Hypothesis Test Power

A statistical hypothesis test is a technique of making decisions using experimental information. In statistics, an effect is called statistically significant if it is doubtful to have happen by possibility. Critical examination of this category may be called tests of significance, and when such examination is available we may determine whether a next sample is or is not significantly dissimilar from the initial. Let us study about the topic hypothesis test power given below content with some example problems.


Example problems for hypothesis test power:

Example 1:

A sample of 900 members is establish to have a mean of 3.4 cm and standard deviation 2.61 cm. is the example in use from a great population of mean 3.25 cm and standard deviation 2.61 cm. If the population is usual and its mean is unknown, Get 95% self-confidence limits of exact mean.

Solution:

Given:

H0 : µ = 3.25
H1 : µ ? 3.25
L.O.S  a = 0.05

Test Statistic:

Z = (barx-mu)/(sigma)/(sqrt(n))

Given bar x = 3.4, µ=3.25, n=900, s=2.61

Z = (3.4- 3.25)/(2.61)/(sqrt(900))

= 1.724

Critical value:

At 5% level, the table  value of Z = 1.96

Conclusion:

Since |Z| <1 .96="" 5="" accepted="" at="" h0="" is="" level="" of="" p="" significance.="">
The sample is taken from population whose mean is 3.25 cm

Mean µ is unknown, 95% confidence limits of µ are = barx+-1.96 sigma/(sqrt(n))

=3.4+- 1.96*(2.61)/(sqrt(900))

= 3.4+- 0.17

=3.23,3.57

Example 2:-using hypothesis test power

A construct maintains that his artificial fishing line has a mean contravention strength of 8 kg and standard deviation 0.5 kg . Can we consider his state if a random sample of 50 lines yield a denote contravention power of 7.8kg?

Solution:

Given:

H0 : µ = 8
H1 : µ ? 8
L.O.S: a = 0.01

Test Stastistic

Z =(barx-mu)/((sigma)/(sqrt(n)))

Given:

barx = 7.8, mu = 8, n = 50, sigma = 0.5

Z = ((7.8)-8)/((0.5)/(sqrt(50)))

= - 2.828

|Z| = 2.828

Critical value:

At 1% level of significance the table value of Z = 2.58

Conclusion:

Since |Z|>2.58,H0 is rejected at 1% level.

The manufacture’s claim is not accepted.


Practice problem for hypothesis test power:

Problem 1: using hypothesis test power

On a test given 60 students at a huge number of several colleges, the mean position was 74.5 and S.D was 8.0. at one exacting college, where 200 students took test, the mean position was 75.9%. Discuss the meaning of this answer at 5% level.

Solution:

Z = 2.45, significant at 5% level.

Problem 2: using hypothesis test power

A random sample of 400 items is pinched from a normal population whose mean is 5 and whose variation is 4. if the sample mean is 4.45, can the sample be regard as truthfully random sample?

Solution:

Z= 5.5; H0 is rejected , No.