Last name:
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First name:
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e270Lastname Firstname HW6
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as an attachment.
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e270Smith Adam HW6
e270 Smith Adam HW6
YES
NO
PAY ATTENTION
Which of the following statements about Type I and Type II errors is correct
Type I: Reject a true alternative hypothesis. Type II: Do not reject a false alternative.
Type I: Do not reject a false null hypothesis. Type II: Reject a true null hypothesis.
Type I: Reject a false null hypothesis. Type II: Reject a true null hypothesis.
Type I: Reject a true null hypothesis. Type II: Do not reject a false null hypothesis.
You are reading a report that contains a hypothesis test you are interested in. The writer of the report
writes that the p-value for the test you are interested in is 0.0625, but does not tell you the value of the
test statistic. From this information you can:
Not reject the hypothesis at a Probability of Type I error = 0.05, and not reject at a Probability of Type I
error = 0.10
Reject the hypothesis at a Probability of Type I error = .05, and reject at a Probability of Type I error =
0.10
Not reject the hypothesis at a Probability of Type I error = .05, but reject the hypothesis at a Probability
of Type I error = 0.10
Reject the hypothesis at a Probability of Type I error = .05, but not reject at a Probability of Type I error
= 0.10
3
The random sample below is obtained to test the following hypothesis about the population mean.
H₀: μ ≥ 1500
H₁: μ < 1500
1509
1028
1640
784
1025
271
2384
888
541
2179
1290
1358
1898
486
460
1383
323
739
1088
2439
966
616
564
2086
1473
724
1879
2301
2454
301
1103
2181
2532
1026
258
2168
1980
1517
2300
1905
673
2274
2473
2125
1669
1724
1928
2287
689
2071
941
2575
1245
1570
1521
1394
1924
1004
1415
1103
2353
1557
1568
979
1185
1790
1939
2088
1550
854
916
2529
447
349
1116
2056
1384
505
1492
547
1170
242
2042
426
1044
523
2227
1328
2560
1416
585
2372
1261
2340
2560
1867
1112
1052
956
1073
1056
2308
1203
293
1713
493
512
788
770
1210
1915
2148
371
1304
966
1607
1926
426
1716
1741
a
b
c
d
The level of significance of the test is α = 0.05. Compute the relevant test statistic.
This is a(n) _______ (two-tail, upper-tail, lower-tail) test. The test statistic is TS = _______.
Lower tail test.
|TS| = 1.97
Reject H₀: μ ≥ 1500. Conclude that the population mean is less than 1500.
Lower tail test.
|TS| = 1.97
Do not reject H₀: μ ≥ 1500. Conclude that the population mean is not less than 1500.
Lower tail test.
|TS| = 1.48
Do not reject H₀: μ ≥ 1500. Conclude that the population mean is not less than 1500.
Upper tail test.
|TS| = 1.48
Reject H₀: μ ≥ 1500. Conclude that the population mean is no greater than 1500.
1164
1479
1181
986
1789
1541
1539
1243
2384
1371
1349
1035
2122
1522
302
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a
b
c
d
e
5
Consider the following hypothesis test.
H₀: μ ≤ 40
H₁: μ > 40
A random sample of n = 20 yielded the following observations
65
44
63
73
69
67
60
50
11
63
59
52
26
24
63
59
14
35
49
30
Use α = 0.05
TS = ______ CV = ______ State the decision rule.
2.068
1.729 Do not reject H₀. Conclude the mean is not greater than 40.
2.068
1.729 Reject H₀. Conclude the mean is greater than 40.
2.068
1.64 Reject H₀. Conclude the mean is greater than 40.
1.847
1.64 Do not reject H₀. Conclude the mean is not greater than 40.
1.847
1.729 Reject H₀. Conclude the mean is greater than 40.
In a recent study, a major fast food restaurant had a mean service time of 145 seconds. The company
embarks on a quality improvement effort to reduce the service time and has developed improvements to
the service process. The new process will be tested in a sample of stores. The new process will be adopted
in all of its stores, if it reduced mean service time by more than 30 seconds compared to the current
mean service time. To perform the hypothesis test, the sample of 40 stores yields the following data
(seconds).
93
113
126
90
112
120
105
115
116
80
92
109
101
137
97
109
138
87
122
116
105
82
117
120
80
114
102
139
84
110
135
113
131
118
126
130
87
96
125
101
a
b
c
d
Use α = 0.05
|TS| = ______ CV = ______
1.94
1.685 Reject H₀. The mean service time is reduced by more than 30 seconds. Adopt
the new process.
1.94
1.685 Do not reject H₀. The mean service time is not reduced by more than 30
seconds. Do not adopt the new process.
1.871
1.938 Do not reject H₀. The mean service time is not reduced by more than 45
seconds. Do not adopt the new process.
1.871
1.640 Reject H₀. The mean service time is reduced by more than 45 seconds. Adopt
the new process.
6
a
b
c
d
7
According to Automotive News, the mean price of 2008-12 used cars nationwide is $18,575. to compare
the average price of similar used cars in central Indiana, a random sample of 120 such cars were selected.
