The human resources director of a university in Macau wants to develop an employee health code scheme and decides to select 40 employees from the employee records to study their preferences for a potential scheme

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The human resources director of a university in Macau wants to develop an employee health code scheme and decides to select 40 employees from the employee records to study their preferences for a potential scheme. The results show that 25 employees support the potential scheme.

1. 1. Identify the population of interest to the human resources director.
   2. Identify the variable of interest to the human resources director.
   3. Is the variable stated in part (b) numerical or categorical?
   4. Based on the data collected by the human resources director, what is the value of the sample statistic that the director can use in her analysis?
   5. What statistical inference that the human resources director can make based on the sample statistic in part (d)?
2. The New Strait Times subscriber survey asked 46 questions about subscriber characteristics and interests. Five out of the 46 questions being asked are shown below. The survey collected 826 questionnaires successfully.

?  What is your age (as of last birthday)?                  

?  Are you male or female?                  

? When did you start reading the New Strait Times? [e.g. High school, college, early

career, mid-career, late career, or retirement]

   What is your annual income?                

?  How many books do you read each year?                    

1. 1. What is the population being studied?
   2. For each of the above questions, (1) determine whether the variable is categorical or numerical; and (2) if the variable is numerical, determine whether the variable is discrete or continuous.
   3. The survey results show that the average number of books read each year is 3.2. Is the value 3.2 a parameter or a statistic? Why?
   4. New Strait Times would like to test whether the average number of books read is less than 4 based on the survey results. Does the value “4” being tested refer to the parameter or statistic? Why?

 

3. Sorting through unsolicited emails and spam affects the productivity of office workers. An Insight Express survey monitored office workers to determine the unproductive time per day devoted to unsolicited emails and spam. The following data show the time (in minutes) devoted to this task.

2	4	8	4	8	1	2	32	12	1
5	7	5	5	3	4	24	19	4	14

1. 1. Construct a “less-than” frequency distribution. Use equal class width of 5 and start with 0.
   2. Construct a percentage distribution and a cumulative percentage distribution based on the frequency distribution constructed in part (a).
   3. Draw a histogram based on the frequency distribution in part (a).
   4. Draw a percentage polygon and percentage ogive based on the distributions in part (b).
   5. Describe the shape of the histogram in part (c), in terms of skewness.
   6. Assuming that this is a population, what is the population size in this study?
   7. Compute the mean and the median of this population.
   8. Compute the variance and standard deviation of this population.

 

4. The Macao Daily Times regularly reports the air quality index (AQI) for various areas of Macao. The higher the AQI value, the greater the level of air pollution, and the greater the health concern. A nine-day sample of AQI values for Taipa District last month provided the following data:

28

42

58

48

45

55

60

49

50

1. 1. Compute the sample mean AQI for Taipa District.
   2. Compute the sample standard deviation in AQI for Taipa District.
   3. A nine-day sample of AQI readings for Central Macau District last month provided a sample mean of 62 and a sample standard deviation of 11.66. Which of these two districts had a more stable air quality last month?

 

5. The mean and median final examination score of 450 students in Statistics last semester is 74 and 72 respectively.
   1. Interpret the mean final examination score, 74.
   2. Interpret the median final examination score, 72.
   3. Discuss the shape of the distribution of final examination score of 450 students in Statistics last semester, in terms of skewness.