chi-square statistic (χ2)?
62 − 142⁄14 = -160⁄14 ≈ -11.43 Incorrect (6 − 14)2⁄84 = 64⁄84 ≈ 0.76 Incorrect (6 − 14)2⁄14 = 64⁄14 ≈ 4.57 Correct (6 − 14)2⁄6 = 64⁄6 ≈ 10.67 Incorrect (39 − 14)2⁄14 = 625⁄14 ≈ 44.64 Incorrect MC95d7_b5aa
| Face | Observed | Expected |
|---|---|---|
| 1 | 24 | 12 |
| 2 | 12 | 12 |
| 3 | 8 | 12 |
| 4 | 7 | 12 |
| 5 | 12 | 12 |
| 6 | 9 | 12 |
You roll a six-sided die 72 times. The null hypothesis (H0) is that each face has probability 1⁄6 on every roll.
Which calculation gives the contribution of face 6 to the chi-square statistic (χ2)?
(9 − 12)⁄12 = -3⁄12 = -0.25 Incorrect (12 − 12)2⁄12 = 0⁄12 = 0.00 Incorrect (9 − 12)2⁄122 = 9⁄144 ≈ 0.06 Incorrect (9 − 12)2⁄72 = 9⁄72 ≈ 0.12 Incorrect (9 − 12)2⁄12 = 9⁄12 = 0.75 Correct MC6f6b_4fe3
| Face | Observed | Expected |
|---|---|---|
| 1 | 24 | 15 |
| 2 | 15 | 15 |
| 3 | 10 | 15 |
| 4 | 19 | 15 |
| 5 | 10 | 15 |
| 6 | 12 | 15 |
You roll a six-sided die 90 times. The null hypothesis (H0) is that each face has probability 1⁄6 on every roll.
Which calculation gives the contribution of face 4 to the chi-square statistic (χ2)?
(19 − 15)2⁄152 = 16⁄225 ≈ 0.07 Incorrect (19 − 15)2⁄90 = 16⁄90 ≈ 0.18 Incorrect (12 − 15)2⁄15 = 9⁄15 = 0.60 Incorrect (19 − 15)2⁄15 = 16⁄15 ≈ 1.07 Correct (24 − 15)2⁄15 = 81⁄15 = 5.40 Incorrect MC13b2_97a2
| Face | Observed | Expected |
|---|---|---|
| 1 | 22 | 26 |
| 2 | 25 | 26 |
| 3 | 29 | 26 |
| 4 | 23 | 26 |
| 5 | 24 | 26 |
| 6 | 33 | 26 |
You roll a six-sided die 156 times. The null hypothesis (H0) is that each face has probability 1⁄6 on every roll.
Which calculation gives the contribution of face 1 to the chi-square statistic (χ2)?
222 − 262⁄26 = -192⁄26 ≈ -7.38 Incorrect (24 − 26)2⁄26 = 4⁄26 ≈ 0.15 Incorrect (29 − 26)2⁄26 = 9⁄26 ≈ 0.35 Incorrect (22 − 26)2⁄26 = 16⁄26 ≈ 0.62 Correct (22 − 26)2⁄6 = 16⁄6 ≈ 2.67 Incorrect MC5afc_923c
| Face | Observed | Expected |
|---|---|---|
| 1 | 16 | 23 |
| 2 | 25 | 23 |
| 3 | 22 | 23 |
| 4 | 15 | 23 |
| 5 | 39 | 23 |
| 6 | 21 | 23 |
You roll a six-sided die 138 times. The null hypothesis (H0) is that each face has probability 1⁄6 on every roll.
Which calculation gives the contribution of face 2 to the chi-square statistic (χ2)?
(25 − 23)2⁄138 = 4⁄138 ≈ 0.03 Incorrect (25 − 23)2⁄23 = 4⁄23 ≈ 0.17 Correct (15 − 23)2⁄23 = 64⁄23 ≈ 2.78 Incorrect 252 − 232⁄23 = 96⁄23 ≈ 4.17 Incorrect (39 − 23)2⁄23 = 256⁄23 ≈ 11.13 Incorrect MCad28_3471
| Face | Observed | Expected |
|---|---|---|
| 1 | 21 | 28 |
| 2 | 34 | 28 |
| 3 | 23 | 28 |
| 4 | 36 | 28 |
| 5 | 25 | 28 |
| 6 | 29 | 28 |
You roll a six-sided die 168 times. The null hypothesis (H0) is that each face has probability 1⁄6 on every roll.
