Multiple Choice Exercise

*** Choose one answer and click [Submit] button

11.1 What tests do you need to investigate whether the sample data follow a theoretical distribution?





        

11.2 In order to test whether sample data of a continuous variable follow a distribution, what is the first necessary work for the goodness of fit test?





        

11.3 How do you test the hypothesis that the two categorical variables of a sample from a population have no relation?





        

11.4 How do you test the hypothesis that the samples from two categorical populations have the same distribution?





        

11.5 Which of the following statistical distributions ise used to test for a contingency table?





        

Practice Exercise

*** Answer the followings

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』.

DayNumber 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』.

BrandNumber 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 intervalNumber 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