TMA01 Question 1 The table below reports the average monthly household income from work among resident employed households by type of dwelling in Singapore in 2018 and 2019. 2018 2019 HDB 1- & 2- Room Flats 2,765 2,886 HDB 3-Room Flats 6,497 6,586 HDB 4-Room Flats 9,306 9,543 HDB 5-Room & Executive Flats 12,716 12,706 …

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**TMA01**

**Question 1**

The table below reports the average monthly household income from work among resident employed households by type of dwelling in Singapore in 2018 and 2019.

2018 | 2019 | |

HDB 1- & 2- Room Flats | 2,765 | 2,886 |

HDB 3-Room Flats | 6,497 | 6,586 |

HDB 4-Room Flats | 9,306 | 9,543 |

HDB 5-Room & Executive Flats | 12,716 | 12,706 |

Condominiums & Other Apartments | 20,593 | 21,023 |

Landed Properties | 27,134 | 27,385 |

Source of data: Department of Statistics. Key Household Income Trends, 2019.

Analyse the percent change in average monthly household income from work for the six types of dwelling.

**Question 2**

The number of reported cases of Singapore’s top six scam categories in 2019 is listed below. Recommend what kind of graph would be appropriate for portraying the data and develop the graph in Excel.

Tops six scam categories | Number of cases reported in 2019 |

E-commerce | 2,809 |

Loan | 1,772 |

Credit-for-sex | 1,065 |

Social media impersonation | 810 |

Internet love | 649 |

Investment | 508 |

Source of data: Singapore 2020 Crime & Safety Report

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**Question 3**

Refer to the data file “TMA01 data1.xlsx”, which reports information on knowledge about science and attitudes toward science and faith. It is a subset of data derived from the 2005 Eurobarometer: Europeans, Science and Technology. All respondents were residents in the respective country and aged 15 and over.

1. Examine the variables from the data file and place each of them in the following classification tables.

Discrete | Continuous | |

Nominal | ||

Ordinal | ||

Interval | ||

Ratio |

2. Select the variable knowledge about science, find the mean, median, mode, range, and standard deviation. *Note: Please cut and paste your Excel output into your answer to demonstrate that you have used Excel.*

3. For the variable knowledge about science, apply the empirical rule to determine an interval that contains approximately 95 percent of the observations. *Note: Please show the necessary calculations in your answers. Round off your final answer to one decimal place.*

4. A cross-tabulation table simultaneously summarises two variables of interest and their relationship. To understand whether attitudes toward science and faith are different in different countries, fill in the following cross-tabulation table by classifying the responses of the survey respondents according to two criteria: (1) country and (2) the attitude toward science or the attitude toward faith (toomuchscience).

*Note: You should not try to count manually. Instead, you should make use of either the**“COUNTIFS” function or the Pivot Table in Excel. Please cut and paste your Excel output into your answer to demonstrate that you have used Excel.*

Variable: toomuchscience (To what extent do you disagree or agree with “We rely too much on science and not enough on faith”?) | Country | |||

Denmark | Austria | Turkey | Total | |

Strongly disagree | ||||

Tend to disagree | ||||

Neither agree or disagree | ||||

Tend to agree | ||||

Strongly agree | ||||

Total | 326 | 318 | 352 | 996 |

Now based on the above cross-tabulation table, calculate the following probabilities: *Note: Please show the necessary calculations in your answers. Round off your final answer to three decimal places.*

- What is the probability of randomly selecting a respondent who is a resident in Denmark?
- What is the probability of randomly selecting a respondent who strongly disagrees or tends to disagree with “We rely too much on science and not enough on faith”?
- Among the respondents residing in Denmark, what is the probability of randomly selecting a person who strongly disagrees or tends to disagree with “We rely too much on science and not enough on faith”?
- Among the respondents residing in Austria, what is the probability of randomly selecting a person who strongly disagrees or tends to disagree with “We rely too much on science and not enough on faith”?
- Among the respondents residing in Turkey, what is the probability of randomly selecting a person who strongly disagrees or tends to disagree with “We rely too much on science and not enough on faith”?

Does p2 equal to p3 or p4 or p5? Interpret what this means.