The sample mean is $17,450 with a standard deviation of $6,954. Does the sample provide significant
evidence that the mean price of 2008-12 used cars is different from the national mean price?
Use α = 0.05
p-value = 0.0384
Reject H₀. Conclude that the mean price in central Indiana is different from the
national mean price.
p-value = 0.0768
Do not reject H₀. Conclude that the mean price in central Indiana is not different
from the national mean price.
p-value = 0.0274
Reject H₀. Conclude that the mean price in central Indiana is different from the
national mean price.
p-value = 0.0548
Do not reject H₀. Conclude that the mean price in central Indiana is not different
from the national mean price.
d
The 2012 mean annual salary of graduates with engineering degrees was $61,200. In a follow-up study in
June 2013, a sample of n = 125 graduating engineering majors yielded a sample mean of $62,414 and
standard deviation of $8,640. Does the 2013 survey provide a significant proof that the mean salary in
2013 is higher than in 2012? Perform this test of hypothesis at a 5% level of significance.
p-value = 0.0582
Do not reject H₀. Conclude that the mean annual salary in 2013 is no greater than
in 2012.
p-value = 0.0582
Reject H₀. Conclude that the mean annual salary in 2013 is greater than in 2012.
p-value = 0.0291
Do not reject H₀. Conclude that the mean annual salary in 2013 is no greater than
in 2012.
p-value = 0.0291
Reject H₀. Conclude that the mean annual salary in 2013 is greater than in 2012.
a
b
c
d
A production line operates with a mean filling weight of 32 ounces per container. Overfilling or under
filling is a serious problem, and the production line should be shut down if either occurs. A quality control
inspector samples 16 items every 2 hours and at that time makes the decision of whether to shut the line
down for adjustment. One sample provides the following data:
Use Excel to find xx and s to avoid rounding problems.
32.0
33.2
32.1
32.0
32.6
33.5
33.5
31.8
32.1
31.1
32.8
31.3
31.8
32.4
32.5
33.2
α = 0.05
TS = ______
1.89 Do not reject H₀. Do not shut the line down for adjustment.
1.89 Reject H₀. Shut the line down for adjustment.
2.02 Do not reject H₀. Do not shut the line down for adjustment.
2.02 Reject H₀. Shut the line down for adjustment.
a
b
c
8
9
a
b
c
d
The mean cholesterol level in women ages 21-40 in the United States is 190 mg/dl. A study is conducted
to determine the cholesterol levels among recent female Asian immigrants. The following is the
cholesterol level of a random sample of 108 recent female Asian immigrants.
152
208
150
182
162
156
195
211
195
270
222
166
207
172
222
163
195
206
175
144
215
149
133
181
135
169
168
144
195
143
160
172
165
218
202
211
156
167
218
169
189
181
205
181
122
110
222
215
147
168
135
146
203
154
143
190
115
195
214
169
192
190
186
222
207
172
181
211
174
169
244
172
172
179
115
165
257
199
293
199
185
192
160
195
143
207
215
183
146
143
247
234
147
222
244
136
156
169
200
228
172
177
203
241
165
179
242
203
Does the sample provide significant evidence that mean cholesterol level of recent female Asian immigrants
is lower than the mean cholesterol level among all females in the United States? State the null and
alternative hypotheses. Compute the test statistic and the p-value. State the decision rule.
p-value = ______
0.032 The evidence is significant at α = 0.01, but not significant at α = 0.05.
0.032 The evidence is significant at α = 0.05, but not significant at α = 0.01.
0.058 The evidence is significant at α = 0.10, but not significant at α = 0.05.
0.058 The evidence is significant at α = 0.05, but not significant at α = 0.10.
10
a
b
c
d
11
a
b
c
d
e
f
12
a
b
c
We want to test the hypothesis that mothers with low socio-economic status (SES) deliver babies whose
birth weights are lower than "normal". To test this hypothesis, a list is obtained of birth weights from 120
consecutive, full-term, live-born deliveries from the maternity ward of a hospital in a low-SES area. The
mean birth weight is xx = 116.1 oz. with a standard deviation s = 18.8 oz. Nationwide, the mean birth
weight in the United States is 120 oz. At α = 0.05, does this sample provide significant evidence that the
mean birth weight of babies born to mother with low SES is lower than "normal"?
p-value = 0.0116
Reject H₀ at the 5 percent level of significance. Conclude that the mean birth
weight of babies born to low-SES mothers is lower than "normal".
p-value = 0.0116
Reject H₀ at the 1 percent level of significance. Conclude that the mean birth
weight of babies born to low-SES mothers is lower than "normal".
p-value = 0.0674
Do not reject H₀ at the 5 percent level of significance. Conclude that the mean birth
weight of babies born to low-SES mothers is not lower than "normal".
p-value = 0.0674
Reject H₀ at the 10 percent level of significance. Conclude that the mean birth
weight of babies born to low-SES mothers is lower than "normal".
In a recent study, it was reported that nationwide, undergraduate students have a mean credit card balance
of $3,850. A random sample of 140 Indiana undergraduate students revealed a sample mean of $3,675
and standard deviation of $1,285. Does the sample provide significant evidence that the mean credit card
balance of Indiana undergraduates is different than the national average?
