Question#1
The null hypothesis is a hypothesis, which is checked for consistency with the existing sampling (empirical) data. Often used as a null hypothesis act hypothesis of no relationship or correlation between the studied variables, no differences (homogeneity) of the distributions (or parameters of distributions) of two and / or more samples. The standard scientific approach for testing hypotheses the researcher attempts to show the failure of the null hypothesis of its inconsistency with the available experimental data, that is, to reject the hypothesis. This implies that there must be adopted another, alternative (competing), excluding the zero hypothesis. Used in the statistical test.
The alternative hypothesis is the assumption taken in case of rejection of the null hypothesis. An alternative hypothesis asserts a positive relationship between the studied variables.
Examples of hypotheses.
1. Situation. Randomly selected group of 200 people looked brand advertising. During the next week noted that some of this group acquired the advertised product.
The null hypothesis. Advertising had no effect. (The percentage of buyers in the group does not differ from the general population).
An alternative hypothesis. Advertising has had an effect. (The percentage of buyers in the group differs from the general population).
2. Situation. You learn additive for gasoline, reduces fuel consumption (as stated by the manufacturer).
The null hypothesis. The additive does not influence the fuel consumption.
An alternative hypothesis. Additive affects fuel consumption.
3. Situation. Your company makes a claim in contradiction salaries by gender.
The null hypothesis. Wages of men and women are equal.
An alternative hypothesis. Wages of men and women are not equal (there is a significant difference).
Question#2
The example of test the hypothesis on one sample. Suppose we study the effect of introducing an additive for increasing output. Average yield to the use of additives is 32.1 kg per day. Based on 7 -day observation period after making supplements enjoyed average yield of 39.6 kg. The standard error in this case was 4.2 kg (SХ = ).).
The question is whether there is really the effect of the introduction of additives, or the results are "random" character?
Decision.
The null hypothesis states that the introduction of additives do not cause any effect (ie the output of products before and after the experiment did not differ). H0: μ = 32,1.
Alternative hypothesis states that there is an effect of making the additive (ie yield before and after the experiment is different).
H1: μ ≠ 32,1.
Confidence interval values takes the form:
39,6 - 2,447 * 4,2 ≤ μ ≤ 39,6 + 2,447 * 4,2
29,3 ≤ μ ≤ 49,9
Conclusion: The set value as 32.1 flagged confidence interval, the results of research experiments did not confirm the hypothesis that the use of additives has effect. Result 32.1 is quite possible, even when using supplements. Therefore, the alternative hypothesis is rejected and accepted the null hypothesis: the use of the additive does not affect the increase in output.
A procedure to test two-sample hypothesis is almost the same. For example, it may be processed with two-sample t-test (for mean difference).
