ST130: Basic Statistics

Assignment, Semester 2, 2022

Due Date: Monday 31st October, 2022, 11.59pm (Fiji-time) Total Marks: 50

Weight: 10%¬¬¬

Instructions:

1. All questions are compulsory.

2. Please complete this assignment in a group of 2 or 3 students. See the group list to know which group you belong you and your group members.

3. Use MS Excel to complete this assignment, that is all calculations should be done using the MS excel functions.

4. Write your group members information (name, ID, signature, etc.) on a new sheet and rename it as Group Information.

5. Each question should be done in different sheets and rename them as Q1 for Question 1, Q2 for Question 2, and so on.

6. One member from each group to upload the groups assignment solution (MS excel file) via drop box created on Moodle.

7. Plagiarized assignments will be given a mark of 0 (zero) and will be reported for disciplinary action.

Access Fiji Farm Survey data set from MOODLE. And use that for all questions.

Fiji Farm Survey data set is taken from a survey of Sugar cane Farmers in Fiji conducted by a research team from the University of Queensland in 2005.

Q1. (8 marks)

a. Produce a histogram for the variable Age. Take class width as 10, starting from 0. Give appropriate title, label to axis and it to be solid lines only and no color fill. (4 marks)

b. Discuss the Histogram result, is there a serious problem in sugar industry regarding farmers age. If yes then recommend a suitable way to minimize this problem. (2 marks)

c. “Samu is recommending Pie chart for Farming status” Comment on appropriateness of Samu’s choice.

(2 marks)

Q2. (11 marks)

Create a new column titled “Level of education” with following criteria:

• all the farmers Education(years) less than equal to eight label it as primary

• all the farmers Education(years) greater than 8 and less than equal to 13 label it secondary.

• all the farmers Education(years) greater than 13 label it as tertiary.

(1 marks)

Now create a new variable ‘cane output per acre’ in a new column. (Cane output per acre = cane output / cultivated area). (1 mark)

a. Calculate the descriptive statistics using MS-Excel for cane output per acre based for farmers with primary education and for farmers with secondary education. (Hint: ignore non-numeric cells in computing). Interpret the following statistic (Mean, Median, Mode, Standard Deviation) obtained for farmers with primary education. (7 marks)

b. What conclusion can be reach from the comparison of descriptive statistics between cane output per acre for farmers with primary education and for farmers with secondary education? Justify why or why note there is significant difference in output? (2 marks)

Q3. (9 marks)

Construct a contingency table and relative contingency table (using Pivot table tool in Excel) for farming status in raw and Land Owned in column. (4 marks)

a. What is the probability that a randomly selected farmer does not own the land? (1 mark)

b. What is the probability that a randomly selected farmer is working full time and does not own the land?

(1 mark)

c. What is the probability that a randomly selected farmer does not own the land given that farming status is full time? (1 mark)

d. What can you conclude from above analysis in regards to land ownership in sugar industry? (2 marks)

Q4. (8 marks)

a. Assume that the annual profit from farming is nearly normally distributed. Individual earning less than $2000 is believed to be in poverty. Calculate what proportion of sugar cane farmers are in poverty?

(3 marks)

b. A researcher intends to estimate population proportions of farmers in Fiji are in poverty. The researcher intends to be 99% confident and expects that his estimation to be within 3% of population proportion. How large sample size should be taken to achieve these conditions. (3 marks)

c. Which sampling procedure would you recommend to the researcher in part (b), provide reason for your answer. (2 marks)

Q5. (6 marks)

a. Construct a 99% confidence interval for the mean cane output per farmer. Interpret. (3 marks)

b. Construct a 95% confidence interval for population mean can output per acre. Comment on your results.

(3 marks)

Q6. (8 marks)

Test whether the mean annual profit from farming is more than $2000 or not. Use a = 0.05 and the P-value method. Show all five steps of Hypothesis testing. Comment on your results in regards to poverty for sugar cane farmers.