Which calculation gives the contribution of face 3 to the chi-square statistic (χ2)?
(23 − 28)2⁄28 = 25⁄28 ≈ 0.89 Correct (34 − 28)2⁄28 = 36⁄28 ≈ 1.29 Incorrect (21 − 28)2⁄28 = 49⁄28 = 1.75 Incorrect (36 − 28)2⁄28 = 64⁄28 ≈ 2.29 Incorrect (23 − 28)2⁄6 = 25⁄6 ≈ 4.17 Incorrect MCf33e_bcb2
| Face | Observed | Expected |
|---|---|---|
| 1 | 17 | 25 |
| 2 | 30 | 25 |
| 3 | 28 | 25 |
| 4 | 24 | 25 |
| 5 | 33 | 25 |
| 6 | 18 | 25 |
You roll a six-sided die 150 times. The null hypothesis (H0) is that each face has probability 1⁄6 on every roll.
Which calculation gives the contribution of face 5 to the chi-square statistic (χ2)?
(33 − 25)2⁄252 = 64⁄625 ≈ 0.10 Incorrect (30 − 25)2⁄25 = 25⁄25 = 1.00 Incorrect (33 − 25)2⁄25 = 64⁄25 = 2.56 Correct (33 − 25)2⁄6 = 64⁄6 ≈ 10.67 Incorrect 332 − 252⁄25 = 464⁄25 = 18.56 Incorrect MC5680_64e4
| Face | Observed | Expected |
|---|---|---|
| 1 | 5 | 13 |
| 2 | 28 | 13 |
| 3 | 7 | 13 |
| 4 | 11 | 13 |
| 5 | 17 | 13 |
| 6 | 10 | 13 |
You roll a six-sided die 78 times. The null hypothesis (H0) is that each face has probability 1⁄6 on every roll.
Which calculation gives the contribution of face 1 to the chi-square statistic (χ2)?
(11 − 13)2⁄13 = 4⁄13 ≈ 0.31 Incorrect (10 − 13)2⁄13 = 9⁄13 ≈ 0.69 Incorrect (17 − 13)2⁄13 = 16⁄13 ≈ 1.23 Incorrect (5 − 13)2⁄13 = 64⁄13 ≈ 4.92 Correct (5 − 13)2⁄6 = 64⁄6 ≈ 10.67 Incorrect MC346c_46cd
| Face | Observed | Expected |
|---|---|---|
| 1 | 25 | 20 |
| 2 | 18 | 20 |
| 3 | 22 | 20 |
| 4 | 16 | 20 |
| 5 | 16 | 20 |
| 6 | 23 | 20 |
You roll a six-sided die 120 times. The null hypothesis (H0) is that each face has probability 1⁄6 on every roll.
Which calculation gives the contribution of face 1 to the chi-square statistic (χ2)?
(25 − 20)2⁄120 = 25⁄120 ≈ 0.21 Incorrect (16 − 20)2⁄20 = 16⁄20 = 0.80 Incorrect (25 − 20)2⁄20 = 25⁄20 = 1.25 Correct (25 − 20)2⁄6 = 25⁄6 ≈ 4.17 Incorrect 252 − 202⁄20 = 225⁄20 = 11.25 Incorrect MCb4dc_4a1d
| Face | Observed | Expected |
|---|---|---|
| 1 | 12 | 17 |
| 2 | 20 | 17 |
| 3 | 14 | 17 |
| 4 | 19 | 17 |
| 5 | 23 | 17 |
| 6 | 14 | 17 |
You roll a six-sided die 102 times. The null hypothesis (H0) is that each face has probability 1⁄6 on every roll.
Which calculation gives the contribution of face 6 to the chi-square statistic (χ2)?
(14 − 17)⁄17 = -3⁄17 ≈ -0.18 Incorrect (14 − 17)2⁄172 = 9⁄289 ≈ 0.03 Incorrect (14 − 17)2⁄17 = 9⁄17 ≈ 0.53 Correct (14 − 17)2⁄6 = 9⁄6 = 1.50 Incorrect (23 − 17)2⁄17 = 36⁄17 ≈ 2.12 Incorrect MC854c_4c72
| Face | Observed | Expected |
|---|---|---|
| 1 | 21 | 19 |
| 2 | 23 | 19 |
| 3 | 25 | 19 |
| 4 | 13 | 19 |
| 5 | 16 | 19 |
| 6 | 16 | 19 |
You roll a six-sided die 114 times. The null hypothesis (H0) is that each face has probability 1⁄6 on every roll.
