# ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 145 - 150 of 165

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## Question number: 145

» Statistical Methods » Correlation Coefficient » Multiple Correlation

Appeared in Year: 2011

### Describe in Detail

Describe a test of independence of two normal random variables based on r, the sample correlation coefficient using the t distribution. If n = 10 and r = 0·9, then carry out the test.

### Explanation

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## Question number: 146

» Statistical Methods » Correlation Ratio

Appeared in Year: 2009

### Describe in Detail

Define correlation ratio η· Show that

0 ≤ ρ ^{2} ≤ η ^{2} ≤ 1.

### Explanation

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## Question number: 147

» Probability » Probability Generating Functions

Appeared in Year: 2009

### Describe in Detail

Find the generating function of X whose probability density function is

P [X = r] =pq ^{r-1}, r = 1, 2, …, 0 < p < 1, q = 1 - p

### Explanation

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## Question number: 148

» Statistical Methods » Non-Parametric Test » Wald-Wolfowitz

Appeared in Year: 2015

### Describe in Detail

Given the random samples

X: 1, 5, 7, 9, 15, 17, 21, 23

Y: 2, 6, 10, 12, 18, 20, 26, 28, 32

From the populations having the distribution function respectively as F _{1} and F _{2}, test the hypothesis

against

at 5 % level of significance by the Wald-Wolfowitz run test. It is given that the critical number of runs at the sample sizes (8, 9) at 5 % level is 5.

### Explanation

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## Question number: 149

» Statistical Methods » Correlation Coefficient » Partial Correlation

Appeared in Year: 2010

### Describe in Detail

Find the most likely price in Mumbai corresponding to the price of Rs. 70 at Kolkata from the following:

Kolkata | Mumbai | |

Average price | 65 | 67 |

Standard deviation | 2.5 | 3.5 |

Correlation coefficient between the prices of commodities in the two cities is 0·8.

### Explanation

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## Question number: 150

» 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

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