A school caretaker looks after 6 children. The ages (in years) of the children are given below:
| Child Name | Age (in years) |
|---|---|
| Meena | 5 |
| Aarav | 4 |
| Nisha | 6 |
| Kabir | 4 |
| Pooja | 5 |
(i) What is the nature (type) of the population of the ages of children?
(ii) Construct the sampling distribution of the sample mean for all possible samples of size .
(iii) Comment on whether the sampling distribution is approximately normal.
(iv) Find the mean and standard error of the sampling distribution.
The population of ages is a finite and discrete population, since it consists of a fixed number of children and the ages take only specific integer values. Taking the ages as 5, 4, 6, 4 and 5, all possible samples of size 2 drawn without replacement are ( \binom{5}{2} = 10 ). The sample _________ ____ ___ ___ _______ _____ ___.
__________ _______ ________ _________ ____ ____ ______ __________ ___.
_____ ____ _____ _______ ______ ______.
__________ __________ ________ ___ ____ ____ _____ _______ ___ ___ ______ ______.
_________ _______ __________ _______ ______ _______ ________ _______ ______ _________.
______ ________ ______ ________ __________ _____.
__________ ______ _____ __________ ____ _______ ______.
___ ___ ________ _____ ______.
________ ___ _______ ____ _______ _____ _____ ____ ___ ______.
_____ __________ _________ ________ ____ _________ ____ ________ __________.
____ __________ ___ _______ _____ __________ _________ __________ ____ _______ __________ _______.
_____ ________ ____ __________ __________ ___ _______ __________.
___ ____ ______ _________ _______.
_________ _________ ______ ___ ________ __________.
_____ ________ ____ ___ ____ __________ _________ _____ __________ ________ _______ _________.
________ _________ __________ _______ ___ __________ ________ _______ __________.
____ __________ ____ _____ _____ ___ ________ _____ __________ _____ _____ _____.
_______ _______ _____ ___ ____.
___ ________ _______ __________ ___ ____ _________ _________ ______ _________.
_________ _____ ____.
Get Full Answer on WhatsApp
5. A researcher wants to compare the average test scores of students taught using Method A and Method B. A random sample of students was selected from each group, and their scores are given below:
| Student | Method A | Method B |
|---|---|---|
| 1 | 68 | 72 |
| 2 | 74 | 75 |
| 3 | 71 | 78 |
| 4 | 69 | 70 |
| 5 | 73 | 76 |
| 6 | 70 | 74 |
| 7 | 72 | 77 |
| 8 | 75 | 79 |
3. Let be a random sample from a population with mean
and variance
. Consider the estimator
(i) Find the bias of the estimator .
(ii) Find the variance of .
(iii) Check whether it is more efficient than sample mean.
6. Let be a random sample from the Exponential distribution with pdf
(i) Obtain the maximum likelihood estimator (MLE) of .
(ii) Hence, find the maximum likelihood estimate of for the observed sample:
2.1, 1.6, 3.4, 0.9, 2.5
A survey was conducted to study the preference for online learning among students from urban and rural areas. Out of 300 urban students, 210 preferred online learning, while out of 250 rural students, 150 preferred online learning. Construct a 95% confidence interval for the difference between the population proportions of students preferring online learning in urban and rural areas.
A school caretaker looks after 6 children. The ages (in years) of the children are given below:
| Child Name | Age (in years) |
|---|---|
| Meena | 5 |
| Aarav | 4 |
| Nisha | 6 |
| Kabir | 4 |
| Pooja | 5 |
(i) What is the nature (type) of the population of the ages of children?
(ii) Construct the sampling distribution of the sample mean for all possible samples of size .
(iii) Comment on whether the sampling distribution is approximately normal.
(iv) Find the mean and standard error of the sampling distribution.
State whether the following statements are True or False. Give reason in support of your answer:
(a) The Wilcoxon rank-sum test is a non-parametric alternative to the two-sample t-test when normality is not assumed.
(b) The power of a statistical test is the probability of accepting the null hypothesis when it is true.
(c) If the sample size tends to infinity, the variance of a consistent estimator must tend to zero.
(d) In the method of moments, population moments are equated to corresponding sample moments.
(e) The chi-square distribution is symmetric for all degrees of freedom.
Describe the following:
(i) t-distribution
(ii) General procedure of Testing of hypothesis