Hypothesis testing is essentially about the search for statistical significance.
ID: 3333330 • Letter: H
Question
Hypothesis testing is essentially about the search for statistical significance. When we make a statement, we want to be able to make it with confidence (statistical confidence, not arrogance). Note that hypothesis testing is never about truth. We make a statement and then attempt to "prove" it. However, we can never prove a statement because it will be based on samples and assumptions. For this reason, we set up our hypotheses so that the null hypothesis contains the opposite of what we want to prove. Why? Because when we gather the facts, calculate the test statitics and p-values, we either reject or fail to reject the null. If we reject the null, then we must then "accept" the alternative. If the opposite is disproved, then what we wanted in the first place must be true, right? Not really. It just means that it is true for now, for this sample, and until it is proven wrong in a later test.
That may seem convoluted, but there are enormous, every-day implications of hypothesis testing. Suppose you make the statement, "The new product/process will increase sales by X%." Your boss says, "Oh, really. Are you sure?" You get to say that you are 95% confident because you have statistical significance on your side. You don't have to set up formal hypotheses to use the technique. How might you use these techniques?
250 words please
Explanation / Answer
SOL:
NULL HYPOTHESIS:
there is no oincrease in sales of the new product
Alternative Hypothesis:
The new product/process will increase sales by X%."
select Level of significance=0.05
Test statistic:
Z=sample proportion-population proportion/sqrt(population proportoon(1-pop proportion)/sample szie
calculate sample proportion for a given sample size as
p^=x/n=successes/total
and calculate Z
Decison riule:
if p<0.05 reject null ypothesis
if p>0.05 accept alternative hypothesis
Concluson:
Basing on p value conclude whether it is in favour of null or alternative hypothesis
Using 95% confidence interval for proportion
Calculate 95% confidence interval for proportion as
p^-zcritsqrt(p^(1-p^)/n,p^+zcritsqrt(p^(1-p^)/n
z crit fro 95%=1.96
If the confidence interval contains null value then accept null hypothesis
else reject null hypothesis
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