## Answer:

Study of Australian Obese

### Introduction:

BMI is a good indicator of health status. The body mass index (BMI) or Quetelet index is calculated from the weight and height of person. It is defined as

BMI= weight in kg/ (Height in metres)^{2}

The unit of BMI is Kg/m^{2}. The general categories of BMI as Follows

Sr. No. |
Category |
Range |

1 |
Underweight |
<18.5 |

2 |
Normal |
18.5-24.99 |

3 |
Overweight |
25-29.99 |

4 |
Obese |
>=30 |

Schousboe et al. (2003) studied the studied the sex differences in BMI. Dalton et al. (2003) studied the correlation of BMI with cardiovascular diseases risk factors. In this study we are interested to know whether the proportion of obese is more than 0.25 or not. We have collected the data from National Health Survey 2014-15, Australian Bureau of Statistics. (https://www.abs.gov.au/AUSSTATS/[email protected]/DetailsPage/4364.0.55.0012014-15?OpenDocument). This survey records the height and weight of 17733 person. For the remaining sections we referred Rajagopalan (2006).

### Hypothesis:

Here we are interested to test the following null and alternative hypothesis.

Null Hypothesis: Proportion of Australian obese is 0.25. i.e. H_{0}: P = P_{0 }= 0.25

Against

Alternative Hypothesis: Proportion of Australian obese is more than 0.25. i.e. H_{1}: P > P_{0 }= 0.25

Where P is population proportion of Australian obese and P_{0} is specified value i.e. 0.25.

Testing of Hypothesis:

For the above null and alternative hypothesis, we calculate the following test statistics

where sample proportion of Australian obese, and .

For our data, out of 17733 persons 4944 persons are found obese means there BMI is equal to and over 30.

So,

= 4944 / 17733 = 0.2788, and

We get

Z cal = 8.8569.

Decision Criteria for rejecting null hypothesis:

We take level of significance 5%. i.e. . As n is large our test statistic Z follows normal distribution with mean 0 and variance 1. This is one sided test as H_{1}: P > P_{0 }= 0.25 so we reject null hypothesis if

Z cal > Z tab

Z tab is obtained from normal distribution table for level of significance 5%. i.e. ,

Z tab = 1.64

So now Z cal = 8.8569 > Z tab = 1.64

So at level of significance 5%. i.e. we reject null hypothesis. We claim that proportion of Australian obese is more than 0.25.

Excel Output:

Sample Size (n) |
17733 |

Obese in Sample |
4944 |

p |
0.2788 |

P0 |
0.25 |

Z cal |
8.8569 |

alpha |
0.050 |

Z tab |
1.645 |

P-Value |
0.000 |

## Conclusion:

From the comparison of Z cal and Z tab, we reject the null hypothesis at 5%. So we can say that more than 25% Australian are obese. We can also observe that P value = 0.000 < 0.05, conclude that reject null hypothesis.

### Interpretation:

We test the above null and alternative hypothesis. We reject the null hypothesis. From the given study using the data from National Health Survey 2014-15, Australian Bureau of Statistics, we conclude that in Australia more than 25% people are obese. It is critical observation. Government need to concentrate on this issue.

## References:

Dalton, Marita, A. J. Cameron, P. Z. Zimmet, J. E. Shaw, D. Jolley, D. W. Dunstan, T. A. Welborn, and AusDiab Steering Committee. "Waist circumference, waist–hip ratio and body mass index and their correlation with cardiovascular disease risk factors in Australian adults." Journal of internal medicine254, no. 6 (2003): 555-563.

Rajagopalan, Vaithilingam. Selected statistical tests. New Age International, (2006).

Schousboe, Karoline, Gonneke Willemsen, Kirsten O. Kyvik, Jakob Mortensen, Dorret I. Boomsma, Belinda K. Cornes, Chayna J. Davis et al. "Sex differences in heritability of BMI: a comparative study of results from twin studies in eight countries." Twin Research and Human Genetics 6, no. 5 (2003): 409-421.

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