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## Statistics Question

Project Situation

Assume that you are a research assistant engaged to investigate and report on the particulars and circumstances of new-borns.

You will be required to use your sample of 116 births to answer several questions relating to the sample or population. For this project, you will assume that the 116 births surveyed were randomly selected from the population of all births in your particular LHD in 2002.

In each part of the project you are required to analyse your sample data in response to given questions and provide a written answer. You can assume that the written answers are components of a longer report on the birth particulars of children born in the LHD.

**Data Analysis Project – Part A**

**Question:** Provide information on the birth weight of babies born in 2002 in a certain Local Health District (LHD). In particular, what are the minimum and maximum weights, the average weight, and how do these weights vary. Also, within what estimated range would you expect a typical baby’s weight to lie?

**Data Analysis Project – Part B**

**Question 1 **– Topic 5 (9 marks)

You are asked for an estimate of the proportion of older women giving birth in your LHD in 2002.

To provide this estimate use age data and an appropriate statistical inference technique to answer the following question

What was the proportion of babies born in your Local Health District in 2002 to women who were at least 35 years of age?

**Question 2 **– Topic 6 (10 marks)

It has been reported that the average weight of babies of European heritage is 3.5kg. You are asked to investigate whether this was also true for babies in your LHD in 2002.

To provide a justified answer to this question use the bwt data and an appropriate statistical inference technique to answer the following question

In your Local Health District in 2002 was the average birth weight significantly different to the European average?

**Data Analysis Project – Part C **

**Question 1 **Statistical Inference Topic 7 (10 marks)

You are asked if the birth weights, in your LHD, of children born to non-smoking mothers are usually higher than those born to smokers.

Use bwt and smoke data and an appropriate statistical inference technique to answer the following question

On average are the birth weights of babies born to non-smoking mothers greater than those born to smokers?

**Question 2** Simple Linear Regression model Topic 8 (7 marks)

You are asked how the length of a pregnancy influences the birth weight.

Use gestation (independent variable, measured in days) and bwt (dependent variable, in gms) to model the relationship between number of length of pregnancy and birth weight.

Explore this relationship by

- Plotting data with a scatter plot.
- Calculating the least squares regression line, correlation coefficient and coefficient of determination.

**Question 3** Multiple Linear Regression model Topic 9 (9 marks)

You are asked what other factors may have an influence on birth weight.

Explore this by adding age (of mother, in years), height (of mother, in cms), weight (of mother before pregnancy, in kgs), and smoke (smoking status of mother, where 0 is non-smoker, 1 is smoker) as additional independent variables to the regression model developed in Question 2 and

- a) Calculating the multiple regression equation, multiple correlation coefficient, and coefficient of multiple determination.
- b) Using appropriate tests to determine which independent variables make a significant contribution to the regression model.

Hence, determine which independent variables to include in your model.

## Business Management Solution

**Question 1**

In order to determine whether the average weights of babies born to smoking and non-smoking mothers are different, t-test: two samples assuming unequal variances is the appropriate statistical inference technique. This technique is appropriate because it is implemented to determine the difference between sample means when population variances are unequal and unknown. Two samples T-test assuming unequal variances is conducted using MS-Excel Data Analysis Toolkit, and output of the test is shown in Appendix 1.

The null hypothesis and alternative hypothesis for the two samples T-test can be formulated as follows:

- H0 = The average weights of babies born to smoking and non-smoking mothers are not different.
- HA = The average weights of babies born to smoking and non-smoking mothers are different.

Here, the two-tail test is the appropriate test. From Appendix 1, it can be inferred that the average weights of babies born to smoking mothers were found to be 3280.428571 while the average weights of babies born to non-smoking mothers were found to be 3545.861538. From the mean value, it is evident that the average weight of babies born to non-smoker mothers are greater than those born to smoker mothers. Since p-value (0.018) < 0.05, we reject the null hypothesis. Hence, it can be concluded that the average weights of babies born to smoking and non-smoking mothers are significantly different.