P-value
p-value is computed by assuming that the null hypothesis is true. When the p value is small enough, we reject the null hypothesis so as we accept the alternative hypothesis.”small enough” is defined as p value ≤α, where α =level of significance(usually0 .05)= 1-confidence interval
Null value
Ho:population parameter =null value
Null value is the specific number.If the parameter equals that number, then the null hypothesis is true.
Two-sided alternative hypothesis:
Ha:population parameter ≠null value
One-sided alternative hypothesis (choose one)
Ha: population parameter > null value
Ha: population parameter < null value
alternative hypothesis never includes the equals sign
Example 1 one-sided hypothesis test:
If researchers wanted to find out whether men have a lower mean pulse than women, the hypotheses for this one-sided hypothesis test would be:
Ho:μ1-μ2=0(μ1=μ2)
Ha:μ1-μ2<0(μ1<μ2)
μ1,μ2 are the mean pulse rates for the population of all men and all women, and the null value is 0.
Example 2
Suppose that a null hypothesis, in words, is that the mean weight for the population of newborn babies is the same in the United States as it is in England.
Ho:μ1-μ2=0
null value =0
Example 3
A legislator who wondered whether more than 50% of the voters in her district favored a law that would reduce the legal blood alcohol level that defines drunk driving. We let p= proportion of all voters in the district favoring the lower limit. A majority is p>0.5, so the null and alternative hypotheses for this situation may be written as:
Ho:p≤ 0.5(not a majority)
Ha:p>0.5(a majority)
The null value in this instance is pο=0.5