MIME-Version: 1.0 Content-Type: multipart/related; boundary="----=_NextPart_01CB96D9.B7DF5E90" This document is a Single File Web Page, also known as a Web Archive file. If you are seeing this message, your browser or editor doesn't support Web Archive files. Please download a browser that supports Web Archive, such as Windows® Internet Explorer®. ------=_NextPart_01CB96D9.B7DF5E90 Content-Location: file:///C:/3409C650/final_exam_review_2010.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Final Exam Suggested Review Problems

Final Exam Suggested Review Problems with Select= ed Answers

 

Chapter 2 Review =       2.99, 2.100, 2.103, 2.106, 2.107, 2.109, 2.113, 2.114, 2.115

Chapter 4 Review =       4.106, 4.109, 4.110, 4.111, 4.113, 4.115, 4.117, 4.120, 4.121

Chapter 5 Review =       5.86, 5.90, 5.91, 5.92, 5.93, 5.97

Chapter 6 Review =       6.55, 6.58, 6.59, 6.63, 6.65, 6.67

Chapter 7 Review =       7.34, 7.37, 7.39, 7.41, 7.43

Chapter 8 Review =       8.78, 8.80, 8.83, 8.84, 8.88, 8.89

Chapter 9 Review =       9.51, 9.52, 9.54, 9.55, 9.56, 9.58, 9.59, 9.60

 

2.99)          b) = ;        Service sector jobs have increased relative to goods producing and government jobs.=

 

2.100)      &= nbsp;   a)         =

Intended Major

Frequency

Humanities

4

Social Science

18

Biological Science<= /p>

18

Physical Science

9

      &= nbsp;           &nbs= p;     b)         =

Year in College

Frequency

1

4

2

10

3

20

4

15

 

2.106)      &= nbsp;   a)         = median =3D 65.5

      &= nbsp;           &nbs= p;     b)         = Q1 =3D 50, Q3 =3D 79

      &= nbsp;           &nbs= p;     c)         = .526 scored below 70, .237 scored 80 and over

 

2.109)      &= nbsp;   b)         = =3D 100 + 7 =3D 107, s =3D 2

 

2.113)      &= nbsp;   a)         = =3D 5.375, s= =3D 3.424

      &= nbsp;           &nbs= p;     b)         = median =3D 5.5

      &= nbsp;           &nbs= p;     c)         = 13 – 0 =3D 13

 

2.114)      &= nbsp;   a)         = 75%

      &= nbsp;           &nbs= p;     b)         = 50%

 &= nbsp;           &nbs= p;          c)         = This interval is two standard deviations from the mean.  Approximately 95% if the data set = is normally distributed.

 &= nbsp;           &nbs= p;          d)         = 50%

 &= nbsp;           &nbs= p;          e)         = This interval is three standard deviations from the mean.  Approximately 99.7% if the data se= t is normally distributed.

 

4.106)      &= nbsp;   a)         = The probabilities sum to more than 1.

 &= nbsp;           &nbs= p;          b)         = The probability of passing is more than 1 and the probabilities sum to more tha= n 1.

 &= nbsp;           &nbs= p;          c)         = The probability of A’s in both classes is more than the probability of an= A in statistics.

 

4.110) &= nbsp;        a)         = (1,2), (1,3), (1,4), (2,3), (2,4), (3,4)

            =        b) = ;        i) .333            =   ii) .333

 

4.113)      &= nbsp;   a)         = .417

      &= nbsp;           &nbs= p;     b)         = .25

 

4.115)      &= nbsp;   a)         = 125, 152, 215, 251, 512, 521

      &= nbsp;           &nbs= p;     c)         = .333

 

4.117)          c)         = Transmission, brakes, exhaust all not faulty.

            = ;            = d)         = Transmission not faulty or brakes not faulty.

