# E270 hw 6 | Numerical analysis homework help

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1
Which of the following statements about Type I and Type II errors is correct
a
Type I: Reject a true alternative hypothesis. Type II: Do not reject a false alternative.
b
Type I: Do not reject a false null hypothesis. Type II: Reject a true null hypothesis.
c
Type I: Reject a false null hypothesis. Type II: Reject a true null hypothesis.
d
Type I: Reject a true null hypothesis. Type II: Do not reject a false null hypothesis.
2
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 0.061, but does not tell you the value of the test statistic. From this information you can:
a
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
b
Reject the hypothesis at a Probability of Type I error = .05, and reject at a Probability of Type I error = 0.10
c
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
d
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 ≤
120
H₁: μ >
120
152
203
67
177
220
101
23
214
134
49
53
177
23
128
181
10
103
214
198
99
126
183
70
16
148
118
69
182
166
199
59
172
40
177
28
42
126
104
157
123
199
76
106
162
135
174
55
64
126
176
62
13
59
154
14
196
164
186
71
150
186
90
140
177
189
209
50
26
233
16
28
135
169
171
198
116
115
236
176
80
130
59
227
212
167
35
61
136
72
123
220
100
135
171
70
58
92
28
141
52
27
181
138
231
80
115
153
187
235
212
235
167
136
16
73
166
156
209
128
166
66
234
76
207
154
188
210
202
198
14
192
10
11
136
170
214
231
28
94
125
214
31
64
72
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 = _______.
a
Upper tail test.
TS =
1.34
Do not reject H₀: μ ≤ 120. Conclude that the population mean is not greater than 120.
b
Upper tail test.
TS =
1.88
Reject H₀: μ ≤ 120. Conclude that the population mean is greater than 120.
c
Upper tail test.
TS =
1.88
Reject H₀: μ ≤ 120. Conclude that the population mean is greater than 120.
d
Lower tail test.
TS =
1.88
Do not reject H₀: μ ≤ 120. Conclude that the population mean is less than 120.
4
Consider the following hypothesis test.
H₀: μ ≥
15
H₁: μ <
15
A random sample of n = 15 yielded the following observations
8
7
11
11
8
13
8
12
13
5
21
21
19
15
18
Use α =
0.05
TS = ______
CV = ______
State the decision rule.
a
-1.743
-1.761
Do not reject H₀. Conclude the mean is not less than 15.
b
-1.74
-1.64
Reject H₀. Conclude the mean is less than 15.
c
1.847
2.145
Do not reject H₀. Conclude the mean is not less than 15.
d
1.847
1.761
Reject H₀. Conclude the mean is less than 15.
5
In a recent study, a major fast food restaurant had a mean service time of 164 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 resulted in decreased service time. To perform the hypothesis test in the previous question, the sample of 54 stores yields the following data (seconds).
157
115
115
115
134
174
128
136
161
127
139
125
145
199
161
182
144
199
156
117
129
193
173
146
128
166
185
147
136
180
184
116
172
116
193
183
184
160
120
161
161
122
191
170
124
130
191
170
190
194
139
114
195
183
Use α =
0.05
|TS| = ______
|CV| = ______
a
2.335
1.674
Do not reject H₀. The mean is not less than 164 seconds. Do not adopt the new process.
b
2.335
1.674
Reject H₀. The mean is less than 164 seconds. Adopt the new process.
c
1.674
1.349
Reject H₀. The mean is less than 164 seconds. Adopt the new process.
d
1.349
1.674
Do not reject H₀. The mean is not less than 164 seconds. Do not adopt the new process.
6
According to Kelley Blue Book, the mean price for one-to three-year-old used cars nationwide is $23,400. to compare the average price of similar used cars in central indiana, a random sample of 120 such cars were selected. The sample mean was $21,824 with a standard deviation of 7,309. Does the sample provide significant evidence that the mean price of one-to-three-year old used cars is different from the national mean price?
Use α =
0.05
a
p-value =
0.044
Reject H₀. Conclude that the dealership’s price is different from the national mean price.
b
p-value =
0.124
Do not reject H₀. Conclude that the dealership’s price is not different from the national mean price.
c
p-value =
0.0091
Do not reject H₀. Conclude that the dealership’s price is not different from the national mean price.
d
p-value =
0.0182
Reject H₀. Conclude that the dealership’s price is different from the national mean price.
