What do you mean by hypothesis? Describe null and alternative hypothesis. A company claims that its light bulbs are superior to those of the competitor on the basis of study which showed that a sample of 40 of its bulbs had an average life time 628 hours of continuous use with a standard deviation of 27 hours. While sample of 30 bulbs made by the competitor had an average life time 619 hours of continuous use with a standard deviation of 25 hours. Test at 5% level of significance, whether this claim is justified.

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A hypothesis is a tentative theory or supposition provisionally adopted to explain certain facts and to guide in the investigation of others.

A statistical hypothesis which is tentative statement or supposition about the estimated value of one or more parameter of the population is called parametric hypothesis. A statistical hypothesis about attributes is called non-parametric hypothesis.

If a hypothesis completely determines the population, It is called a simple hypothesis, otherwise composite hypothesis.

In testing of hypothesis a static is computed from a sample drawn from the parent population and on the basis of the statistics it is observed whether the sample so drawn has come from the population with certain specified characteristic.

Null Hypothesis:

The supposition about the population parameter is called null hypothesis. It is set for testing a statistical hypothesis only to decide whether to accept or reject the null hypothesis which is tested for possible rejection under the assumption that is true.

It is the hypothesis of no difference between sample statistics and parameter. It is hypothesis of no difference between parameters.

Null hypothesis is denoted by Ho. It is set up H0 = μ0

Suppose we want to test the average score of students in Bsc. entrance exam is 55 then to start testing the hypothesis we assume the average score is 55. There is not difference between sample average and population average. Then the null hypothesis is H0 = 55.

Alternative Hypothesis:

A hypothesis which is complementary to null hypothesis is called an alternative hypothesis.

Any hypothesis which is not null is also called alternative hypothesis. It is hypothesis of difference between parameters.

Alternative hypothesis is denoted by H1.

Alternative Hypothesis are

  1. two tailed
  2. one tailed right
  3. one tailed left

Alternative hypothesis is set up as H1 ≠ μ0 for two tailed or H1 > μ0 for one tailed right or H0 < μ for one tailed left.

Let μ1 and μ2 be mean life of bulbs of company and it’s competitor respectively.

Sample number of company (n1) = 40

Sample mean life of bulb of company (x̄1) = 628

Sample Sd of life of bulb of company (S1) = 27

Sample number of bub of competitor (n2) = 30

Sample mean life of bulb of competitor (x̄2) = 619

Sample Sd of life of bulb of competitor(S2) = 25

Let μ1 = Population mean wage of workers from Pokhara and

μ2 = Population mean wage of workers from Kathmandu

Problem to test:

H0 = μ2

H1 > μ2

Test statistics

Z = \(\frac{\overline{x}_1 – \overline{x}_2}{\sqrt{\frac{S_1^2}{n_1} + \frac{S_2^2}{n_2} }}\)

Z = \(\frac{628 – 619}{\sqrt{\frac{27^2}{40} + \frac{25^2}{30} }}\)

Z = \(\frac{9}{\sqrt{39.058}}\)

Z = 1.44

Critical Value

Let α = 0.05 be the level of significance then the critical vale for one tailed test is

Ztabulated = Zα = 1.645

Dcision

Z = 1.44 < Ztabulated = 1.645, accept H0 at 0.05 level of significance.

Conclusion:

The claims of company that is light bulbs are superior to those of the competitor is not correct.

 

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