 

4.120)          P() =3D .68, P(AB) =3D .02, P(B U C) =3D .6, P(BC) =3D 0

 

4.121)          a)         = ABC

            = ;            = b)         = A U B U C

            = ;            = c)         =

            = ;            = d)         =


5.86)= a)         = -3, -1, 1, 3

   &nbs= p;        b)         = X =3D -3: TTT

   &nbs= p;            &= nbsp;       X =3D -1: HTT, THT, TTH

   &nbs= p;            &= nbsp;       X =3D 1: HHT, HTH, THH

   &nbs= p;            &= nbsp;       X =3D 3: HHH

 

5.90)= a)

X

Possible = Outcomes

Individual Probabilities

Number of= Events

Total Pro= babilities

3

AAA

.43<= /sup> =3D .064

1

.064

3

BBB

.63<= /sup> =3D .216

1

.216

4

ABBB, BAB= B, BBAB

.4 x .63 =3D .0864

3

.2592

4

BAAA, ABA= A, AABA

.43<= /sup> x .6 =3D .0384

3

.1152

5

BBAAA, BA= BAA, BAABA, ABBAA, ABABA, AABBA

.43<= /sup> x .62 =3D .02304

6

.13824

5

AABBB, AB= ABB, ABBAB, BAABB, BABAB, BBAAB

.42<= /sup> x .63 =3D .03456

6

.20736

   &nbs= p;        b)

x

f(x)

3

.2800

4

.3744

5

.3456

 

5.92)

x=

f(x)

xf(x)

x2f(x)

0

.08

0

0

1

.20

.20

.20

2

.19

.38

.76

3

.24

.72

2.16

4

.14

.56

2.24

5

.13

.65

3.25

6

.02

.12

.72

 

 

2.63

9.33

a)   &n= bsp;     E(X) =3D 2.63

b)   &n= bsp;     sd(X) =3D √9.33 – 2.632 =3D √2.41 =3D 1.55

 

6.58)= a)         = .8962

   &nbs= p;        b)         = Between .1056 and .1075

   &nbs= p;        c)         = .9726 - .7291 =3D.2435

   &nbs= p;        d)         = .8531 - .0708 =3D .7823

 

6.59)= b)         = -1.675

   &nbs= p;        d)         = 1 – .12 =3D .88    →        1.175

 

6.63)= b)         = (240 – 280)/58 =3D -.69  ͛= 4;        .2451

   &nbs= p;        d)         = (90 – 280)/58 =3D -3.28  U= 94;        1 – .0005 =3D .9995

   &nbs= p;        f)         = (305 – 280)/58 =3D .43   = (405 – 280)/58 =3D 2.16 →        .9846 – .6664 =3D .3182

 

6.65)= b)         = 90th percentile → z-score =3D = 1.28         = (x – 499)/120 =3D 1.28 →= ; x =3D 652.6

 

7.34)= a)

Possible = Samples

Probabili= ty

(0,0)

0

.0625

(0,2)

1

.0625

(0,4)

2

.0625

(0,6)

3

.0625

(2,0)

1

.0625

(2,2)

2

.0625

(2,4)

3

.0625

(2,6)

4

.0625

(4,0)

2

.0625

(4,2)

3

.0625

(4,4)

4

.0625

(4,6)

5

.0625

(6,0)

3

.0625

(6,2)

4

.0625

(6,4)

5

.0625

(6,6)

6

.0625

   &nbs= p;        b)

Distinct = Values of

0

.0625

0

0

1

.125

.125

.125

2

.1875

.375

.75

3

.25

.75

2.25

4

.1875

.75

3

5

.125

.625

3.125

6

.0625

.375

2.25

&nbs= p;

&nbs= p;

3

11.5

   &nbs= p;        c)         = μ =3D 3 &nbs= p;  σ =3D 2.23

   &nbs= p;        d)         = E( ) =3D 3 =3D &= #956;        &= nbsp;    sd() =3D √11.5 – 32 =3D 1.58 =3D 2.23= / √2

 

7.37)

1.0

.04

.04

.04

1.5

.24

.36

.54

2.0

.44

.88

1.76.

