# Statistics Binomial Random Variable Questions

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User_ID

AnswerSheets

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2357749

4

209-4

Multiple Choice. Select the answer that you believe is most likely to be correct.

1

A significance test based on a small sample may not produce a statistically significant result even if the true value dif

as

A) t-test

B) Sasquatch evidence

C) type I error

D) type II error

2

Which of the following conditions is not a condition for the hypergeometric distribution?

A) the probability of success is the same on each trial

B) sampling is done without replacement

C) trials are dependent

D) there are only two possible outcomes

3

The Central Limit theorem for a sample mean is a critical result because

A) it states that for large sample sizes, the sample is approximately normal.

B) it states that for any population, the sampling distribution is normal regardless of sample size.

C) it states that for large sample sizes, the population distribution is approximately normal.

D) None of the answers are correct.

4

If the p-value for a one-tailed test is 0.005, then the null hypothesis

A) can be rejected at a significance level of 0.01.

B) can be rejected at a significance level of 0.10.

C) may or may not be rejected, but there is no enough information to answer this question

D) would be rejected or not rejected depending on the value of the statistic and the critical value.

5

The number of bags arriving on the baggage claim conveyor belt in a 3 minute time period would best be modeled w

A) hyperbinomial distribution

B) binomial distribution

C) exponential distribution

D) Poisson distribution

6

In a hypothesis test, if difference between the sample mean and the hypothesized mean divided by the standard erro

values, we ___ the null hypothesis. If this number falls in the critical regions and beyond the critical values, we ___ th

A) Fail to Reject, Reject

B) Reject, Reject

C) Fail to Reject, Fail to Reject

D) Reject, Fail to Reject

nt result even if the true value differs substantially from the null value. This type of result is known

select answer below

ution?

select answer below

select answer below

ze.

ue.

select answer below

period would best be modeled with the

select answer below

mean divided by the standard error falls in the middle of the distribution and in between the critical

eyond the critical values, we ___ the null hypothesis.

select answer below

No additional data

Please answer all questions based on the data provided below. If you cannot answer the question due to insufficient dat

Do not change the formatting of the yellow cells. Round to four digits after decimal.

1)

The probability that a student is accepted to a prestigious college is 21%. If 8 students from the same school apply, wh

at most 2 are accepted?

answer

Bloomberg L.P. lists the top 25 U.S. companies by revenue. Walmart stores is number one followed by Exxon Mobil an

2) companies on the list, 8 are in some type of electronics-related business. Suppose five firms are randomly selected. W

fewer than two of the firms are in some type of electronics-related business?

answer

Your were instructed to conduct a study in which a population mean will be estimated using a 90% confidence interva

3) be within 12 of the actual population mean. The population standard deviation is estimated to be around 45. You esti

sample size should be at least (round up!):

answer

4)

The average number of accidents at a level-crossing every year is 8. Calculate the probability that there are exactly 3 a

Assume a Poisson distribution.

answer

The investment management company reports that the daily increase in the dollar value of its stock portfolio is norma

5) mean of $1.7 million and a standard deviation of $7.1 million. Find the value x such that the probability that the portf

dollars in one day is 5% (A negative increase is a loss.).

answer

6)

(enter the absolute value!)

The number of days ahead travelers purchase their airline tickets can be modeled by an exponential distribution with

time equal to 15 days. Find the probability that a traveler will purchase a ticket more than 9 days in advance.

answer

estion due to insufficient data, enter ‘NA’.

om the same school apply, what is the probability that

e followed by Exxon Mobil and Chevron. Of the 25

ms are randomly selected. What is the probability that

sing a 90% confidence interval. The estimate needs to

ted to be around 45. You estimate the necessary

ility that there are exactly 3 accidents there this year.

of its stock portfolio is normally distributed with a

the probability that the portfolio will lose more than x

exponential distribution with the average amount of

n 9 days in advance.

No additional data

Dataset_3 contains a variable, Annual Household Income, which represents the amount of $ income earned per househo

variable that is approximately normally distributed.

Please answer all questions based on the data provided below and Dataset_3. If you cannot answer the question due to

yellow cells. Round to four digits after decimal.

