## Likelihood Ratios and Statistical Tests

In the first question, we make valid conclusions on the given likelihood ratio tests. The question that follows involves using a sample size to estimate parameters like the mean, standard deviation, and the standard error of the mean. What's more, we find the confidence interval of the mean and recommends a sample size suitable for finding the mean value under given conditions

## Likelihood Ratios

Q4.1 The following table shows the Likelihood ratio for test positive and likelihood ratio for test negative of 3 biomarkers to diagnose Disease A. Answer the following question.

**Likelihood Ratio**

Test | Test Positive | Test Negative |

Biomarker 1 | 2.4 | 0.3 |

Biomarker 2 | 5.7 | 0.6 |

Biomarker 3 | 1.07 | 0.9 |

**(i)**Which test/biomarker would be the best to rule in Disease A?

**Biomarker 2
**

** (ii) **Which test/biomarker would be the best to rule out Disease A?

**Biomarker 1
**

** (iii) **Which test/biomarker is the least useful test for both rulings in and ruling out disease A?

**Biomarker 3**

## Statistical Estimation Using Tests

**Q5.1 You would like to estimate the birth weight and rate of low birth weight(<2.500kg) of Chinese male babies in Hong Kong. Worksheet A provides the birthweight of boys delivered in Hospital A in Hong Kong. Provide answers for the following. Give answers to 3 decimal places.**

- (i) What is the sample size?

**The sample size is 200
**

(ii) What is the mean and its standard deviation?

**The mean is 3.077 and the standard deviation is 0.467
**

(iii) Standard Error of the mean

**The standard error of the mean is 0.033
**

(iv) Margin of error for the mean at the 95% confidence level

**Margin of error = 1.96 * 0.467/√200
**

** = 1.96 * 0.033
**

** = 0.065
**

(v) 95% confidence interval of the mean

**95% C.I for mean
**

**= (3.077 – 0.065, 3.077+0.065)
**

**= (3.012, 3.142)
**

(vi) What is the sample size required in a survey to assess the mean value with an error at half of the current error?

**The sample size is based on confidence level, the larger the required confidence level, the higher the sample size.
**

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