Using the sample information, first build a 95% confidence interval for the mean credit card balance of all
Indiana undergraduates.
L=
U=
The confidence interval captures µ₀ = 3,850. Do not reject H₀. Conclude that the mean credit card
balance of Indiana undergraduates in not different from the national average.
Compared to the MOE, xx − µ₀ is within the margin of error. Conclude that the mean credit card balance
of Indiana undergraduates in not different from the national average.
The confidence interval does not capture µ₀ = 3,850. Reject H₀. Conclude that the mean credit card
balance of Indiana undergraduates in different from the national average.
Compared to the MOE, xx − µ₀ is outside the margin of error. Conclude that the current mean score is
different from the historical mean score.
Both a and b are correct.
Both c and d are correct.
Consider the following hypothesis test.
H₀: π ≤ 0.48
H₁: π > 0.48
A sample of n = 300 provided a sample proportion of px = 0.524. At α = 0.05, what is your conclusion?
TS = ______ CV = ______ State the decision rule.
1.53
1.64 Conclude the population proportion is greater than 0.48.
1.53
1.64 Conclude the population proportion is not greater than 0.48.
1.98
1.64 Conclude the population proportion is not greater than 0.48.
d
13
a
b
c
d
1.98
1.96
Conclude the population proportion is greater than 0.48.
In the previous question, the prob value for the test is:
0.0630
0.0315
0.0239
0.0120
Next THREE questions are based on the following
Consider the following hypothesis test.
H₀: π ≥ 0.64
H₁: π < 0.64
Compute the test statistic and the p-value for the following three cases.
14
n = 300
px = 0.595
α = 0.05
a
p-value = 0.0823
Conclude that the population proportion is less than 0.64.
b
p-value = 0.0823
Conclude that the population proportion is not less than 0.64.
c
p-value = 0.0526
Conclude that the population proportion is less than 0.64.
d
p-value = 0.0526
Conclude that the population proportion is not less than 0.64.
15
a
b
c
d
n = 500
p-value = 0.0411
p-value = 0.0411
p-value = 0.0808
p-value = 0.0808
px = 0.610
α = 0.10
Conclude that the population proportion is less than 0.64.
Conclude that the population proportion is not less than 0.64.
Conclude that the population proportion is less than 0.64.
Conclude that the population proportion is not less than 0.64.
16
a
b
c
d
n = 1000
p-value = 0.0655
p-value = 0.0655
p-value = 0.0351
p-value = 0.0351
∑x = 617
Reject H₀ at α = 0.10, but do not reject at α = 0.05.
Reject H₀ at α = 0.05, but do not reject at α = 0.10.
Reject H₀ at α = 0.05, but do not reject at α = 0.01.
Reject H₀ at α = 0.10, but do not reject at α = 0.05.
17
a
b
c
d
18
a
b
c
d
19
a
b
c
d
20
a
b
c
d
One of the different statistics reported by the Centers for Disease Control regarding incidence of obesity
among adults in the United States provides that 27.4% of men with college degree are obese. The study
also reports that 32.1% of men without a college degree are obese. Assume the latter statistic is based on
a sample of 700 men without a college degree.
At a 5% level of significance, does the data provide statistically significant evidence that the incidence of
obesity among men without a college degree is greater than among those with a college degree?
Compute the p-value for this hypothesis test.
p-value = ______.
0.0344 Do not reject H₀. The evidence is not statistically significant.
0.0344 Do not reject H₀. The evidence is statistically significant.
0.0027 Reject H₀. The evidence is statistically significant.
0.0027 Reject H₀. The evidence is not statistically significant.
We want to test the hypothesis that at least 85% of drivers on a freeway violate the speed limit. In a
random sample of n = 1,100 vehicles, 83% violated the speed limit. Compute the test statistic.
State the null and alternative hypotheses and the decision rule. Use α = 0.05.
TS = 1.85
Reject H₀. The proportion of violators is less than 0.85.
TS = 1.85
Do not reject H₀. The proportion of violators is not less than 0.85.
TS = 1.45
Do not reject H₀. The proportion of violators is not less than 0.85.
TS = 1.45
Reject H₀. The proportion of violators is less than 0.85.
In a sample of 845 coffee growers from southern Mexico, 494 growers were certified to sell to organic
coffee markets. Is there evidence to indicate that fewer than 60% of the coffee growers in southern
Mexico are organic certified? State your conclusion so that there is only 5% chance of making Type I error.
Round your px to three decimal points.
p-value = 0.0867
At a 10% level of significance, evidence that fewer than 60% are organic certified
is statistically significant.
p-value = 0.0867
At a 5% level of significance, the evidence that fewer than 60% are organic
certified is not statistically significant.
p-value = 0.1867
At a 10% level of significance, evidence that fewer than 60% are organic certified
is statistically significant.
p-value = 0.1867
At a 5% level of significance, the evidence that fewer than 60% are organic
certified is not statistically significant.
In the previous question, the margin of error for rejecting the null hypothesis is.
0.023
0.028
0.033
0.037
