ISS (Statistical Services) Statistics Paper III: Questions 34 - 39 of 109
Access detailed explanations (illustrated with images and videos) to 109 questions. Access all new questions we will add tracking exam-pattern and syllabus changes. Unlimited Access for Unlimited Time! View Sample Explanation or View Features.
Rs. 300.00 or
How to register?
Question number: 34
» Sampling Techniques » Cluster Sampling with SRS - Intra-Class Correlation Coefficient
Appeared in Year: 2010
Describe in Detail
What is cluster sampling? In the case of cluster sampling for proportions, obtain an unbiased
Estimator of population proportion. Also, compute variance of your estimator.
Explanation
Cluster sampling:
Cluster sampling is a type of sampling method. In this method, the population is divided into separate groups, called clusters. Then, a simple random sample of clusters is selected from the population. Then analysis is done on the data from the obtained sampled clusters.
The samplings lead to several difficulties if the population s
… (380 more words) …
Question number: 35
» Sampling Techniques » Simple Random Sampling with and Without Replacement
Appeared in Year: 2011
Write in Short
Explain the concept of simple random/sampling with and without replacement. In a simple Random sampling, show that is an unbiased estimator of .
Question number: 36
» Applied Statistics » Index Numbers » Price Relatives and Quantity or Volume Relatives
Appeared in Year: 2011
Describe in Detail
Explain the errors in the measurement of price and quantity index number.
Explanation
All index numbers are affected by mainly three types of errors.
Formula error
Sampling error
Homogeneity error
Formula error:
There is no universally accepted index number formula that will measure the price or quantity changes excatly. Each formula in common use has its own defeat and consequently some error is natural in all index number formula. This
… (233 more words) …
Question number: 37
» Sampling Techniques » Stratified Random Sampling
Appeared in Year: 2011
Describe in Detail
Let for a stratified random sampling where is constant, is the-cost per unit-in ith stratum, is the mean square based on units.
Estimate the sample sizen under optimum allocation for fixed cost .
Explanation
Under optimum allocation, are obtained such that
(i) minimize the variance of the estimate for (a) fixed sample size n;
(i) var ( is minimum for fixed n
(ii) var ( is minimum for fixed total cost C
(iii) Total cost C is minimum for fixed value of var (
And the cost function C in stratified sampling is given b
… (456 more words) …
Question number: 38
» Econometrics » Ordinary Least Squares (OLS)
Appeared in Year: 2011
Describe in Detail
If is an individual’s utility function of two goods, show that the demand for the goods is and
Where and are the fixed price and µ be the individual fixed income.
Explanation
For consumer’s equilibrium, we have
and hence, we get
→
→
→
→
→
→
→ ………………. (i)
since, µ the indivi
… (97 more words) …
Question number: 39
» Econometrics » Auto-Correlation
Appeared in Year: 2011
Describe in Detail
Discuss the effect of imperfect multicollinearity on tests and errors. Consider a model
with
and with
, ,
and
Do you think multicollinearity is present in the model? If yes, give reasons. Further show that as
increases, also increases.
Explanation
Effect of imperfect multicollinearity on tests and errors:
OLS estimators will be BLUE, but they have large variances and covariances. this makes the estimation difficult.
The confidence intervals will be wider. and hence, we may not reject the ‘zero null hypothesis i. e. , We may conclude that B’s are not significantly different from zero even thoug
… (513 more words) …