1) Using the mean and standard deviation, calculate the probability that a randomly selected household earns more than

answer

2) What is the probability that a randomly selected household earns less than $118,000 annually?

answer

3) What is the probability that a randomly selected household earns between $125,000 and $150,000 annually?

answer

4)

Create a probability table to obtain the probabilities of counting between 1 and 6 people in each household using Dat

members?

answer

5) Find the mean number of members per household.

answer

6)

Assuming a Poisson distribution and using the mean number of members/household from part 5), compute the proba

your answer to part 4). How much higher or lower is the probability that three or more people live in household follow

answer

of $ income earned per household per year. Calculate the mean and standard deviation for this

nnot answer the question due to insufficient data, enter ‘NA’. Do not change the formatting of the

ected household earns more than $129,000 annually.

annually?

and $150,000 annually?

ople in each household using Dataset_3. What is the probability that an household has more than three

from part 5), compute the probabilities that one and more people live in a household. Compare these to

re people live in household following a Poisson distribution?

Dataset_3

You can assume a clean dataset.

Annual Food Spending ($)

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

16,584

7,241

6,014

9,473

4,742

14,083

17,432

12,762

11,407

5,546

11,727

13,857

25,475

6,111

7,525

9,197

8,894

18,318

14,062

15,018

4,863

9,547

20,699

9,074

18,029

5,553

23,611

14,035

2,586

17,357

10,095

23,709

8,048

7,182

10,444

4,890

14,672

13,102

14,385

10,378

14,030

9,603

14,305

12,939

5,285

Annual Household Income ($)