Which calculation gives the contribution of face 2 to the chi-square statistic (χ2)?
(23 − 19)2⁄192 = 16⁄361 ≈ 0.04 Incorrect (23 − 19)2⁄114 = 16⁄114 ≈ 0.14 Incorrect (23 − 19)⁄19 = 4⁄19 ≈ 0.21 Incorrect (16 − 19)2⁄19 = 9⁄19 ≈ 0.47 Incorrect (23 − 19)2⁄19 = 16⁄19 ≈ 0.84 Correct MC5146_302e
| Face | Observed | Expected |
|---|---|---|
| 1 | 7 | 13 |
| 2 | 14 | 13 |
| 3 | 6 | 13 |
| 4 | 34 | 13 |
| 5 | 12 | 13 |
| 6 | 5 | 13 |
You roll a six-sided die 78 times. The null hypothesis (H0) is that each face has probability 1⁄6 on every roll.
Which calculation gives the contribution of face 6 to the chi-square statistic (χ2)?
(5 − 13)⁄13 = -8⁄13 ≈ -0.62 Incorrect (5 − 13)2⁄78 = 64⁄78 ≈ 0.82 Incorrect (5 − 13)2⁄13 = 64⁄13 ≈ 4.92 Correct (5 − 13)2⁄6 = 64⁄6 ≈ 10.67 Incorrect (5 − 13)2⁄5 = 64⁄5 = 12.80 Incorrect MCb795_3f2e
| Face | Observed | Expected |
|---|---|---|
| 1 | 27 | 19 |
| 2 | 18 | 19 |
| 3 | 20 | 19 |
| 4 | 16 | 19 |
| 5 | 12 | 19 |
| 6 | 21 | 19 |
You roll a six-sided die 114 times. The null hypothesis (H0) is that each face has probability 1⁄6 on every roll.
Which calculation gives the contribution of face 4 to the chi-square statistic (χ2)?
(16 − 19)2⁄19 = 9⁄19 ≈ 0.47 Correct (16 − 19)2⁄16 = 9⁄16 ≈ 0.56 Incorrect (16 − 19)2⁄6 = 9⁄6 = 1.50 Incorrect (12 − 19)2⁄19 = 49⁄19 ≈ 2.58 Incorrect (27 − 19)2⁄19 = 64⁄19 ≈ 3.37 Incorrect MC7502_355a
| Face | Observed | Expected |
|---|---|---|
| 1 | 10 | 11 |
| 2 | 5 | 11 |
| 3 | 8 | 11 |
| 4 | 6 | 11 |
| 5 | 30 | 11 |
| 6 | 7 | 11 |
You roll a six-sided die 66 times. The null hypothesis (H0) is that each face has probability 1⁄6 on every roll.
Which calculation gives the contribution of face 5 to the chi-square statistic (χ2)?
(7 − 11)2⁄11 = 16⁄11 ≈ 1.45 Incorrect (30 − 11)2⁄30 = 361⁄30 ≈ 12.03 Incorrect (30 − 11)2⁄11 = 361⁄11 ≈ 32.82 Correct (30 − 11)2⁄6 = 361⁄6 ≈ 60.17 Incorrect 302 − 112⁄11 = 779⁄11 ≈ 70.82 Incorrect MCdab6_8ada
| Face | Observed | Expected |
|---|---|---|
| 1 | 24 | 18 |
| 2 | 21 | 18 |
| 3 | 24 | 18 |
| 4 | 13 | 18 |
| 5 | 14 | 18 |
| 6 | 12 | 18 |
You roll a six-sided die 108 times. The null hypothesis (H0) is that each face has probability 1⁄6 on every roll.
Which calculation gives the contribution of face 5 to the chi-square statistic (χ2)?
