Question 1 A social scientist suspected that females tend to feel more stressed in life as compared to males. As such, he devised an instrument to assess a person’s stress level. The result of the test ranges from 0 to 400 points. A higher point means the person feels more stressed. This instrument was used …

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**Question 1**

A social scientist suspected that females tend to feel more stressed in life as compared to males. As such, he devised an instrument to assess a person’s stress level. The result of the test ranges from 0 to 400 points. A higher point means the person feels more stressed. This instrument was used on 46 males and 51 females who volunteered for the test. The dataset can be found in the TOA Data File ‘Question_1’ worksheet.

- Describe three (3) measures of location and three (3) measures of dispersion. State the values of these measures for both males and females. You are required to present the relevant Excel output table.
- Show three (3) statistical concerns on the approach used in the study. If you have a free hand to study this research question starting from data collection to analysis, illustrate how you would conduct the project.

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**Question 2**

- The following table shows a recent study on the relationship between gender and interest in swimming:

Like Swimming | Dislike Swimming | TOTAL | |

Males | 250 | 50 | 300 |

Females | 110 | 110 | 220 |

TOTAL | 360 | 160 | 520 |

If a person is randomly selected, identify the probability that the person is

- Male
- Female and Likes Swimming
- Male or Likes Swimming
- Female given that the person Likes Swimming

- The weight of a bag of grapes is normally distributed with a mean of 600g and a standard deviation of 25g.

- If a bag of grapes is randomly selected, identify the probability that the weight is between 585g and 623g.
- If 20 bags are randomly selected, report the probability that the mean weight is greater than 610g.

**Question 3**

A marketing specialist wanted to study the brand recall time of two brands (Brand A and Brand B). He randomly selected 30 participants and showed them each brand, one after another, and measured the amount of time (in seconds) they took to recall the brand names. The dataset can be found in the TOA Data File ‘Question_r worksheet.

- Describe the 90% confidence intervals for the mean recall time of each brand. Based on the confidence intervals, discuss whether we can conclude that the recall time for both brands is similar. You are required to present the relevant Excel output table.
- Apply an appropriate hypothesis test at the 10% significant level to determine whether the recall time of both brands are similar. You are required to present the relevant Excel output table.
- Interpret the results from Part (a) and (b). Should the conclusion be different or similar? Please provide your justification.

**Question 4**

Espiriki Hotel International is a 200-room hotel situated near Changi Airport. It has a lounge in the lobby but was not doing very well. Mr. John Tan, the Lounge Manager, wanted to analyse the monthly beverage sales in the lounge. He collected the following data for the most recent 60 months:

BEVTOTAL: Total monthly beverage sales (S$’000)

FOODTOT: Total amount spent on food (S$’000)

ROOMS: Total room occupancy (room-nights)

PERFORMANCE: 1 means there were some performances during that month

0 means there was no performance during that month

The dataset can be found in the TOA Data File ‘Question_4’ worksheet. The beverage sales are the dependent variable and the other variables are independent variables.

- Describe the relationship between beverage sales and the three (3) independent variables by writing down the linear equation. Interpret the coefficients to show how each of the independent variables impacts beverage sales. You are required to present the relevant Excel output table.
- Mr. Tan wants to estimate the monthly beverage sales for a particular month in which the total food sales are S2.5 million, total room occupancy is 5,000 and there are three performances in the lounge during that month. What is your estimate of the beverage sales for that month?
- Interpret the coefficient of multiple determination and the adjusted coefficient of multiple determination. Explain which is a better measure in this case. You are required to present the relevant Excel output table.
- Execute hypothesis tests to advise Mr. Tan which variable(s) is/are significant at the 5% significance level. Write down your steps carefully.

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