7
The 2009 mean annual salary of business degree graduates in accounting was $47,900. In a follow-up study in June 2011, a sample of n = 120 graduating accounting majors yielded a sample mean of $49,500 and standard deviation of $8,200. Does the 2011 study provide a significant proof that the mean salary in 2011 is higher than in 2009? Perform this test of hypothesis at a 5% level of significance.
a
p-value =
0.0524
Do not reject H₀. Conclude that the mean annual salary in 2011 is no greater than in 2009.
b
p-value =
0.0524
Reject H₀. Conclude that the mean annual salary in 2011 is greater than in 2009.
c
p-value =
0.0162
Reject H₀. Conclude that the mean annual salary in 2011 is greater than in 2009.
d
p-value =
0.0162
Do not reject H₀. Conclude that the mean annual salary in 2011 is no greater than in 2009.
8
A production line operates with a mean filling weight of 16 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 20 items every 2 hours and at that time makes the decision of whether to shut the line down for adjustment. On sample provides the following data:
15.8
16.1
16.2
16.1
16.1
16.6
16.3
16.3
15.9
16.1
16.2
15.8
16
16.3
15.9
16
15.9
16.1
15.9
16.2
α =
0.05
Decision Rule: Reject H₀ if TS > CV
TS = ______
CV = ______
a
2.000
2.093
Do not reject H₀. Do not shut the line down for adjustment.
b
2.000
1.96
Reject H₀. Shut the line down for adjustment.
c
1.786
1.729
Reject H₀. Shut the line down for adjustment.
d
2.04
1.64
Do not reject H₀. Shut the line down for adjustment.
9
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.
239
105
251
216
220
120
218
195
129
125
196
193
108
178
187
111
176
178
141
190
214
180
172
204
118
108
124
238
248
253
208
135
146
122
209
254
209
232
238
251
110
224
249
219
219
124
226
252
189
212
163
205
202
190
195
116
125
250
244
140
237
192
191
224
105
201
194
136
245
118
150
165
132
171
245
166
218
159
130
255
131
185
210
223
153
167
174
239
200
107
235
123
224
221
106
212
212
130
154
200
140
170
202
247
112
153
150
205
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.
Round x̅ to two decimal points and the standard error to three decimal points.
p-value = ______
a
0.069
The evidence is significant at α = 0.05, but not significant at α = 0.01.
b
0.069
The evidence is significant at α = 0.10, but not significant at α = 0.05.
c
0.034
The evidence is significant at α = 0.05, but not significant at α = 0.01.
d
0.034
The evidence is significant at α = 0.01, but not significant at α = 0.05.
10
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 100 consecutive, full-term, live-born deliveries from the maternity ward of a hospital in a low-SES area. The mean birth weight is x̅ = 115 oz. with a standard deviation s = 24 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”?
a
p-value =
0.0188
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”.
b
p-value =
0.0188
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”.
c
p-value =
0.0785
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 no lower than “normal”.
d
p-value =
0.0785
Do not reject H₀ at the 10 percent level of significance. Conclude that the mean birth weight of babies born to low-SES mothers is no lower than “normal”.
11
At Western University the historical mean scholarship examination score of entering students has been 900. Each year a sample of applications is taken to see whether the examination scores are at the same level as in previous years. The null hypothesis tested is H₀: μ = 900. A sample of n = 81 students in this year’s class provided a sample mean score of x̅ = 935 and a standard deviation of s = 180.
First build a 95% confidence interval for the population mean score.
a
The confidence interval captures µ₀ = 900. Do not reject H₀. Conclude that the current mean score is not different from the historical mean score.
b
Compared to the MOE, x̅ − µ₀ is within the margin of error. Conclude that the current mean score is not different from the historical mean score.
c
Compared to the MOE, x̅ − µ₀ is outside the margin of error. Conclude that the current mean score is different from the historical mean score.
d
Both a and b are correct.
12
Consider the following hypothesis test.
H₀: π ≤
0.5
H₁: π >
0.5
A sample of n = 200 provided a sample proportion of p̅ = 0.57. At α = 0.05, what is your conclusion?
TS = ______
CV = ______
State the decision rule.
a
1.98
1.64
Conclude the population proportion is no greater than 0.50.
b
1.98
1.64
Conclude the population proportion is greater than 0.50.
c
2.98
1.96
Conclude the population proportion is no greater than 0.50.
d
2.98
1.96
Conclude the population proportion is greater than 0.50.