142 − 182⁄18 = -128⁄18 ≈ -7.11 Incorrect (14 − 18)2⁄182 = 16⁄324 ≈ 0.05 Incorrect (14 − 18)2⁄108 = 16⁄108 ≈ 0.15 Incorrect (21 − 18)2⁄18 = 9⁄18 = 0.50 Incorrect (14 − 18)2⁄18 = 16⁄18 ≈ 0.89 Correct MCdd14_e444
| Face | Observed | Expected |
|---|---|---|
| 1 | 17 | 18 |
| 2 | 18 | 18 |
| 3 | 14 | 18 |
| 4 | 32 | 18 |
| 5 | 11 | 18 |
| 6 | 16 | 18 |
You roll a six-sided die 108 times. The null hypothesis (H0) is that each face has probability 1⁄6 on every roll.
Which calculation gives the contribution of face 6 to the chi-square statistic (χ2)?
(16 − 18)2⁄18 = 4⁄18 ≈ 0.22 Correct (16 − 18)2⁄16 = 4⁄16 = 0.25 Incorrect (16 − 18)2⁄6 = 4⁄6 ≈ 0.67 Incorrect (14 − 18)2⁄18 = 16⁄18 ≈ 0.89 Incorrect (32 − 18)2⁄18 = 196⁄18 ≈ 10.89 Incorrect MC7a74_edb7
| Face | Observed | Expected |
|---|---|---|
| 1 | 19 | 15 |
| 2 | 14 | 15 |
| 3 | 10 | 15 |
| 4 | 13 | 15 |
| 5 | 21 | 15 |
| 6 | 13 | 15 |
You roll a six-sided die 90 times. The null hypothesis (H0) is that each face has probability 1⁄6 on every roll.
Which calculation gives the contribution of face 5 to the chi-square statistic (χ2)?
(14 − 15)2⁄15 = 1⁄15 ≈ 0.07 Incorrect (21 − 15)⁄15 = 6⁄15 = 0.40 Incorrect (19 − 15)2⁄15 = 16⁄15 ≈ 1.07 Incorrect (21 − 15)2⁄15 = 36⁄15 = 2.40 Correct 212 − 152⁄15 = 216⁄15 = 14.40 Incorrect MCc5dc_d3e9
| Face | Observed | Expected |
|---|---|---|
| 1 | 19 | 28 |
| 2 | 22 | 28 |
| 3 | 24 | 28 |
| 4 | 26 | 28 |
| 5 | 55 | 28 |
| 6 | 22 | 28 |
You roll a six-sided die 168 times. The null hypothesis (H0) is that each face has probability 1⁄6 on every roll.
Which calculation gives the contribution of face 1 to the chi-square statistic (χ2)?
192 − 282⁄28 = -423⁄28 ≈ -15.11 Incorrect (26 − 28)2⁄28 = 4⁄28 ≈ 0.14 Incorrect (24 − 28)2⁄28 = 16⁄28 ≈ 0.57 Incorrect (19 − 28)2⁄28 = 81⁄28 ≈ 2.89 Correct (19 − 28)2⁄6 = 81⁄6 = 13.50 Incorrect MCfd3e_cf50
| Face | Observed | Expected |
|---|---|---|
| 1 | 16 | 16 |
| 2 | 15 | 16 |
| 3 | 12 | 16 |
| 4 | 18 | 16 |
| 5 | 20 | 16 |
| 6 | 15 | 16 |
You roll a six-sided die 96 times. The null hypothesis (H0) is that each face has probability 1⁄6 on every roll.
Which calculation gives the contribution of face 5 to the chi-square statistic (χ2)?
(16 − 16)2⁄16 = 0⁄16 = 0.00 Incorrect (20 − 16)2⁄162 = 16⁄256 ≈ 0.06 Incorrect (20 − 16)2⁄96 = 16⁄96 ≈ 0.17 Incorrect (20 − 16)⁄16 = 4⁄16 = 0.25 Incorrect (20 − 16)2⁄16 = 16⁄16 = 1.00 Correct MC8e7f_893f
| Face | Observed | Expected |
|---|---|---|
| 1 | 7 | 9 |
| 2 | 7 | 9 |
| 3 | 15 | 9 |
| 4 | 9 | 9 |
| 5 | 8 | 9 |
| 6 | 8 | 9 |
You roll a six-sided die 54 times. The null hypothesis (H0) is that each face has probability 1⁄6 on every roll.
Which calculation gives the contribution of face 1 to the chi-square statistic (χ2)?
