Statistics Questions on Education Psychology, Marketing, Confidence Intervals, and Regression Analys

Question 1
An education psychologist believed that part-time students are more motivated than full-time students in their study. As such, he devised an instrument to assess a person's motivation level. The result of the test ranged from 0 to 800 points. The higher the point means the person is more motivated. This instrument was used on 46 full-time and 51 part-time students. The dataset can be found in the TOA Data File ‘Question_1’ worksheet.
(a) Describe three (3) measures of location and three (3) measures of dispersion. State the values of these measures for both full-time and part-time students. You are required to present the relevant Excel output table.
(12 marks)
(b) Interpret the results presented and report them as an executive summary. You should include comments on the central tendency, dispersion and histograms, and address the psychologist's belief.
(13 marks)
Question 2
(a) A marketing student in SUSS conducted a survey on students' preference for iPhone. She collected responses from 600 male and 400 female students. Of which, 400 male students used iPhone and 100 female students used other phones.
(i) Construct a contingency table based on the information given.
(ii) Identify the probability that a randomly selected student is female and uses iPhone.
(iii) Identify the probability that a randomly selected student is male or uses iPhone?
(iv) What is the probability that a randomly selected student uses iPhone given that the student is female?
(12 marks)
(b) The weight of a bag of rice is normally distributed with a mean of 5kg and standard deviation of 50g.
(i) If a bag of rice is randomly selected, identify the probability that the weight is between 4,980g and 5,080g.
(ii) If 30 bags were randomly selected, report the probability that the mean weight is greater than 5,020g.
(13 marks)
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Timed Online Assignment – July Semester 2021
Question 3
The Exam Office in SUSS would like to find out whether gender affects students' reading time before they start their attempt on the first question in a Statistics exam. 30 male students and 30 female students were randomly selected and their reading time (in minutes) were recorded. The dataset can be found in the TOA Data File ‘Question_3’ worksheet.
(a) Describe the 99% confidence intervals for the mean reading time of male and female students. Based on the confidence intervals, discuss whether we can conclude that the mean reading time for both genders is similar.
(10 marks)
(b) Apply an appropriate hypothesis test at the 1% significant level to determine whether the mean reading time of both genders is similar.
(10 marks)
(c) Compare the results from Part (a) and (b). Should the conclusion be different or similar? Please provide your justification.
(5 marks)
Question 4
Ms Jenny Wong is a property agent dealing with rental of private property in Singapore. She wanted to examine what the key factors affecting the rent of private property are. She recorded the following data for her most recent 105 transactions:
RENT: Monthly rent of property (S$)
SIZE: Build-up area (sq ft)
TIME: Walking time to the nearest MRT station (minutes)
POOL: 1 means the property has a swimming pool
0 means the property does not have a swimming pool
The dataset can be found in the TOA Data File ‘Question_4’ worksheet. The RENT is the dependent variable and the other variables are independent variables.
(a) Describe the relationship between RENT and the three (3) independent variables by writing down the linear equation. Interpret the coefficients to show how each of the independent variables impacts the rent. You are required to present the whole regression output table.
(6 marks)
(b) Jenny wants to estimate the rent for a particular property in which the build-up area is 4,500 sq ft, the walking time to the nearest MRT station is 15 minutes, and it has a swimming pool. What is your estimate of the rent?