Part -1:
Task 1:
• Organize your sample data in a spreadsheet (See Sample Selection Sheet below).
Please follow instruction above!
(Students who failed to follow the instruction will not be marked and "0" mark will be awarded to them)
• Do you think it is necessary to use 50 samples (n=50) in order to represent the whole population of household (N=1000)? Why don't we just use 5 or 10 samples?
Task 2:
• Plot the 50 sample points of WI and WEF values that you obtained in 1 on a scatter diagram. (Plot WI values along the X-axis and WEF values along the Y-axis.
• Do you think putting W1 at X-axis and WEF at Y-axis seem a reasonable suggestion? Explain!
Task 3:
• Develop a suitable tabular form and graphical bar charts of the HLE, G, FS and frequency.
Task 4:
• Determine estimates of the median, mode, mean of WEF, WI and FS of WEF, WI and FS.
• Is there any of your median is greater and / or smaller than mean? What does that indicate?
• Is there any of your median is equal with mean? If yes, what do you think is the reason of it? If no, what do you think is the reason of it?
Task 5:
• Determine estimates of range, 1st & the 3rd Quartiles or (25th & 75th percentiles), Inter Quartile Range (IQR) of WEF, WI and FS.
• Explain the differences and similarities of range and IQR?
• Which one (either, Range or IQR) is more useful in order to compare these variables (WEF, WI, and FS)? Why?
Task 6:
• Determine estimates of the standard deviation (SD), variance and coefficient of variation (CV) of WEF, WI and FS.
• Explain the differences and similarities of SD and CV?
• Which one (either, SD or CV) is more useful in order to compare those variables (WEF, WI, and FS)? Why?
Task 7:
Write a non-technical report interpreting your descriptive statistics, tabular and Graphic results obtained from Task 3 to 6, and parts in light of sample report given below (See sample report writing). Avoid repeating exact sample report wording. Present this report as the main body of this assignment. (Write in less than 300 words)
Part -2:
Answer the following questions:
1. Provide 95% confidence interval estimates for the mean FS (µFS) WEF (µWEF) and WI (µWI) for the population of 1000 households based on your selected sample of size 50 households.
2. Test the following Hypothesis that the population average
(i) Family Size is three.
(ii) WI is at least $500.
(iii) WEF is greater than $300
Against a suitable alternative at the 10% level of significance. What can you conclude?
3. Estimate the following least square regression lines and explain the meaning of the y-intercept (b0) term and the estimate of slope coefficients (b1) in (i) and (ii) below but (b1 & b2) in (iii) :
(i) WEF on WI
(ii) WEF on FS
(iii) WEF on WI and FS
4. Construct confidence intervals for the estimates of the slope coefficients in (i) to (iii) of Question 3. Explain the meaning of these confidence intervals and comment on your results about the width of the confidence intervals, if sample size increases from 50 to 100.
5. Find the values of the correlation coefficients and the coefficients of determination, and explain their meaning for the 50 pairs of:
(i) WI and WEF values
(ii) WEF and FS values
6. In that excel file (Oslo tab), there is 50 sample data of Weekly Income (WI), Weekly Expenditure on Food (WEF) of one of the most prosper city in the world, Oslo, Norway. Prime Minister of Norway Erna Solberg claimed that:
(i) The population average of Weekly Income (WI) for her city is higher compared to your sample of 50 households.
(ii) The population mean of Family Size (FS) for her city is at least the same with your sample of 50 households.
Based on the Erna Solberg's statement, perform the analysis on hypothesis testing with level of significance of 5%. Do you think Erna Solberg's statement is true?
There are few assumptions that you may need to put in your mind, when you perform this test:
A. Populations for both of your sample data and OSLO are normally distributed and samples are independent.
B. Population variances for Weekly Income (WI) are unknown and unequal.
C. Population variances for FS are unknown and equal.
7. As one of the largest city in USA, New York also known as the food city. In this city people spend so much money in food, and Bill de Blasio, Mayor of New York believe, that the average amount of weekly food expenditure (WEF) spent by households is equal with your sample data. In order to prove that he collects a random sample of 50 households data of his city. (The data is attached on extra file for assignment 2, New York tab).
Based on the Bill de Blasio's statement, perform the analysis on hypothesis testing with level of significance of 5%. Do you think Bill de Blasio's statement is correct?
You may consider the following assumptions while performing this test:
A. Populations for both of your sample data and New York are normally distributed and samples are not independent.
B. Population variances of Weekly Food on Expenditure (WEF) are unknown and unequal.