Final Review Answers

Final Review Answers

Two-Tailed t Test Solution -1

• H0: • Ha: • = • df = • Critical Value(s):

Test Statistic:

Decision:

= 368 368.0525 - 1 = 24

t0 2.064-2.064

.025Reject H0 Reject H0

.025

372.5 368 4.5525

Xt Sn

Reject at = .05

P-value = 0

Two-Tailed Z Test Solution -2

• H0: • Ha: • = • n = • Critical Value(s):

Test Statistic:

Decision:

= 70 70.0536

Z0 1.96-1.96

.025Reject H 0 Reject H0

.025

69.7 70 .513.536

XZ

n

Do not reject at = .05

One-Tailed Z Test Solution -3

• H0: • Ha: • = • n =• Critical Value(s):

Test Statistic:

Decision:

= 32 < 32.0160

Z0-2.33

.01Reject

30.7 32 2.653.860

XZ

n

Reject at = .01

Two-Tailed t Test Solution-4

• H0: • Ha: • • df • Critical Value(s):

Test Statistic:

Decision:

= 3.25 3.25.0164 - 1 = 63

t0 2.656-2.656

.005Reject H0 Reject H0

.005

3.238 3.25 .82.11764

Xt Sn

Do not reject at = .01

One-Tailed t Test Solution - 5

• H0: • Ha: • =• df =• Critical Value(s):

Test Statistic:

Decision:

= 140 < 140.0520 - 1 = 19

t0-1.729

.05

Reject H0

138.47 140 2.572.66

20

XtSn

Reject at = .05

One-Tailed t Test Solution -6

• H0: • Ha: • = • df = • Critical Value(s):

Test Statistic:

Decision:

= 5 < 5.0510 - 1 = 9

t0 1.833

.05

Reject H0

6.4 5 1.313.373

10

XtSn

Do not reject at = .05

One-Proportion Z Test Solution - 7

• H0: • Ha: • = • n =• Critical Value(s):

Test Statistic:

Decision:

p = .10p < .10.05200

Z0-1.645

.05Reject H0

0

0 0

11 .10ˆ 200 2.12.10 .90

200

p pZp q

n

Reject at = .05

One-Proportion Z Test Solution - 8

• H0: • Ha: • = • n = • Critical Value(s):

Test Statistic:

Decision:

p = .04p .04.05500

Z0 1.96-1.96

.025Reject H 0 Reject H0

.025

0

0 0

25 .04ˆ 500 1.14.04 .96

500

p pZp q

n

Do not reject at = .05

1. Miles per gallon ratings of cars before and after mounting radial tires - DEPENDENT

2. The life expectancy of light bulbs made in two different factories - INDEPENDENT

3. Difference in hardness between two metals: one contains an alloy, one doesn’t - INDEPENDENT

4. Tread life of two different motorcycle tires: one on the front, the other on the back - DEPENDENT

9

• H0:• Ha:• • df • Critical Value(s):

1 - 2 = 0 (1 = 2)1 - 2 0 (1 2).0511 -1 = 10

t0 2.228-2.228

.025Reject H 0 Reject H0

.025

Small-Sample Test Solution 10-A

1 2 1 2

2 22 21 2

1 2

3.27 2.53 01.43

1.30 1.1611 15

X Xt

S Sn n

Test Statistic:

Do not reject at = .05

• H0:• Ha:• • df • Critical Value(s):

1 - 2 = 1% (1 = 2)1 - 2 < 1% (1 2).0511 -1= 10

Small-Sample Test Solution 10-B

1 2 1 2

2 22 21 2

1 2

3.27 2.53 10.505

1.30 1.1611 15

X Xt

S Sn n

Test Statistic:

Do not reject at = .05

t0-1.812

.05Reject H0

Large-Sample Test Solution - 11

• H0:• Ha:• • n1 = , n2 =• Critical Value(s):

t0 1.761-1.761

.05Reject H0 Reject H0

.05

1 - 2 = 0 (1 = 2)1 - 2 0 (1 2).10 15 15

1 2 1 2

2 22 21 2

1 2

6012 5832 00.86

602 49715 15

X Xt

S Sn n

Do not reject at = .10

Paired-Difference Solution-12

• H0:• Ha: • = • df =• Critical Value(s):

d = 0 (d = A - B)d < 0.104 - 1 = 3

t0-1.638

.10

Reject H0

Computation Table

Observation Before After Difference

Sam 85 94 9

Tamika 94 87 -7

Brian 78 79 1

Mike 87 88 1

Total 4

d = 1 Sd = 6.53

Test Statistic:

Decision:

Do not reject at = .10

0 1 0 .3066.53

4d

d

d Dt

Sn

• H0: • Ha: • = • n1 = n2 = • Critical Value(s):

p1 - p2 = 0p1 - p2 0

.0178 82

z0 2.58-2.58

Reject H0 Reject H0

.005 .005

Test for Two Proportions Solution -13

1 21 2

1 2

63 49ˆ ˆ.808 .59878 82

X Xp pn n

.808 .598 0

(.808)(.192) (.598)(.402)78 82

2.90

Z

Reject at = .01

• H0:• Ha:• = • nMA = nCA =• Critical Value(s):

pMA – pCA = 0pMA – pCA < 0

.051500 1500

Z0-1.645

.05Reject H0

Test for Two Proportions Solution - 14

74 129ˆ ˆ.0493 .08601500 1500

CAMAMA CA

MA CA

XXp pn n

.0493 .0860 0

(.0493)(.9507) (.0860)(.914)1500 1500

4.01

Z

Reject at = .05

• H0:• Ha:• =• n1 = n2 = n3 =• Critical Value(s):

p1 = p2 = p3 = 1/3

At least 1 is different

.05

63 45 72

= .05

c20

Reject H0

5.991

c2 Test for k Proportions Solution - 15

,0

1 2 3 180 1 3 60i iE n np

E n E n E n

2

2

all cells

2 2 263 60 45 60 72 606.3

60 60 60

i i

i

n E nE n

c

Reject at = .05

c2 Test of Independence Solution - 16

• H0: • Ha: • = • df = • Critical Value(s):

No Relationship

Relationship

.05

(2 - 1)(2 - 1) = 1

c20

Reject H0

3.841

= .05

House Location Urban Rural

House Style Obs. Exp. Obs. Exp. Total Split-Level 63 54.6 49 57.4 112 Ranch 15 23.4 33 24.6 48 Total 78 78 82 82 160

112·82 160

48·78 160

48·82 160

112·78 160

2

2

all cells

2 2 211 11 12 12 22 22

11 12 22

2 2 263 54.6 49 57.4 33 24.68.41

54.6 57.4 24.6

ij ij

ij

n E

E

n E n E n EE E E

c

Reject at = .05

c2 Test of Independence Solution -17

• H0: • Ha: • = • df = • Critical Value(s):

No Relationship

Relationship

.05

(2 - 1)(2 - 1) = 1

c20

Reject H0

3.841

= .05

Diet Pepsi No Yes

Diet Coke Obs. Exp. Obs. Exp. Total No 84 53.5 32 62.5 116 Yes 48 78.5 122 91.5 170 Total 132 132 154 154 286

170·132 286

170·154 286

116·132 286

154·132 286

2

2

all cells

2 2 211 11 12 12 22 22

11 12 22

2 2 284 53.5 32 62.5 122 91.554.29

53.5 62.5 91.5

ij ij

ij

n E

E

n E n E n EE E E

c

Reject at = .05