QUESTIONS
Question 1
Assume the distribution of commute times to a major city follows the normal probability distribution and the standard deviation is 4.5 minutes. A random sample of 38 commute times is given below in minutes. Use Excel to find the 98% confidence interval for the mean travel time in minutes. Round your answers to one decimal place and use ascending order.
Time
21
15
35
40
40
34
32
11
18
35
9
31
15
29
41
37
40
10
31
14
39
14
11
33
38
21
35
33
34
27
31
26
35
27
32
18
40
17
Question 2
The number of hours worked per year per adult in a state is normally distributed with a standard deviation of 37. A sample of 115 adults is selected at random, and the number of hours worked per year per adult is given below. Use Excel to calculate the 98% confidence interval for the mean hours worked per year for adults in this state. Round your answers to two decimal places and use ascending order.
Number of hours
2250
1987
2029
2018
1938
2197
2099
2228
2245
1913
1903
2298
2231
2200
1902
2161
2211
2124
2082
2257
2087
2123
1929
1948
2124
2013
1973
2000
2030
1932
1993
2014
2118
1900
2195
2222
2035
2088
2010
1962
2166
1918
2070
2277
2114
1975
2045
2050
1921
2103
1954
2017
2235
1993
2156
1984
2057
2200
2133
2144
2145
2219
2222
2210
2143
2163
2168
2246
2186
1907
2072
2142
2187
2036
2207
2270
2262
2159
1914
1926
2261
2006
1948
2028
2256
2182
1955
1969
1941
1924
2176
2256
2051
2111
2221
2222
2190
2068
1942
2024
2258
2201
2085
2061
2004
2260
2136
2244
1989
1941
2297
2159
2260
2093
2293
Question 3
A large company is concerned about the commute times of its employees. Of the 333 employees who were surveyed, 131 said that they had a daily commute longer than 30 minutes. Create a 95% confidence interval for the proportion of employees who have a daily commute longer than 30 minutes. Use Excel to create the confidence interval, rounding to four decimal places.
Question 4
A city is holding a referendum on increasing property taxes to pay for a new high school. In a survey of 458 likely voters, 254 said that they would vote “yes” on the referendum. Create a 95% confidence interval for the proportion of likely voters who will vote “yes” on the referendum. Use Excel to create the confidence interval, rounding to four decimal places.
Question 5
A sample of 22 test-tubes tested for number of times they can be heated on a Bunsen burner before they crack is given below. Assume the counts are normally distributed. Use Excel to construct a 99% confidence interval for μ. Round your answers to two decimal places and use increasing order.
Number of times test-tubes can be heated
1189
886
921
1021
1074
1233
1697
1293
747
1233
1158
1536
1961
922
1546
1157
1814
1334
1434
1079
1830
975
Question 6
The heart rates for a group of 21 students taking a final exam are given below. Assume the heart rates are normally distributed. Use Excel to find the 95% confidence interval for the true mean. Round your answers to two decimal places and use increasing order.
Beats per minute
94
93
90
84
93
92
102
98
93
89
91
101
94
90
95
95
95
89
98
93
89
Question 7
The amounts of time that customers stay in a certain restaurant for lunch is normally distributed with a standard deviation of 17 minutes. A random sample of 50 lunch customers was taken at this restaurant. Construct a 99% confidence interval for the true average amount of time customers spend in the restaurant for lunch. Round your answers to two decimal places and use ascending order.
Time
69
18
70
52
22
17
29
21
106
36
45
14
38
58
26
49
51
34
49
61
69
56
92
65
24
50
41
69
14
54
5
49
116
56
103
102
45
69
48
54
38
10
14
7
53
90
60
59
93
84
Question 8
The yearly incomes, in thousands, for 24 random married couples living in a city are given below. Assume the yearly incomes are approximately normally distributed. Use Excel to find the 95% confidence interval for the true mean, in thousands. Round your answers to three decimal places and use increasing order.