2.5

.24

.60

1.5

3.0

.04

.12

.36

&nbs= p;

&nbs= p;

2

4.2

b)   &n= bsp;     E( ) =3D 2

   &nbs= p;        Var() =3D 4.2 – 22 =3D .2

c)   &n= bsp;     Var() =3D Var (X)/n    &nb= sp;           SO       .2 = =3D Var (X)/2=         &= nbsp;     So        Var (X) = =3D .4

 

   &nbs= p;        If n =3D 81, then Var() =3D .4/81 =3D .0049

 

7.39)= a)         = E( ) =3D 32.4   sd() =3D .4 / √9 =3D .133

 

7.41)= b)         = sd() =3D 3.2 / √9 =3D 1.067       (10 – 12.1)/1.067 =3D -1.97

   &nbs= p;            &= nbsp;       P[ < 10] =3D P[z < -1.97] =3D .0244

8.78)  = ;        a) = ;        1.949<= /p>

      &= nbsp;           &nbs= p;     b)         = S.E. =3D .203

      &= nbsp;           &nbs= p;     c)         = Error Margin =3D (±2.32)(.203) =3D ±.47<= o:p>

 

8.80) a)         = 47 minutes

      &= nbsp;           &nbs= p;     b)         = (±2.00)(.791) =3D ±1.58

 

8.83)      &= nbsp;      a)         = (±2.00)(1.416) =3D ±2.83           126.9 ± 2.83

      &= nbsp;           &nbs= p;     b)         = (±1.64)(1.416) =3D ±2.32           (124= .58, 129.22)

 

8.84)      &= nbsp;      a)         = (±2.32)(.293) =3D ±.681             = (2.606,1.244)

      &= nbsp;           &nbs= p;     b)         = 98% of the intervals should cover the population mean.

 

8.88)      &= nbsp;      a)         = H0:  μ =3D 9.1     = H1:  μ ≠ 9.1

            = ;            = b)         = z =3D  =3D = 2.50

            = ;            = c)         = R:  | Z | > 1.65

        &= nbsp;           &nbs= p;   d)         = Since 2.50 is in the rejection region, we reject H0.  We conclude that H1 is supported by the data, the mean number of words per sentence is different than 9.1.

            = ;            = e)         = P[ | Z | &= gt; 2.50 ] =3D 2(.0062) =3D .0124

            = ;            = f)         = We could have incorrectly rejected H0.

 

8.89)      &= nbsp;      a)         = H0:  μ ≤ 30.5   H1:  μ > 30.5

            = ;            = b)         = z =3D  =3D = 2.51

            = ;            = c)         = R:  Z > 1.28

        &= nbsp;           &nbs= p;   d)         = Since 2.51 is in the rejection region, we reject H0.  We conclude that H1 is supported by the data, the toothpaste lasts longer than 30.5 days.

            = ;            = e)         = P[ Z > = 2.51 ] =3D .0060

            = ;            = f)         = We could have incorrectly rejected H0.

 

9.51)      &= nbsp;      b)         = 2.228

      &= nbsp;           &nbs= p;     d)         = -1.812

 

9.52)      &= nbsp;      a)         = .00625

      &= nbsp;           &nbs= p;     b)         = 1 – .005 =3D .995

      &= nbsp;           &nbs= p;     c)   &n= bsp;     .01 + .01 =3D .02

      &= nbsp;           &nbs= p;     d)         = .975 – .10 =3D .875

 

9.54)      &= nbsp;      (±2.160)(2.512) =3D 5.43 = ;            &n= bsp;          (41.57, 52.43)

      &= nbsp;           &nbs= p;     We assume that the population is normally distributed.

 

9.56)      &= nbsp;      (±2.086)(1.112) =3D ±2.32            =          (36.08, 40.72)

 

9.58)      &= nbsp;      H0:  μ ≥ 49      H1:  μ < 49

            = ;            = R:  T < -1.771

            = ;            = t =3D  =3D = -.80

        &= nbsp;           &nbs= p;   Since -.80 is not in the rejection region, we retain H0.  We cannot conclude anything about the water quality.

 

9.60)      &= nbsp;      H0:  μ =3D 3.5     = H1:  μ > 3.5

            = ;            = R:  T > 1.740

            = ;            = t =3D  =3D = 1.59

        &= nbsp;           &nbs= p;   Since 1.59 is not in the rejection region, we retain H0.  We= cannot conclude anything about the time to complete the audit operation.

 

 

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