13
In the previous question, the prob value for the test is:
a
0.0239
b
0.0427
c
0.0618
d
0.0808
Next THREE questions are based on the following
Consider the following hypothesis test.
H₀: π ≥ 0.75
H₁: π < 0.75
Compute the test statistic and the p-value for the following three cases.
14
n =
200
p̅ =
0.70
α =
0.05
a
p-value =
0.0258
Conclude that the population proportion is not less than 0.75.
b
p-value =
0.0258
Conclude that the population proportion is less than 0.75.
c
p-value =
0.0516
Conclude that the population proportion is not less than 0.75.
d
p-value =
0.0516
Conclude that the population proportion is less than 0.75.
15
n =
200
p̅ =
0.70
α =
0.10
a
p-value =
0.0516
Conclude that the population proportion is less than 0.75.
b
p-value =
0.0516
Conclude that the population proportion is not less than 0.75.
c
p-value =
0.0258
Conclude that the population proportion is less than 0.75.
d
p-value =
0.0258
Conclude that the population proportion is not less than 0.75.
16
n =
900
p̅ =
0.72
a
p-value =
0.0188
Reject H₀ at α = 0.10, but do not reject at α = 0.05.
b
p-value =
0.0188
Reject H₀ at α = 0.05, but do not reject at α = 0.01.
c
p-value =
0.0672
Reject H₀ at α = 0.10, but do not reject at α = 0.05.
d
p-value =
0.0672
Reject H₀ at α = 0.05, but do not reject at α = 0.10.
17
The Center for Workforce Development found that 40% of Internet users received more than 15 e-mail messages per day in 2008. In 2012, a similar study on the use of e-mail was repeated. The purpose of the study was see whether use of e-mail has increased. Formulate the null and alternative hypotheses to determine whether an increase has occurred in the proportion of Internet users receiving more than 10 e-mail messages per day.
To test the hypothesis at a 5% level of significance, a sample of 420 Internet users found 189 receiving more than 10 e-mail messages per day. Compute the test statistic and the p-value.
p-value = ______.
a
0.0183
Reject H₀ at α = 0.10. Conclude the population proportion is greater than 0.40.
b
0.0183
Reject H₀ at α = 0.05. Conclude the population proportion is greater than 0.40.
c
0.0544
Do not reject H₀ at α = 0.05. Conclude the population proportion is not greater than 0.40.
d
Both a and b are correct.
18
We want to test the hypothesis that at least 75% of drivers on a freeway violate the speed limit. In a random sample of n = 900 vehicles, 657 violated the speed limit. Compute the sample proportion.
State the null and alternative hypotheses and the decision rule.
a
Reject H₀ at α = 10% and conclude less than 75% of drivers violate the speed limit. But, do not reject H₀ at α = 5% and conclude 75% or more of drivers violate the speed limit.
b
Reject H₀ at α = 5%. Conclude less than 75% of drivers violate the speed limit.
c
Reject H₀ at α = 5%. Conclude more than 75% of drivers violate the speed limit.
d
Reject H₀ at α = 1%. Conclude less than 75% of drivers violate the speed limit.
19
At least 20% of all workers are believed to be willing to work fewer hours for less pay to obtain more time for personal and leisure activities. A recent poll consisting of 600 respondents found 17% willing to work fewer hours for less pay to obtain more personal and leisure time. At 5% level of significance, does the sample result support the claim that at least 20% of all workers are willing to work fewer hours for less pay to obtain more time for personal and leisure activities? Round the proportion to two decimal point.
a
1.64
1.84
Do not reject H₀. Conclude that no less than 20% are willing to work fewer hours for less pay to obtain more time for personal and leisure activities.
b
1.84
1.96
Do not reject H₀. Conclude that no less than 20% are willing to work fewer hours for less pay to obtain more time for personal and leisure activities.
c
1.84
1.64
Reject H₀. Conclude that less than 20% are willing to work fewer hours for less pay to obtain more time for personal and leisure activities.
d
1.56
1.64
Do not reject H₀. Conclude that no less than 20% are willing to work fewer hours for less pay to obtain more time for personal and leisure activities.
20
In the previous question, the p-value is _______.
a
0.0594
b
0.0329
c
0.0233
d
0.0158