Yearly Income
59.015
58.962
58.935
58.989
58.997
58.970
59.000
59.014
59.001
59.003
58.992
58.926
59.032
58.958
59.093
58.955
59.003
58.952
59.057
59.056
59.074
59.128
59.001
59.007
Question 9
In a city, 22 coffee shops are randomly selected, and the temperature of the coffee sold at each shop is noted. Use Excel to find the 90% confidence interval for the population mean temperature. Assume the temperatures are approximately normally distributed. Round your answers to two decimal places and use increasing order.
Temperature
151
158
163
155
155
144
140
148
145
146
158
143
152
167
163
171
147
177
170
168
176
164
Question 10
In a random sample of 350 attendees of a minor league baseball game, 184 said that they bought food from the concession stand. Create a 95% confidence interval for the proportion of fans who bought food from the concession stand. Use Excel to create the confidence interval, rounding to four decimal places.
Question 11
The owner of a restaurant is reviewing customer complaints. In a random sample of 227 complaints, 57 complaints were about the slow speed of the service. Create a 95% confidence interval for the proportion of complaints that were about the slow speed of the service. Use Excel to create the confidence interval, rounding to four decimal places.
Question 12
Suppose the weights of tight ends in a football league are normally distributed such that σ2=1,369. A sample of 49 tight ends was randomly selected, and the weights are given below. Use Excel to calculate the 95% confidence interval for the mean weight of all tight ends in this league. Round your answers to two decimal places and use ascending order.
Weight
300
294
155
270
218
242
150
364
298
167
297
299
221
266
261
301
269
267
219
165
198
359
240
263
160
171
169
259
196
197
268
271
200
295
258
199
260
303
264
241
220
265
262
343
321
302
364
296
170
Question 13
The following data represent a sample of the assets (in millions of dollars) of 28 credit unions in a state. Assume that the population in this state is normally distributed with σ=3.5 million dollars. Use Excel to find the 99% confidence interval of the mean assets in millions of dollars. Round your answers to three decimal places and use ascending order.
Assets
12.23
2.89
13.19
73.25
11.59
8.74
7.92
40.22
5.01
2.27
16.56
1.24
9.16
1.91
6.69
3.17
4.78
2.42
1.47
12.77
4.39
2.17
1.42
14.64
1.06
18.13
16.85
21.58
ANSWERS:
Question 1
Assume the distribution of commute times to a major city follows the normal probability distribution and the standard deviation is 4.5 minutes. A random sample of 38 commute times is given below in minutes. Use Excel to find the 98% confidence interval for the mean travel time in minutes. Round your answers to one decimal place and use ascending order.
Time
21
15
35
40
40
34
32
11
18
35
9
31
15
29
41
37
40
10
31
14
39
14
11
33
38
21
35
33
34
27
31
26
35
27
32
18
40
17
Answers:
25.9, 29.3
Question 2
The number of hours worked per year per adult in a state is normally distributed with a standard deviation of 37. A sample of 115 adults is selected at random, and the number of hours worked per year per adult is given below. Use Excel to calculate the 98% confidence interval for the mean hours worked per year for adults in this state. Round your answers to two decimal places and use ascending order.
Number of hours
2250
1987
2029
2018
1938
2197
2099
2228
2245
1913
1903
2298
2231
2200
1902
2161
2211
2124
2082
2257
2087
2123
1929
1948
2124
2013
1973
2000
2030
1932
1993
2014
2118
1900
2195
2222
2035
2088
2010
1962
2166
1918
2070
2277
2114
1975
2045
2050
1921
2103
1954
2017
2235
1993
2156
1984
2057
2200
2133
2144
2145
2219
2222
2210
2143
2163
2168
2246
2186
1907
2072
2142
2187
2036
2207
2270
2262
2159
1914
1926
2261
2006
1948
2028
2256
2182
1955
1969
1941
1924
2176
2256
2051
2111
2221
2222
2190
2068
1942
2024
2258
2201
2085
2061
2004
2260
2136
2244
1989
1941
2297
2159
2260
2093
2293
Answer:
(2,090.03, 2,106.09)
Question 3
A large company is concerned about the commute times of its employees. Of the 333 employees who were surveyed, 131 said that they had a daily commute longer than 30 minutes. Create a 95% confidence interval for the proportion of employees who have a daily commute longer than 30 minutes. Use Excel to create the confidence interval, rounding to four decimal places.
Answers:
0.3409
0.4459
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