(7 − 9)2⁄54 = 4⁄54 ≈ 0.07 Incorrect (7 − 9)2⁄9 = 4⁄9 ≈ 0.44 Correct (7 − 9)2⁄7 = 4⁄7 ≈ 0.57 Incorrect (7 − 9)2⁄6 = 4⁄6 ≈ 0.67 Incorrect (15 − 9)2⁄9 = 36⁄9 = 4.00 Incorrect MC2008_ac97
| Face | Observed | Expected |
|---|---|---|
| 1 | 15 | 9 |
| 2 | 10 | 9 |
| 3 | 9 | 9 |
| 4 | 5 | 9 |
| 5 | 6 | 9 |
| 6 | 9 | 9 |
You roll a six-sided die 54 times. The null hypothesis (H0) is that each face has probability 1⁄6 on every roll.
Which calculation gives the contribution of face 4 to the chi-square statistic (χ2)?
(9 − 9)2⁄9 = 0⁄9 = 0.00 Incorrect (5 − 9)2⁄9 = 16⁄9 ≈ 1.78 Correct (5 − 9)2⁄6 = 16⁄6 ≈ 2.67 Incorrect (5 − 9)2⁄5 = 16⁄5 = 3.20 Incorrect (15 − 9)2⁄9 = 36⁄9 = 4.00 Incorrect MC68ec_7809
| Face | Observed | Expected |
|---|---|---|
| 1 | 10 | 9 |
| 2 | 9 | 9 |
| 3 | 4 | 9 |
| 4 | 12 | 9 |
| 5 | 13 | 9 |
| 6 | 6 | 9 |
You roll a six-sided die 54 times. The null hypothesis (H0) is that each face has probability 1⁄6 on every roll.
Which calculation gives the contribution of face 5 to the chi-square statistic (χ2)?
(10 − 9)2⁄9 = 1⁄9 ≈ 0.11 Incorrect (13 − 9)2⁄92 = 16⁄81 ≈ 0.20 Incorrect (13 − 9)2⁄54 = 16⁄54 ≈ 0.30 Incorrect (13 − 9)2⁄13 = 16⁄13 ≈ 1.23 Incorrect (13 − 9)2⁄9 = 16⁄9 ≈ 1.78 Correct MCbf7e_11df
| Face | Observed | Expected |
|---|---|---|
| 1 | 12 | 10 |
| 2 | 15 | 10 |
| 3 | 10 | 10 |
| 4 | 10 | 10 |
| 5 | 8 | 10 |
| 6 | 5 | 10 |
You roll a six-sided die 60 times. The null hypothesis (H0) is that each face has probability 1⁄6 on every roll.
Which calculation gives the contribution of face 2 to the chi-square statistic (χ2)?
(12 − 10)2⁄10 = 4⁄10 = 0.40 Incorrect (15 − 10)2⁄15 = 25⁄15 ≈ 1.67 Incorrect (15 − 10)2⁄10 = 25⁄10 = 2.50 Correct (15 − 10)2⁄6 = 25⁄6 ≈ 4.17 Incorrect 152 − 102⁄10 = 125⁄10 = 12.50 Incorrect MC3bb9_e601
| Face | Observed | Expected |
|---|---|---|
| 1 | 6 | 9 |
| 2 | 4 | 9 |
| 3 | 5 | 9 |
| 4 | 7 | 9 |
| 5 | 25 | 9 |
| 6 | 7 | 9 |
You roll a six-sided die 54 times. The null hypothesis (H0) is that each face has probability 1⁄6 on every roll.
Which calculation gives the contribution of face 5 to the chi-square statistic (χ2)?
(6 − 9)2⁄9 = 9⁄9 = 1.00 Incorrect (4 − 9)2⁄9 = 25⁄9 ≈ 2.78 Incorrect (25 − 9)2⁄54 = 256⁄54 ≈ 4.74 Incorrect (25 − 9)2⁄25 = 256⁄25 = 10.24 Incorrect (25 − 9)2⁄9 = 256⁄9 ≈ 28.44 Correct MCd00a_6888
| Face | Observed | Expected |
|---|---|---|
| 1 | 28 | 28 |
| 2 | 22 | 28 |
| 3 | 31 | 28 |
| 4 | 34 | 28 |
| 5 | 30 | 28 |
| 6 | 23 | 28 |
You roll a six-sided die 168 times. The null hypothesis (H0) is that each face has probability 1⁄6 on every roll.
Which calculation gives the contribution of face 3 to the chi-square statistic (χ2)?