**Question 4**

Refer to the data file “TMA01 data2.xlsx”, which reports information on weekly household expenditure in the UK. It is a subset of data derived from the 2010 UK Living Cost and Food Survey.

1. The mean weekly household expenditure (in British Pound) is 375.4, with a standard deviation of 233.86. Apply the necessary formula and use the normal distribution to estimate the percent of households with a weekly expenditure of more than 650 British Pound.

*Note: Please show the necessary calculations in your answers. Round off your final answer to two decimal places.*

2. Compare this to the actual results. Does the normal distribution yield a good approximation of the actual results? Why or why not?

3. Let’s assume the data includes a normal population. Suppose we select a random sample of 25 households and compute the mean weekly household expenditure. What is the standard error of the mean? What happens to the standard error of the mean if the sample size is increased?

*Note: Please show the necessary calculations in your answers. Round off your final answer to two decimal places.*

4. To understand whether household expenditure differs as a consequence of the tenure agreement on the property in which someone resides, researchers also collected information on respondents’ tenure agreement. As you can see from the data file “TMA01 data2.xlsx”, there are three types of tenure agreement among the survey respondents: public rented property, private rented property, or owned property.

Using Excel, analyse the appropriate descriptive statistics and frequency distribution graphs for weekly household expenditure separately by tenure agreement. Interpret the output and report your findings. What would you conclude?

*Note: Please cut and paste your Excel output into your answer to demonstrate that you have used Excel.*

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**TMA02**

**Question 1**

1. Using Excel, analyse the dataset, and obtain the descriptive statistics and graphs for the variables: age, gender, major, and statistics anxiety. Present the results in one table and four separate graphs.

*Note: Please cut and paste your Excel output into your answer to demonstrate that you have used Excel.*

2. It has been proposed that higher levels of social support negatively predict perceived stress. Formulate the appropriate hypotheses and use Excel to analyse the data using the most appropriate statistical test. Interpret the results to determine if the above proposal is supported by the data, and report the findings.

*Note 1: Include all important steps in the analysis and report all necessary descriptive and inferential statistics and results. Also please cut and paste your Excel output into your answer to demonstrate that you have used Excel.*

*Note 2: Do elaborate on the reasons why you think a particular statistical test is appropriate.*

*Note 3: For the six-item Social Support scale, the score is calculated by adding up the scores for each item. For the 4-item Perceived Stress Scale, the score is calculated by first reversing the responses to the two positively stated items and then summing across all items. For more details on the scales, refer to the following articles.*

3. Recommend an appropriate population of interest to which you can generalise the results from the sample. Explain why.

**Question 2**

According to a national study on social ties among Singapore citizens and permanent residents conducted by the Institute of Policy Studies of the National University of Singapore from January 2016 to October 2017, 49 percent of Singaporeans knew someone of a different nationality they feel close enough to casually chat with.

Suppose a recent random sample of 200 Singaporeans showed that 120 named someone of a different nationality they feel close enough to casually chat with. Is the sample sufficient to conclude that there has been a significant increase in the proportion of Singaporeans naming a non-Singaporean in their social ties since the 2016-17 survey? Use the .05 significance level. You are expected to formulate the appropriate hypotheses and interpret the results.

*Note: Show the necessary steps and calculations in your answers.*

**Question 3**

Refer to the data file “TMA02 data.xlsx”, which reports information on the length of TV news stories (measured in seconds) for different broadcast start times and media types. It is a subset of data derived from the Pew Research Centre’s Project for Excellence in Journalism News Coverage Index for 2012.

1. At the .05 significance level, is there a difference in the mean length of TV news stories among the three broadcast start times? Formulate the appropriate hypotheses and apply Excel to analyse the data using the most appropriate statistical test. Interpret the results and report the findings.

*Note 1: Include all necessary steps. Also please cut and paste your Excel output into your answer to demonstrate that you have used Excel.*

*Note 2: Do elaborate on the reasons why you think a particular statistical test is appropriate.*

2. Suppose the Pew Research Centre (PRC) wants to know whether Cable TV and Network TV spend different amounts of time covering news stories. Recommend the most appropriate statistical test that can be used by PRC to analyse the data. Now recommend another alternative statistical test. Elaborate on the reasons why you think each statistical test is appropriate.

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