# 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

Under the model, the parameter space is

Under the null hypothesis, the p

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## 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 the smoker in 2012. Le

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## 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 →α=0.05

σ = 1 and z _{α/2} =1.96

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## 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 each other. The test of hypothesis is

The sample size of X is n = 12 and Y is m = 10

The test is depend upon the population variance is kno

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## 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 hypothesis is

The sample size is n = 8

then tes

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