(31 − 28)2⁄28 = 9⁄28 ≈ 0.32 Correct (23 − 28)2⁄28 = 25⁄28 ≈ 0.89 Incorrect (22 − 28)2⁄28 = 36⁄28 ≈ 1.29 Incorrect (31 − 28)2⁄6 = 9⁄6 = 1.50 Incorrect 312 − 282⁄28 = 177⁄28 ≈ 6.32 Incorrect MC69b7_00c0
| Face | Observed | Expected |
|---|---|---|
| 1 | 3 | 5 |
| 2 | 8 | 5 |
| 3 | 2 | 5 |
| 4 | 7 | 5 |
| 5 | 6 | 5 |
| 6 | 4 | 5 |
You roll a six-sided die 30 times. The null hypothesis (H0) is that each face has probability 1⁄6 on every roll.
Which calculation gives the contribution of face 4 to the chi-square statistic (χ2)?
(7 − 5)2⁄30 = 4⁄30 ≈ 0.13 Incorrect (6 − 5)2⁄5 = 1⁄5 = 0.20 Incorrect (7 − 5)⁄5 = 2⁄5 = 0.40 Incorrect (7 − 5)2⁄6 = 4⁄6 ≈ 0.67 Incorrect (7 − 5)2⁄5 = 4⁄5 = 0.80 Correct MC8b44_f262
| Face | Observed | Expected |
|---|---|---|
| 1 | 7 | 7 |
| 2 | 6 | 7 |
| 3 | 5 | 7 |
| 4 | 9 | 7 |
| 5 | 10 | 7 |
| 6 | 5 | 7 |
You roll a six-sided die 42 times. The null hypothesis (H0) is that each face has probability 1⁄6 on every roll.
Which calculation gives the contribution of face 5 to the chi-square statistic (χ2)?
(7 − 7)2⁄7 = 0⁄7 = 0.00 Incorrect (5 − 7)2⁄7 = 4⁄7 ≈ 0.57 Incorrect (10 − 7)2⁄7 = 9⁄7 ≈ 1.29 Correct (10 − 7)2⁄6 = 9⁄6 = 1.50 Incorrect 102 − 72⁄7 = 51⁄7 ≈ 7.29 Incorrect MC417c_c2b0
| Face | Observed | Expected |
|---|---|---|
| 1 | 16 | 14 |
| 2 | 17 | 14 |
| 3 | 14 | 14 |
| 4 | 11 | 14 |
| 5 | 10 | 14 |
| 6 | 16 | 14 |
You roll a six-sided die 84 times. The null hypothesis (H0) is that each face has probability 1⁄6 on every roll.
Which calculation gives the contribution of face 5 to the chi-square statistic (χ2)?
(10 − 14)2⁄142 = 16⁄196 ≈ 0.08 Incorrect (16 − 14)2⁄14 = 4⁄14 ≈ 0.29 Incorrect (17 − 14)2⁄14 = 9⁄14 ≈ 0.64 Incorrect (10 − 14)2⁄14 = 16⁄14 ≈ 1.14 Correct (10 − 14)2⁄10 = 16⁄10 = 1.60 Incorrect MCff54_b81c
| Face | Observed | Expected |
|---|---|---|
| 1 | 12 | 5 |
| 2 | 8 | 5 |
| 3 | 3 | 5 |
| 4 | 2 | 5 |
| 5 | 1 | 5 |
| 6 | 4 | 5 |
You roll a six-sided die 30 times. The null hypothesis (H0) is that each face has probability 1⁄6 on every roll.
Which calculation gives the contribution of face 4 to the chi-square statistic (χ2)?
(4 − 5)2⁄5 = 1⁄5 = 0.20 Incorrect (2 − 5)2⁄30 = 9⁄30 = 0.30 Incorrect (2 − 5)2⁄52 = 9⁄25 = 0.36 Incorrect (2 − 5)2⁄5 = 9⁄5 = 1.80 Correct (12 − 5)2⁄5 = 49⁄5 = 9.80 Incorrect MC95d3_2d9a
| Face | Observed | Expected |
|---|---|---|
| 1 | 26 | 30 |
| 2 | 32 | 30 |
| 3 | 29 | 30 |
| 4 | 35 | 30 |
| 5 | 28 | 30 |
| 6 | 30 | 30 |
You roll a six-sided die 180 times. The null hypothesis (H0) is that each face has probability 1⁄6 on every roll.
