# ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 99 - 103 of 165

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## Question number: 99

» Statistical Methods » Standard Errors and Large Sample Tests

Appeared in Year: 2009

### Describe in Detail

A sample of 100 records on lengths of stay of patients in a hospital gave a standard deviation of days of stay as 4·9. In order to estimate the mean number of days of stay within 0·25 day with 95 % confidence, what should be the sample size?

### Explanation

Let the patients in a hospital gave a standard deviation of days of stay as 4.9. The mean number of days of stay within 0·25 day that is margin error is the estimate fraction days between the difference of estimated and the true number of days. So, the test statistic for 95 % confidence is

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## Question number: 100

» Statistical Methods » Association and Contingency

Appeared in Year: 2013

### Describe in Detail

Out of 200 persons appeared for an examination, 80 % were males and the rest were females. Among 30 married males, 14 were successful; 110 unmarried males were successful. In respect of 10 married females, 4 were successful; 20 unmarried females were successful. Compute Yule’s coefficient of association between success in the examination and the marital status for males as well as females.

### Explanation

Out of 200 persons appeared for an examination, 160 males and 40 are females.

The frequencies for various attributes be show in this contingency table

Male | Successful (A) | unsuccessful (a) |

married (B) | (AB) =14 | (aB) =16 |

unmarried (b) | (Ab) =110 | (ab) =20 |

Female | successful (A) | unsuccessful (a) |

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## Question number: 101

» Probability » Convergence » In Distribution

Appeared in Year: 2014

### Describe in Detail

{X _{n}} is a sequence of independent variables. Show that

where X is a random variable. Is the converse true?

### Explanation

The sequence X _{n} converges to X in probability if for any ε > 0

The sequence X _{n} converges to the distribution of X as n tends to infinity if

For ε > 0,

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## Question number: 102

» Statistical Methods » Bivariate Distributions » Bivariate Normal Distribution

Appeared in Year: 2009

### Describe in Detail

Given the joint density of (X _{1}, X _{2}),

Find the marginal densities of X _{1} and X _{2}. Also find E [X _{1}].

### Explanation

The joint density is written as

The marginal distribution of X _{1}

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## Question number: 103

» Statistical Methods » Non-Parametric Test » Wilcoxon

Appeared in Year: 2011

### Describe in Detail

Apply the Wilcoxon two-sample test to the following data on the first breakdown times of two brands of computers:

Brand A 98,102,47,85,99,140,130

Brand B 95,125,160,155,148.

Use 1·96 as the critical point for the appropriate test.

### Explanation

Let n _{1} be the number of breakdown times in the Brand A with median time m _{1}, and n _{2} the number of breakdown times in the Brand B with median time m _{2}. Then the hypothesis is that the median times of the two brands are equal against the alternative that they are unequal.

For this f

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