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Associate Degree / Higher Diploma Programmes Semester 2, 2020-21

End of Term Assessment

Instructions to Candidates

· This paper has 8 pages.

· Answer ALL questions.

· Your solution must be handwritten on papers and all questions must be answered in English. Electronic file created from iPad / tablet device is not accepted.

· Show clear calculation steps. Correct your answer to 4 decimal places and report the measurement unit when applicable.

· Scan your answer sheets with declaration form as a single pdf file (no other file format is accepted).

· Upload your pdf file to SOUL class link before 10:50 am 10 May 2021.

· Check your pdf file and make sure:

i. Your signed declaration form is included

ii. your writing is clear

iii. all pages are included

iv. the file can be opened properly by Acrobat Reader

ANSWER ALL QUESTIONS (60 MARKS)

Question 1

The weight of a box of chocolates of  a certain brand follows a normal distribution with a mean of  85 grams and a standard deviation of 7 grams. During the promotion period, there are special sets, each include two randomly selected boxes of chocolates. Use T to denote the total weight of chocolates in a special set.

(a) Find the expectation, median, and standard deviation of T. (5 marks)

(b) What is the probability that the weight of chocolates in a special set is less than 160 grams?

(5 marks)

(Total: 10 marks)

Question 2

The weights (in kg) of a sample of 13 customers in a physical center are shown as follows: 95, 73, 83, 64, 58, 48, 53, 49, 68, 65, 57, 70, 72

(a) Find the following statistical measurements

(i) range;

(ii) median;

(iii) mean;

(iv) standard deviation; (6 marks)

(b) If the optimum weight is defined as one standard deviation less than the mean, find the optimum weight based on this sample’s data. (2 marks)

(c) If one customer is randomly selected from this sample, what is the probability that the selected customer’s weight is below the optimum weight as in part (b). (2 marks)

(Total: 10 marks)

Question 3

Tom is a guitarist and he always wonders which colour of guitar body is most popular. Based on his experience, he estimated that 50% people would like red, 30% people would like black, 10% people would like Sky blue, and the rest would like white. He asks his followers on Twitter which colour do they like most for their guitars. Below is the summary of the result of the Twitter survey:

Test, at the 5% level of significance, is there sufficient evidence that the Twitter survey result is different from Tom’s estimate. (The test report must include (i) null hypothesis and alternative hypothesis, (ii) rejection region, (iii) calculation of test statistics, and (iv) conclusion.)

(Total: 10 marks)

Question 4

The education department conducts a survey to investigate the relationship between time spent (in hour) on social media in a week and the average score obtained by the student in the Territory-wide System Assessment (TSA). The following is 10 sets of data obtained in the study:

(a) Calculate the correlation coefficient of the above data. (1 mark)

(b) Comment on the relationship between the time spent on social media and the average score of a student by referring to your answer in part (a). (2 marks)

(c) Find the values of a and b in the regression line y = a + bx of the above data. (2 marks)

(d) Interpret the value of b in the regression line in part (c). (1 mark)

(e) Use the regression line in part (c) to estimate the average score of a student who spends 14 hours on social media per week. (2 marks)

(f) Comment on the reliability of the estimation in part (e) with reason. (2 marks)

(Total: 10 marks)

Question 5

A social study is developed to review the proportion of teenagers spend more than $2000 on clothing in a month. The result of the survey is as follow:

(a) Find the sample proportion of (i) male teenagers, (ii) female teenagers, (iii) teenagers who spend more than $2000 on clothing in a month. (3 marks)

(b) Refer to the below Excel summary report generated at 5% significance level, prepare a report in p-value approach to conclude if there is higher proportion of female spends more than $2000 on clothing in a month than male. (The test report must include (i) null hypothesis and alternative hypothesis, (ii) calculated test statistics, (iii) p-value and (iv) conclusion with reason.)

(7 marks)

(Total: 10 marks)

Question 6 (For Question 6, write down the answers only, no explanation is needed.)

(a) John is asked to prepare the probability distribution function of the number of customers (X) visiting a beauty salon during 8:00 – 9:00 pm in business days. The following table is prepared by John.

There  are  two problems  in  the above probability distribution function. Write down the two problems. (4 marks)

(b) State which test (z-test, t-test, ANOVA, χ2 test) is most suitable for each of the following cases:

(i) A social study is developed to compare the amount of time (hours) three groups of students spent on playing online game in a week. The three groups of students come from public schools, government subsidized schools and private schools. Students from each group are randomly selected to participate in the survey. (2 marks)

(ii) A research is conducted to test if elderly has a significant reaction to a new developed treatment. The decrease in blood sugar of each participant is measured. The average decrease in blood sugar is used in the test. (2 marks)

(c) A study is conducted to investigate the hygiene status during COVID-19. Referring to the following two variables, write down if the variable be quantitative (discrete), quantitative (continuous), or qualitative.

(i) The number of times you used hand sanitizer or hand cleansing gel during your last trip by public transport. (1 mark)

(ii) When you back home after work, how long (in seconds) would you wash your hand.

(1 mark)

(Total: 10 marks)