# Statistical Methods-Tests of Significance (ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern)): Questions 15 - 17 of 17

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## Question number: 15

» 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: 16

» 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

## Question number: 17

» Statistical Methods » Tests of Significance » Chi-Square

Appeared in Year: 2009

### Describe in Detail

Explain the method of testing normality by using chi-squared test.

### Explanation

Let X is a random variable follows normal distribution with mean µ and variance σ ^{2}. The testing of null hypothesis is that the population variance σ ^{2} equals a specified value against one of the usual alternatives σ ^{2} < , σ ^{2} > ,