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

71,769

165,741

119,167

157,277

72,523

175,545

181,695

193,181

93,663

157,678

92,126

198,990

217,250

115,959

64,000

144,252

60,079

129,450

89,801

171,118

100,945

193,705

163,954

86,795

85,240

72,772

98,384

155,330

70,492

175,378

188,661

175,031

178,821

110,791

61,811

120,930

87,848

124,975

200,632

66,359

196,253

175,618

160,621

105,528

182,539

household members

5

4

2

3

2

3

4

3

4

2

3

5

6

3

2

3

2

4

3

4

2

4

5

3

4

2

5

4

1

4

4

5

3

2

4

2

4

5

3

3

3

5

3

3

3

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

8,219

7,322

14,526

18,710

19,629

20,294

6,787

3,823

12,984

9,479

8,105

2,133

12,323

4,168

13,645

4,712

6,937

9,088

19,380

9,810

11,436

3,998

7,525

9,153

10,991

23,589

7,539

6,185

9,197

4,172

9,427

10,171

4,363

9,050

2,951

6,343

5,436

7,582

11,958

7,714

13,780

9,706

13,092

9,137

6,581

23,105

4,915

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

181,132

139,314

83,255

143,073

61,001

159,341

155,994

116,437

211,176

116,216

72,103

52,255

190,096

162,653

153,396

55,698

54,904

37,529

111,189

116,667

138,288

89,116

196,945

167,412

114,565

51,802

47,659

106,169

157,339

19,357

148,890

149,587

146,688

102,130

96,966

134,173

74,792

103,052

80,037

118,858

184,939

169,256

125,322

125,767

91,270

162,337

27,906

4

3

4

4

4

5

3

2

4

3

3

1

6

2

3

1

3

2

4

4

5

2

3

4

5

5

2

2

2

1

3

6

2

4

1

3

3

2

4

4

5

4

5

2

3

5

1

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

3,635

2,178

10,912

18,564

16,905

8,411

13,773

19,244

11,925

8,719

8,631

21,789

17,119

14,553

8,300

18,316

4,829

8,353

14,249

9,703

13,391

14,041

5,409

9,413

3,160

3,473

14,768

16,340

7,690

5,413

6,355

6,374

13,436

3,873

6,992

8,127

8,769

8,380

6,902

7,821

7,819

7,663

17,311

7,467

8,175

8,922

7,704

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

22,890

67,948

190,544

81,980

89,315

115,015

172,055

126,318

114,885

214,447

127,053

186,818

67,270

168,168

83,993

127,132

145,440

106,951

78,890

59,447

201,501

192,079

57,603

94,682

74,041

48,768

130,669

165,311

95,379

112,598

180,251

118,581

115,373

78,805

111,268

126,491

101,210

62,987

204,859

94,684

135,887

184,521

149,176

156,254

98,973

110,642

62,683

1

1

6

4

5

4

3

4

5

3

3

5

5

4

2

4

2

4

3

2

5

5

3

3

1

1

3

4

2

3

3

2

5

1

2

2

4

3

3

4

3

4

5

4

4

2

2

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

3,410

16,342

5,429

4,584

18,307

19,102

19,949

10,343

6,725

6,480

17,671

12,931

6,151

4,262

3,576

9,561

9,782

8,323

10,796

17,050

13,110

4,832

13,172

8,240

8,805

8,934

16,129

7,911

14,674

6,786

21,900

6,352

7,309

8,943

3,780

9,869

11,805

16,814

13,854

5,724

3,760

13,280

6,445

12,776

11,094

6,989

7,813

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

$

136,110

132,305

114,521

115,115

176,492

184,862

186,026

212,302

90,838

182,139

166,128

126,364

52,074

137,109

66,203

108,154

79,772

92,573

152,096

166,781

146,162

63,338

72,411

168,130

120,407

84,005

131,406

108,081

85,003

195,101

169,450

66,105

55,521

127,379

90,256

160,794

140,321

184,534

144,376

64,179

119,243

128,559

115,203

131,547

73,788

131,362

189,988

2

5

3

2

4

4

5

3

2

3

4

3

2

2

1

2

3

4

3

4

3

2

3

5

3

3

4

4

5

3

5

2

3

2

2

2

3

4

3

2

2

5

2

3

3

2

3

$

$

$

$

$

$

$

$

$

$

$

$

$

$

11,970

13,840

14,942

4,097

6,979

10,627

17,339

17,088

6,477

9,870

7,968

14,642

5,308

11,155

$

$

$

$

$

$

$

$

$

$

$

$

$

$

65,077

62,677

98,871

130,583

71,460

158,223

112,012

163,311

111,553

107,560

166,945

189,702

89,923

144,997

3

3

4

2

2

3

4

6

2

2

4

4

3

3

You have just taken ownership of a coffee shop. The previous owner told you that you would save money if you bought t

purchase a pack of beans, you weigh it to ensure that you are receiving 72 ounces of beans. The results of 7 random mea

these differences due to chance? Analyze the results by using the ‘process for testing hypotheses’ discussed in class.

Please answer all questions based on the data provided below and Dataset_4. If you cannot answer the question due to

formatting of the yellow cells. Round to four digits after decimal.

1) Establish a null and alternative hypothesis, determine the appropriate statistical test, and formulate the decision rule

confidence interval

lower bound

upper bound

2) Would the null hypothesis be rejected at the α = 0.10? The α = 0.05? The α = 0.01?

reject?

α = 0.10

α = 0.05

α = 0.01

3) Use the test statistic to determine the p-value:

answer

You believe that your supplier is overcharging you by delivering a product that is below the target weight. To strength

4) Dataset_4, “sample2”) and increase the confidence level to 98%. Analyze the data. Does this sample present enough e

product? (hint: step 6-8)

test statistic

5) (continue 4) Find the probability of a Type I error when the true mean is 71.4.

answer

6) (continue 4) Find the probability of a Type II error when the true mean is 71.4.

answer

would save money if you bought the coffee beans in 4.5-pound packs. Each time you

ans. The results of 7 random measurements are 70, 69, 73, 68, 71, 69 and 71 ounces. Are

potheses’ discussed in class.

nnot answer the question due to insufficient data, enter ‘NA’. Do not change the

and formulate the decision rule below at a confidence level of 90%.

ow the target weight. To strengthen your suspicions, you decided to take a new sample (see

oes this sample present enough evidence to accuse the supplier of overcharging its

Dataset_4

sample2

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

You can assume a clean dataset.

ounces

69.82

72.36

69.19

70.23

72.02

66.86

72.22

67.44

63.02

69.04

82.10

69.42

67.76

71.14

70.74

73.04

62.85

73.54

67.24

71.01

72.44

70.55

74.16

70.09

69.36

71.60

69.75

61.65

74.46

71.57

70.13

72.04

71.57

70.05

70.46

74.00

67.79

69.99

75.27

77.92

69.26

76.55

67.78

67.53

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

61

62

63

64

65

66

67

68

69

70

71

72

73

74

75

76

77

78

79

80

81

82

83

84

85

86

87

88

89

90

68.30

73.84

73.48

77.25

73.37

72.86

68.08

69.25

65.56

71.07

66.10

75.87

75.82

74.25

67.17

75.33

59.28

69.52

75.86

67.71

74.08

68.70

66.67

67.00

66.48

71.29

70.84

63.06

73.16

67.52

69.59

73.49

67.67

70.27

70.34

67.99

67.70

69.76

66.03

74.37

71.28

63.15

70.28

71.61

75.74

62.50

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