# Statistical Inference and Hypothesis Testing-Sufficient Estimator (ISS Statistics Paper II (New 2016 MCQ Pattern)): Questions 5 - 8 of 8

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## Question number: 5

» Statistical Inference and Hypothesis Testing » Sufficient Estimator

### Question

Let be a random sample from . Then the sufficient estimator for is

### Choices

Choice (4) | Response | |
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a. |
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b. |
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c. |
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d. | Question does not provide sufficient data or is vague |

## Question number: 6

» Statistical Inference and Hypothesis Testing » Sufficient Estimator

### Question

If a statistic provides as much information as the random variable could provide, Then T is a ________ Statistic

### Choices

Choice (4) | Response | |
---|---|---|

a. | Efficient | |

b. | Unbiased | |

c. | Sufficient | |

d. | Consistent |

## Question number: 7

» Statistical Inference and Hypothesis Testing » Sufficient Estimator

### Question

An estimator is said to be sufficient for a parameter , if it

### Choices

Choice (4) | Response | |
---|---|---|

a. | If it converges to the parameter in probability | |

b. | Contains all the information in the sample regarding the parameter. | |

c. | Contains no information in the sample regarding the parameter | |

d. | Question does not provide sufficient data or is vague |

## Question number: 8

» Statistical Inference and Hypothesis Testing » Sufficient Estimator

### Question

Which of the definition is true for Sufficiency of an estimator?

### Choices

Choice (4) | Response | |
---|---|---|

a. | A statistic is sufficient estimator of parameter if and only if the likelihood function (joint p. d. f. of the sample) can be expressed as where is the p. d. f. of statistic and is a function of sample observations only independent of | |

b. | If is a estimator of parameter based on a sample of size n from the population with density such that the conditional distribution of given T is independent of then T is sufficient estimator of . | |

c. | An estimator is said to be sufficient for if it provides all the information contained in the sample about the parametric function | |

d. | All a. , b. and c. are correct |