# Statistics Binomial Random Variable Questions

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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
ution?
ze.
ue.
period would best be modeled with the
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.
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?
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?
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!):
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.
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.).
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.
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
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
2) What is the probability that a randomly selected household earns less than \$118,000 annually?
3) What is the probability that a randomly selected household earns between \$125,000 and \$150,000 annually?
4)
Create a probability table to obtain the probabilities of counting between 1 and 6 people in each household using Dat
members?
5) Find the mean number of members per household.
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
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 (\$)
\$
\$
\$
\$
\$
\$
\$
\$
\$
\$
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\$
\$
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\$
\$
\$
\$
\$
\$
\$
\$
\$
\$
\$
\$
\$
\$
\$
\$
\$
\$
\$
\$
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 (\$)
\$
\$
\$
\$
\$
\$
\$
\$
\$
\$
\$
\$
\$
\$
\$
\$
\$
\$
\$
\$
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\$
\$
\$
\$
\$
\$
\$
\$
\$
\$
\$
\$
\$
\$
\$
\$
\$
\$
\$
\$
\$
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
\$
\$
\$
\$
\$
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\$
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\$
\$
\$
\$
\$
\$
\$
\$
\$
\$
\$
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
\$
\$
\$
\$
\$
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\$
\$
\$
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
\$
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\$
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
\$
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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
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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
\$
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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:
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.
6) (continue 4) Find the probability of a Type II error when the true mean is 71.4.
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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