# Statistical Methods-Tests of Significance (ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern)): Questions 10 - 14 of 17

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## Question number: 10

» Statistical Methods » Tests of Significance » Chi-Square

Appeared in Year: 2011

### Describe in Detail

Explain how to carry out the chi-squared test for on the basis of a random sample

X _{1}, X _{2}, …, X _{n} from N (µ, σ ^{2}) population.

### Explanation

Given that a random sample X _{1}, X _{2}, …, X _{n} from N (µ, σ ^{2}) population. The hypothesis is

The null hypothesis is test by chi-square test only assume the sample size is less than 30.

For this we use the likelihood ratio test

## Question number: 11

» Statistical Methods » Tests of Significance » Z-Test

Appeared in Year: 2012

### Describe in Detail

125out of 285 college-going male students in 1995 from a city were found to be smokers. Another sample of 325 such students from the same city in 2012 included 95 smokers. Examine at 5 % level of significance if smoking habit among college-going students is on the decrease in this city.

### Explanation

The given information can be written as in a table:

Year | Smoker | Non-smoker | Total |

1995 | 125 | 160 | 285 |

2012 | 95 | 230 | 325 |

Total | 220 | 390 | 610 |

Here, the null hypothesis is that the proportion of smoker in this two year is same and the alternative is there is decrease in

## Question number: 12

» Statistical Methods » Tests of Significance » Z-Test

Appeared in Year: 2010

### Describe in Detail

How large a sample must be taken in order that the probability will be at least 0.95 that X _{n} will be within 0.5 of µ (µ is unknown and σ = l).

### Explanation

Here, you would know the standard deviation of a population but not know the mean of that population. So, you want to estimate the mean μ to within a given margin of error in a given confidence interval. The required sample size is

Margin of error E = 0.5,

1-α=0.95

## Question number: 13

» Statistical Methods » Tests of Significance » T-Test

Appeared in Year: 2015

### Describe in Detail

Let X _{1}, X _{2}, …, X _{12} be a random sample from a normal N (µ _{1}, σ _{1}^{2}) and Y _{1}, Y _{2}, …Y _{10} be another random sample from normal N (µ _{2}, σ _{2}^{2}), independently to each other. Carry out an appropriate test for testing

at 5 % level of significance. It is given that .

### Explanation

Let X _{1}, X _{2}, …, X _{12} be a random sample from a normal N (µ _{1}, σ _{1}^{2}) and Y _{1}, Y _{2}, …Y _{10} be another random sample from normal N (µ _{2}, σ _{2}^{2}), independently to

## Question number: 14

» 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