Which calculation gives the contribution of face 1 to the chi-square statistic (χ2)?
(26 − 30)2⁄302 = 16⁄900 ≈ 0.02 Incorrect (26 − 30)2⁄180 = 16⁄180 ≈ 0.09 Incorrect (32 − 30)2⁄30 = 4⁄30 ≈ 0.13 Incorrect (26 − 30)2⁄30 = 16⁄30 ≈ 0.53 Correct (35 − 30)2⁄30 = 25⁄30 ≈ 0.83 Incorrect MC972f_3746
| Face | Observed | Expected |
|---|---|---|
| 1 | 23 | 29 |
| 2 | 22 | 29 |
| 3 | 33 | 29 |
| 4 | 37 | 29 |
| 5 | 30 | 29 |
| 6 | 29 | 29 |
You roll a six-sided die 174 times. The null hypothesis (H0) is that each face has probability 1⁄6 on every roll.
Which calculation gives the contribution of face 1 to the chi-square statistic (χ2)?
(23 − 29)⁄29 = -6⁄29 ≈ -0.21 Incorrect (30 − 29)2⁄29 = 1⁄29 ≈ 0.03 Incorrect (23 − 29)2⁄29 = 36⁄29 ≈ 1.24 Correct (22 − 29)2⁄29 = 49⁄29 ≈ 1.69 Incorrect (23 − 29)2⁄6 = 36⁄6 = 6.00 Incorrect MC30e1_c42d
| Face | Observed | Expected |
|---|---|---|
| 1 | 15 | 13 |
| 2 | 16 | 13 |
| 3 | 14 | 13 |
| 4 | 11 | 13 |
| 5 | 9 | 13 |
| 6 | 13 | 13 |
You roll a six-sided die 78 times. The null hypothesis (H0) is that each face has probability 1⁄6 on every roll.
Which calculation gives the contribution of face 4 to the chi-square statistic (χ2)?
(11 − 13)2⁄132 = 4⁄169 ≈ 0.02 Incorrect (14 − 13)2⁄13 = 1⁄13 ≈ 0.08 Incorrect (11 − 13)2⁄13 = 4⁄13 ≈ 0.31 Correct (16 − 13)2⁄13 = 9⁄13 ≈ 0.69 Incorrect (9 − 13)2⁄13 = 16⁄13 ≈ 1.23 Incorrect MC0c77_4503
| Face | Observed | Expected |
|---|---|---|
| 1 | 28 | 26 |
| 2 | 26 | 26 |
| 3 | 25 | 26 |
| 4 | 24 | 26 |
| 5 | 25 | 26 |
| 6 | 28 | 26 |
You roll a six-sided die 156 times. The null hypothesis (H0) is that each face has probability 1⁄6 on every roll.
Which calculation gives the contribution of face 6 to the chi-square statistic (χ2)?
(26 − 26)2⁄26 = 0⁄26 = 0.00 Incorrect (28 − 26)2⁄262 = 4⁄676 ≈ 0.01 Incorrect (28 − 26)⁄26 = 2⁄26 ≈ 0.08 Incorrect (28 − 26)2⁄26 = 4⁄26 ≈ 0.15 Correct 282 − 262⁄26 = 108⁄26 ≈ 4.15 Incorrect MC7934_cf07
| Face | Observed | Expected |
|---|---|---|
| 1 | 7 | 19 |
| 2 | 8 | 19 |
| 3 | 15 | 19 |
| 4 | 12 | 19 |
| 5 | 53 | 19 |
| 6 | 19 | 19 |
You roll a six-sided die 114 times. The null hypothesis (H0) is that each face has probability 1⁄6 on every roll.
Which calculation gives the contribution of face 4 to the chi-square statistic (χ2)?
122 − 192⁄19 = -217⁄19 ≈ -11.42 Incorrect (12 − 19)⁄19 = -7⁄19 ≈ -0.37 Incorrect (12 − 19)2⁄114 = 49⁄114 ≈ 0.43 Incorrect (12 − 19)2⁄19 = 49⁄19 ≈ 2.58 Correct (8 − 19)2⁄19 = 121⁄19 ≈ 6.37 Incorrect MC82ae_5eb1
| Face | Observed | Expected |
|---|---|---|
| 1 | 4 | 5 |
| 2 | 4 | 5 |
| 3 | 7 | 5 |
| 4 | 3 | 5 |
| 5 | 5 | 5 |
| 6 | 7 | 5 |
You roll a six-sided die 30 times. The null hypothesis (H0) is that each face has probability 1⁄6 on every roll.