THE END

Assignment, Semester 2, 2022

Due Date: Monday 31st October, 2022, 11.59pm (Fiji-time) Total Marks: 50

Weight: 10%¬¬¬

Instructions:

1. All questions are compulsory.

2. Please complete this assignment in a group of 2 or 3 students. See the group list to know which group you belong you and your group members.

3. Use MS Excel to complete this assignment, that is all calculations should be done using the MS excel functions.

4. Write your group members information (name, ID, signature, etc.) on a new sheet and rename it as Group Information.

5. Each question should be done in different sheets and rename them as Q1 for Question 1, Q2 for Question 2, and so on.

6. One member from each group to upload the groups assignment solution (MS excel file) via drop box created on Moodle.

7. Plagiarized assignments will be given a mark of 0 (zero) and will be reported for disciplinary action.

Access Fiji Farm Survey data set from MOODLE. And use that for all questions.

Fiji Farm Survey data set is taken from a survey of Sugar cane Farmers in Fiji conducted by a research team from the University of Queensland in 2005.

Q1. (8 marks)

a. Produce a histogram for the variable Age. Take class width as 10, starting from 0. Give appropriate title, label to axis and it to be solid lines only and no color fill. (4 marks)

b. Discuss the Histogram result, is there a serious problem in sugar industry regarding farmers age. If yes then recommend a suitable way to minimize this problem. (2 marks)

c. “Samu is recommending Pie chart for Farming status” Comment on appropriateness of Samu’s choice.

(2 marks)

Q2. (11 marks)

Create a new column titled “Level of education” with following criteria:

• all the farmers Education(years) less than equal to eight label it as primary

• all the farmers Education(years) greater than 8 and less than equal to 13 label it secondary.

• all the farmers Education(years) greater than 13 label it as tertiary.

(1 marks)

Now create a new variable ‘cane output per acre’ in a new column. (Cane output per acre = cane output / cultivated area). (1 mark)

a. Calculate the descriptive statistics using MS-Excel for cane output per acre based for farmers with primary education and for farmers with secondary education. (Hint: ignore non-numeric cells in computing). Interpret the following statistic (Mean, Median, Mode, Standard Deviation) obtained for farmers with primary education. (7 marks)

b. What conclusion can be reach from the comparison of descriptive statistics between cane output per acre for farmers with primary education and for farmers with secondary education? Justify why or why note there is significant difference in output? (2 marks)

Q3. (9 marks)

Construct a contingency table and relative contingency table (using Pivot table tool in Excel) for farming status in raw and Land Owned in column. (4 marks)

a. What is the probability that a randomly selected farmer does not own the land? (1 mark)

b. What is the probability that a randomly selected farmer is working full time and does not own the land?

(1 mark)

c. What is the probability that a randomly selected farmer does not own the land given that farming status is full time? (1 mark)

d. What can you conclude from above analysis in regards to land ownership in sugar industry? (2 marks)

Q4. (8 marks)

a. Assume that the annual profit from farming is nearly normally distributed. Individual earning less than $2000 is believed to be in poverty. Calculate what proportion of sugar cane farmers are in poverty?

(3 marks)

b. A researcher intends to estimate population proportions of farmers in Fiji are in poverty. The researcher intends to be 99% confident and expects that his estimation to be within 3% of population proportion. How large sample size should be taken to achieve these conditions. (3 marks)

c. Which sampling procedure would you recommend to the researcher in part (b), provide reason for your answer. (2 marks)

Q5. (6 marks)

a. Construct a 99% confidence interval for the mean cane output per farmer. Interpret. (3 marks)

b. Construct a 95% confidence interval for population mean can output per acre. Comment on your results.

(3 marks)

Q6. (8 marks)

Test whether the mean annual profit from farming is more than $2000 or not. Use a = 0.05 and the P-value method. Show all five steps of Hypothesis testing. Comment on your results in regards to poverty for sugar cane farmers.

THE END

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