Quizzes and exercises of estimation

These quizzes and exercises help us review and practice what we obtained in this chapter. They are presented in "show-hide" form similar to the sections of a web page as we are already familiar. Quizzes are multiple choice questions. After choosing an option, an announcement of result appears. To return back to this page, we click "OK" on the announcement. Of course we can choose again.

In exercises, we are required to calculate a value then fill it in an empty rectangle. Note that in this rectangle, only value is acceptable, its unit is not required. After filling the result, we click on "Answer". If the answer is correct, the border of the rectangle is green and there is green "V" symbol in the adjacent square. If the answer is wrong, the border of the rectangle is red and there is red "X" symbol in the adjacent square. We can erase the answer and retry by clicking on "Retry".

For each exercise, there is a hidden solution. To show this solution, we click on "Solution" tab. But try to solve exercises by ourself, don't abuse these solutions.

Quiz 1

By central limit theorem,

Quiz 2

Standard error is

Quiz 3

A statistic can be considered as

Quiz 4

If we increase the number of elements of sample and keep other quantities unchanged, confidence interval will

Quiz 5

Assume that `X` is a random variable conforming to normal distribution. We take a sample, and determine mean and standard deviation of `X` (for sample). From these two statistics, we can not yet determine confidence interval of mean corresponding to

Quiz 6

The higher confidence level is,

Quiz 7

The estimate is unbiased when

Exercise 1

A survey was conducted at supermarket S with 80 customers. The result shows that there are 56 customers preferring soft drink. What is the standard error of proportion of customers preferring soft drink at supermarket S ?

Solution

Proportion of customers preferring soft drink in sample `p=56//80=0,70`

Standard error of this proportion is :

`SE=sqrt((p(1-p))/n)=sqrt((0,70xx0,30)/80)=0,0512`

Exercise 2

Pulse rates of 12 patients of hospital H are shown in Table 1.

Table 1 Pulse rates of 12 patients of hospital H
72	86	94	83	66	88
74	71	85	77	86	75

With confidence level 95%, determine lower bound and upper bound of confidence interval of mean of pulse rates of patients in hospital H.

• Lower bound of confidence interval:

• Upper bound of confidence interval:

Solution

Confidence interval of mean of pulse rates µ is determined by:

`bar x-t_(alpha//2,nu)\ s/sqrt(n)<=mu<=bar x+t_(alpha//2,nu)\ s/sqrt(n)`

In which :

`bar x` : mean of pulse rates of 12 patients. `bar x=79,75`
`alpha` : significance level of estimation. With confidence level of 95% then `alpha=0,05`
`nu` : degree of freedom. With sample of `n=12` then `nu=n-1=11`
`t_(alpha//2,nu)` is determined from percentage point table of Student's distribution,
`t_(0,025,11)=2,2010`
`s` : standard deviation of pulse rates. From sample of 12 patients: `s=8,4`

Hence : `t_(alpha//2,nu)\ s/sqrt(n)=2,2010xx(8,40)/sqrt(12)=5,337`

So : `79,75-5,337<=mu<=79,75+5,337`

Or `75,41<=mu<=85,09`

This web page was last updated on 03 December 2018.