Which calculation gives the contribution of face 4 to the chi-square statistic (χ2)?
32 − 52⁄5 = -16⁄5 = -3.20 Incorrect (3 − 5)⁄5 = -2⁄5 = -0.40 Incorrect (3 − 5)2⁄30 = 4⁄30 ≈ 0.13 Incorrect (3 − 5)2⁄6 = 4⁄6 ≈ 0.67 Incorrect (3 − 5)2⁄5 = 4⁄5 = 0.80 Correct MCc496_b2e4
| Face | Observed | Expected |
|---|---|---|
| 1 | 18 | 19 |
| 2 | 19 | 19 |
| 3 | 26 | 19 |
| 4 | 12 | 19 |
| 5 | 16 | 19 |
| 6 | 23 | 19 |
You roll a six-sided die 114 times. The null hypothesis (H0) is that each face has probability 1⁄6 on every roll.
Which calculation gives the contribution of face 5 to the chi-square statistic (χ2)?
162 − 192⁄19 = -105⁄19 ≈ -5.53 Incorrect (16 − 19)⁄19 = -3⁄19 ≈ -0.16 Incorrect (19 − 19)2⁄19 = 0⁄19 = 0.00 Incorrect (16 − 19)2⁄114 = 9⁄114 ≈ 0.08 Incorrect (16 − 19)2⁄19 = 9⁄19 ≈ 0.47 Correct MC3965_17cc
| Face | Observed | Expected |
|---|---|---|
| 1 | 7 | 11 |
| 2 | 11 | 11 |
| 3 | 9 | 11 |
| 4 | 9 | 11 |
| 5 | 10 | 11 |
| 6 | 20 | 11 |
You roll a six-sided die 66 times. The null hypothesis (H0) is that each face has probability 1⁄6 on every roll.
Which calculation gives the contribution of face 4 to the chi-square statistic (χ2)?
(9 − 11)⁄11 = -2⁄11 ≈ -0.18 Incorrect (11 − 11)2⁄11 = 0⁄11 = 0.00 Incorrect (9 − 11)2⁄112 = 4⁄121 ≈ 0.03 Incorrect (10 − 11)2⁄11 = 1⁄11 ≈ 0.09 Incorrect (9 − 11)2⁄11 = 4⁄11 ≈ 0.36 Correct MC0962_c6a7
| Face | Observed | Expected |
|---|---|---|
| 1 | 12 | 19 |
| 2 | 12 | 19 |
| 3 | 43 | 19 |
| 4 | 19 | 19 |
| 5 | 15 | 19 |
| 6 | 13 | 19 |
You roll a six-sided die 114 times. The null hypothesis (H0) is that each face has probability 1⁄6 on every roll.
Which calculation gives the contribution of face 2 to the chi-square statistic (χ2)?
(12 − 19)2⁄192 = 49⁄361 ≈ 0.14 Incorrect (12 − 19)2⁄19 = 49⁄19 ≈ 2.58 Correct (12 − 19)2⁄12 = 49⁄12 ≈ 4.08 Incorrect (12 − 19)2⁄6 = 49⁄6 ≈ 8.17 Incorrect (43 − 19)2⁄19 = 576⁄19 ≈ 30.32 Incorrect MCc71a_f245
| Face | Observed | Expected |
|---|---|---|
| 1 | 15 | 15 |
| 2 | 16 | 15 |
| 3 | 14 | 15 |
| 4 | 16 | 15 |
| 5 | 17 | 15 |
| 6 | 12 | 15 |
You roll a six-sided die 90 times. The null hypothesis (H0) is that each face has probability 1⁄6 on every roll.
Which calculation gives the contribution of face 5 to the chi-square statistic (χ2)?
(16 − 15)2⁄15 = 1⁄15 ≈ 0.07 Incorrect (17 − 15)2⁄15 = 4⁄15 ≈ 0.27 Correct (12 − 15)2⁄15 = 9⁄15 = 0.60 Incorrect (17 − 15)2⁄6 = 4⁄6 ≈ 0.67 Incorrect 172 − 152⁄15 = 64⁄15 ≈ 4.27 Incorrect