Question

Discuss, if there is any relationship between "point estimate", "the standard deviation", "the hypothesis testing" and explain with your own words and explain with your own example.

Answer 1

Point estimate:

Point estimate represnts a single value of statistics.

example: A sample mean represents point estimate of given population mean ().

Standard deviation:

Standard deviation represents square root of average value of (x₁ -)

Therefore SD= = =(x-)²/n

Hypothesis testing:

To decide whether there is significant difference between sample statistics. There is no difference between sample statistics.

* Relation between point estimate, standard deviation and hypothesis testing

Ztest statistics Z= /

Example:

There is sample of 100 persons having mean 165 cms, height 158cms. Height of persons are normally distributed with standard deviation 6 cms. So that the hypothesis that mean height of person is 165 cms.

Given that

=158 cms

=6 cms

n=100

= 165 cms

Null hypothesis: H₀

  =

Alternative hypothesis: H_a

  

Test statistics Z= /

= 165-158/6/

= 7/0.6

Z=11.7

At 5% level of significance,Z_1ab=1.96.

At 1% level of significance , Z_1ab=2.58

Z_cal value is greater than both cases.

At both 1% & 5% level of significance.

Z_cal > Z_+ab.

Therefore Null hypothesis is rejected. So there is significance difference between sample statistics.

Hence proved.