11.1 300 customers selected randomly are asked on which day of the week
they usually went to the grocery store and received the following votes. Can you
conclude that the percentage of days customers prefer is different? Use the 5%
significance level. Check the test result using 『eStatU』.
Day | Number of Customers |
Mon | 10 |
Tue | 20 |
Wed | 40 |
Thr | 40 |
Fri | 80 |
Sat | 60 |
Sun | 50 |
Total | 300v |
11.2 The market shares of toothpaste brands A, B, C and D are known to be 0.3,
0.6, 0.08, and 0.02 respectively. The result of a survey of 600 people for the
toothpaste brands are as follows. Can you conclude from these data that the existing
market share is incorrect? Use and check your test result using 『eStatU』.
Brand | Number of Customers |
A | 192 |
B | 342 |
C | 44 |
D | 22 |
Total | 600 |
11.3 The following table shows the distribution by score by conducting an aptitude
test on 223 workers at a plant. The mean and variance from the sample data are 75
and 386 respectively. Test whether the scores of the aptitude test follow a normal
distribution. Use and check your test result using 『eStatU』.
Score interval | Number of Workers |
X < 40 | 10 |
40 \(\le\) X < 50 | 12 |
50 \(\le\) X < 60 | 17 |
60 \(\le\) X < 70 | 37 |
70 \(\le\) X < 80 | 55 |
80 \(\le\) X < 90 | 51 |
90 \(\le\) X < 100 | 34 |
X \(\ge\) 100 | 7 |
Total | 223 |
11.4 The following data shows the highest temperature of a city during the month of
August. Test whether the temperature data follow a normal distribution with the 5%
significance level. (Unit: °C)
29, 29, 34, 35, 35, 31, 32, 34, 38, 34, 33, 31, 31, 30, 34, 35,
34, 32, 32, 29, 28, 30, 29, 31, 29, 28, 30, 29, 29, 27, 28.
11.5 For market research, a company obtained data on the educational level and
socio-economic status of 375 housewives and summarized a contingency table as
follows. Test the null hypothesis that social and economic status and educational
level are independent at the significance level of 0.05. Check the test result using 『eStatU』.
Socio-economic status |
Elementary |
Middle |
High |
College |
Above |
Total |
1 |
10 |
7 |
3 |
4 |
1 |
25 |
2 |
14 |
10 |
7 |
4 |
2 |
37 |
3 |
9 |
25 |
13 |
18 |
3 |
68 |
4 |
7 |
9 |
38 |
44 |
6 |
104 |
5 |
3 |
8 |
14 |
18 |
62 |
105 |
6 |
2 |
3 |
8 |
10 |
13 |
36 |
Total |
45 |
62 |
83 |
98 |
87 |
375 |
11.6 Government agencies surveyed workers who wanted to get a job and classified
532 respondents according to the gender and technical level as follows. Does these
data provide sufficient evidence that the technical level and gender are related? Use
and check your test result using 『eStatU』.
Technical Level |
Male |
Female |
Total |
Skilled worker |
106 |
6 |
112 |
Semi-skilled worker |
93 |
39 |
132 |
Unskilled worker |
215 |
73 |
288 |
Total |
414 |
118 |
532 |
11.7 A guidance counselor surveyed 110 high school students for reading and
watching TV. The following table was obtained by classifying each item as high and
low. At the significance level of 0.05, are these data sufficient to claim that the
reading and TV viewing are related? Check the test result using 『eStatU』.
|
Reading High |
Reading Low |
Total |
TV viewing High |
40 |
18 |
58 |
TV viewing Low |
41 |
11 |
52 |
Total |
81 |
29 |
110 |
11.8 165 defective products produced in two plants operated by the same company
were classified depending on whether they were due to low occupational awareness
or low quality raw materials by each plant. Test the null hypothesis that the cause of
the defect and production plant are independent with the significance level of 0.05.
Check the test result using 『eStatU』.
Cause of Defect |
Plant A |
Plant B |
Total |
Low occupational awareness |
21 |
72 |
93 |
Low quality raw materials |
46 |
26 |
72 |
Total |
67 |
98 |
165 |
11.9 To evaluate the effectiveness of typing training, 110 documents by company
employees who received type training and 120 documents by employees who did not
receive typing training were evaluated. Evaluated documents are classified as good,
normal, and low. The following table shows a classification of the evaluation for total
230 documents according to whether or not they received training. Test the null
hypothesis that typing training and document evaluation are independent. Use and
check your test result using 『eStatU』.
|
Good |
Normal |
Low |
Total |
Typing training |
48 |
39 |
23 |
110 |
No typing training |
12 |
36 |
72 |
120 |
Total |
60 |
75 |
95 |
230 |
11.10 A company with three large plants applied different working conditions and
wage systems to three plants to ask them for satisfaction with the new system six
months later. 250 workers from each of three plants were randomly selected and the
survey results were as follows. Is there sufficient evidence that workers at each plant
have different satisfaction levels? Test with the significance level of 0.05. Check the
test result using 『eStatU』.
Plant |
Very satisfied |
Satisfied |
Average |
Not Satisfied |
Total |
Plant 1 |
135 |
70 |
25 |
20 |
250 |
Plant 2 |
145 |
80 |
15 |
10 |
250 |
Plant 3 |
140 |
75 |
20 |
15 |
250 |
Total |
420 |
225 |
60 |
45 |
750 |