ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 113 - 115 of 164

Access detailed explanations (illustrated with images and videos) to 164 questions. Access all new questions- tracking exam pattern and syllabus. View the complete topic-wise distribution of questions. Unlimited Access, Unlimited Time, on Unlimited Devices!

View Sample Explanation or View Features.

Rs. 550.00 -OR-

How to register? Already Subscribed?

Question 113


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.


The given information can be written as in a table:


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. Let P1 and P2 are the proportion of smoker in year 1995 and 2012 with sample size n1 an…

… (51 more words) …

Question 114

Appeared in Year: 2014

Describe in Detail


If fx (x) be the probability density function of a N (µ, σ 2) distribution, then show that

where , and φ (x) and Φ (x) are the probability density function and distribution function of the standard normal distribution respectively.


Given that fX (x) be the probability density function follows N (µ, σ 2) .


… (1)

Let assume that = z, then differentiate

The limit is also change, the lower limit is and upper limit is

Equation (1) can be written as

The first integral is the distribution function of standard normal distribution

… (4 more words) …

Question 115

Appeared in Year: 2012

Describe in Detail


Ten short-distance runners were put to a rigorous training for two months. Times taken by them to clear 100 metres before and after the training were as follows:

Sl. no. of runner12345678910
Time (in sec)



Time (in sec)



Use Wilcoxon՚s paired sample signed rank test to examine at 1 % level if the training was at all effective. (The critical value of Wilcoxon՚s statistic at 1 % level of significance for n = 10 is 5)


In Wilcoxon՚s paired sample signed rank test, the null hypothesis that we are sampling two continuous symmetric populations with for the paired-sample case, we rank the differences of the paired observations without regard to sign and proceed as in the single-sample case

Let and represent the median time of all runner put to a rigorous training b…

… (141 more words) …