Project Description and requirements:

Part A: Group work(50%)

This is group project with a group size of 2 to 3 members. Each group will work on a continuous data set that has a minimum of 50 values.

The following are the tasks to be completed for the project:

1.Use descriptive statistics to summarize the chosen data. (Section 1)

2.Check for the normality of this data.(Section 2)

3.Estimate the population parameter ()of this data using samples of different sizes and at different Confidence Levels.(Section 3)

4.Perform hypothesis testing about the mean to verify or dispute a claim based on the chosen data set.(Section 4)

Further requirements of the project are:

MS-Excel, Megastat Add-in program should be used as and when required by the tasks.

An appropriately formatted MS-Word report describing all the project tasks should be submitted at the end of the project.

Part B: Individual Oral Defense (50%)

Each student will be assessed after the submission of the group project report through an oral defense/viva. This will contribute to 50% of their project grade.

Section I: Descriptive Statistics- Population Parameters and Sample Statistics (17 Marks)

a.Select a Data set from the attached excel file (No Two Groups can choose the Same Dataset)0 Marks

Or, you can obtaining data sets from the following links

i)Data.govhttp://data.gov

ii)US Census Bureauhttp://www.census.gov/data.html

iii)Data.gov.ukhttp://data.gov.uk/

iv)Dubai Statistics Center https://www.dsc.gov.ae/en-us

b.Write a short introduction about the source of data, the data set chosen, the objectives of the study with regard to the chosen data set.0 Mark

c.Summarize and present the Population using Descriptive Statistics (Mean, Median, Modal class, Variance and Standard Deviation, range). .[CLO1]4 Marks

d.Use Excel Megastat to describe data graphically. Make Boxplot and Histogram for population data on Excel.[CLO4]

e.Compare the shape of the histogramobtainedwith common shapes of histograms. (Refer to PPT in Week 2 of BB-Learn) and state which is the closest fit (if any).Explain your answer suitably.

3 Marks

f.Take a Sample of 15 from the above Population using any of the probability-sampling methods studied by you. State and describe clearly, the method of sampling used.

g.Summarize and present the chosen sample using measures of central tendency and dispersion. (Mean, Median, Modal class, Variance, Standard Deviation, Range) 4 Marks

PART II: Checking the Normality of Population (6 Marks)

a. read pages 322-324 of the textbook (provided in BBL in the project folder). 0 Mark

b. Determine normality (i.e. decide whether the distribution is normal or not)

Step 1: Check if the shape of the histogram you created in previous steps is normal

Step 2: calculate Pearson's coefficient of skewness (but use the population's mean and median, and standard deviation, not the sample's) (3 marks)

Step 3: Check for outliers using the formulas in the book(2 marks)

c. Using the values/findings from the above 3 steps, make a decision about whether the population is normally distributed or not (follow the examples in the book). 1 Mark

PART III: Estimation of Population Mean (20 Marks)

a.For the Random sample of size 17 taken above in PART 1, make

1:Point estimate

2: Interval estimates (i.e. confidence interval) for the Population mean at a Confidence level of 99%.

5 Marks

b.Repeat previous step (finding point estimate and interval estimates.) for samples of sizes 36 and 4910 Marks

c.As the sample size changes (increases or decreases), do the widths (upper-lower) of the above three confidence intervals increase or decreases, or there's no relationship?

Comment on this (i.e. why?) 2 Marks

d.The confidence intervals are used to estimate the population mean. From the sample mean you estimated the population mean to be between 2 values. Did the population mean actually fall in the 3 intervals? In other words, was the estimation good?

3 Marks

PART IV: Hypothesis testing (13 marks)

a.Write down a clear 'Research Problem/question/scenario' (This should be a paragraph mentioning the variable and the Hypothesis Test you intend to perform on it.)

For population mean: Use the population mean found in the previous steps

For sample mean and Sample size: pick one of the sample sizes and its corresponding sample mean.

b.Perform Hypothesis Testing for the research problem. Use your own confidence/significance level, type of test and any other data you need to conduct the hypothesis test.

Show all your work clearly, including calculations, sketch of the normal curve, the chosen test and the values of level of significance, critical value(s), etc.

Answer the following:

Population Mean:

Sample Mean:

Sample size:

Standard deviation: (also specify whether you'll choose the sample mean or population mean)

Significance level:

Confidence level:

State the null Hypothesis

State the alternative Hypothesis

How many tails?

Specify if you're going to use z or t test , and state the reason for your answer

Find the Critical Value z/t

Find the test statistic z/t

Make a conclusion/ decision

c.Summarize the results (What do the test results indicate - Reject the Null hypothesisOR Fail to reject the Null Hypothesis?). Write a Final Conclusion connecting your results obtained above with the stated "Research Problem"[CLO5]

Project Report Format (3 marks)

Cover page, page numbers, table of contents and appendices if needed. 3 Marks

SUBMIT BOTH : Excel file + Report