# Statistical Methods (ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern)): Questions 66 - 69 of 72

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## Question number: 66

» Statistical Methods » Measures of Location

Appeared in Year: 2013

### Describe in Detail

For the following frequency distribution on 229 values:

Class | Frequency |

0 - 10 | 12 |

10 - 20 | 30 |

20 - 30 | x |

30 - 40 | 65 |

40 - 50 | y |

50 - 60 | 25 |

60 - 70 | 18 |

the median is found to be 46. Find the values of x and y.

### Explanation

The cumulative frequency is

Class | Frequency | Cumulative frequency |

0 - 10 | 12 | 12 |

10 - 20 | 30 | 42 |

20 - 30 | x | 42 + x |

30 - 40 | 65 | 107 + x |

40 - 50 | y | 107 + x+y |

50 - 60 | 25 | 132 + x+y |

60 - 70 | 18 |

## Question number: 67

» Statistical Methods » Tests of Significance » T-Test

Appeared in Year: 2009

### Describe in Detail

Two set of students were given different teaching methods. Their IQ’s are given below:

Set I | 77 | 74 | 82 | 73 | 87 | 69 | 66 | 80 |

Set II | 72 | 68 | 76 | 68 | 84 | 68 | 61 | 76 |

Test whether the two teaching methods differ significantly at 5 % level of significance. (Assume critical value of test statistic to be 1.96)

### Explanation

Let X _{i} is random variable of student were given different teaching methods in set I with mean and variance σ _{1}^{2} and Y _{j} is random variable of student were given different teaching methods in set II with mean and variance σ _{2}^{2}. The

## Question number: 68

» Statistical Methods » Tests of Significance » T-Test

Appeared in Year: 2013

### Describe in Detail

The memory capacities ·of nine student were tested before and after some training. The data are given below. Test whether the training was effective: (Given t-value at 8 d. f. = 2.36)

Student Number | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |

Before Training | 10 | 15 | 9 | 3 | 7 | 12 | 16 | 17 | 4 |

After Training | 12 | 17 | 8 | 5 | 6 | 11 | 18 | 20 | 3 |

### Explanation

Let X _{i} is random variable of nine student were tested for after training with mean and variance σ _{1}^{2} and Y _{j} is random variable of nine student were tested for before training with mean and variance σ _{2}^{2}. The hypothesis is

The

## Question number: 69

» Statistical Methods » Tests of Significance » F-Test

Appeared in Year: 2014

### Describe in Detail

Explain the procedure for testing the hypothesis of equality of variances of two independent normal populations when population means are unknown. Write down the sampling distribution of the statistic. A sample of size 10 is drawn from each of two uncorrelated normal populations. Sample means and variances are:

1 ^{st} population: mean = 7, variance = 26

2 ^{nd} population: mean = 4; variance = 10

Test at 5 % level of significance whether the first population has greater standard deviation than that of the second population. [Given F _{0.05, 9, 9} = 3.18]

### Explanation

Let X _{1}, X _{2}, …, X _{n} and Y _{1}, Y _{2}, …Y _{m} are the samples taken from independent N (µ _{1}, σ _{1}^{2}) and N (µ _{2}, σ _{2}^{2}).

In this question the hypothesis for testing is