Hypothesis testing — Critical Value Method

Unlike the inferential statistics, hypothesis testing is about confirming a conclusion about a given population that you have. The conclusion arrived at for a given population can be any of these —

1. Null Hypothesis (H0)
   - Prevailing belief about the hypothesis
   - Assumes that the status quo is true
   * You cannot accept a null hypothesis. You can at most fail to reject the null hypothesis. The null hypothesis is always written with the “equal to” or “less than or equal to” or “more than or equal to” sign.
2. Alternate Hypothesis or Research hypothesis (H1)
   - Opposes the null hypothesis

You can either do one of the following —
1. Reject the null hypothesis (If enough evidence is in favor of the alternate hypothesis)
2. Fail to reject the null hypothesis (if enough evidence is not in favor of the alternate hypothesis)

1. Critical value method :
   i. There is one critical value where you take a decision. Like if the mean sales is 70 as H0, you decide if you get a mean which is say greater than 80 and less than 20 you will reject the mean to be 70. i.e. you choose what are your critical values. Now, mind that these critical values are means themselves in the sampling distribution. There are several means in the sampling distributions. Their probability is plotted as a normal distribution. So, you choose what probability you consider as your inflection point. That is the alpha value. That decides which mean value is too big or too small. This absolute value of the mean that is too far, might be different for different cases. So, we always talk about the alpha value as the probability, since that will help us to dynamically contextualize based on what is the mean for a given case. This probability level is known as Significance Level (α). Significance level is 1-confidence level.
   ii. From the significance level just figure out the z score using the formula = NORM.S.INV(). If not specified use 0.05
   iii. From the z score find the actual mean by multiplying the Standard error of the means SEM * zscore. This zscore is known as z-critical or Zc
   iv. From the Zc find the actual mean by multiplying with SEM. (Same way you find the confidence interval’s margin of error)
   v. Add and subtract the margin of error got from step iv to the mean value to get the UCV and LCV
2. The problem statement might be upper tailed, lower tailed or dual tailed, with max and min boundaries. But in either case the z score will be just one value. Only the sign would change for two tailed case!