# Support or Reject Null Hypothesis

A related criticism is that a significant rejection of a null hypothesis might not be biologically meaningful, if the difference is too small to matter. For example, in the chicken-sex experiment, having a treatment that produced 49.9% male chicks might be significantly different from 50%, but it wouldn't be enough to make farmers want to buy your treatment. These critics say you should estimate the effect size and put a on it, not estimate a *P* value. So the goal of your chicken-sex experiment should not be to say "Chocolate gives a proportion of males that is significantly less than 50% (*P*=0.015)" but to say "Chocolate produced 36.1% males with a 95% confidence interval of 25.9 to 47.4%." For the chicken-feet experiment, you would say something like "The difference between males and females in mean foot size is 2.45 mm, with a confidence interval on the difference of ±1.98 mm."

## “Accept null hypothesis” or “fail to ..

### accept their null hypothesis no matter what the p-value ..

1. Using the data from sample 1, perform a hypothesis test on the sample data using a significance level of 0.01. Answer the following questions below:

a. What is the sample mean and sample standard deviation?

b. What is the p-value

c. Do you accept the null hypothesis or reject the null hypothesis?

d. Should any action be taken?

### Is a p-value of 0.04993 enough to reject null hypothesis?

2. Using the data from sample 2, perform a hypothesis test on the sample data using a significance level of 0.01. Answer the following questions below:

a. What is the sample mean and sample standard deviation?

b. What is the p-value

c. Do you accept the null hypothesis or reject the null hypothesis?

d. Should any action be taken?

## When should a null hypothesis be rejected or accepted

The probability that was calculated above, 0.030, is the probability of getting 17 or fewer males out of 48. It would be significant, using the conventional *P**P*=0.03 value found by adding the probabilities of getting 17 or fewer males. This is called a one-tailed probability, because you are adding the probabilities in only one tail of the distribution shown in the figure. However, if your null hypothesis is "The proportion of males is 0.5", then your alternative hypothesis is "The proportion of males is different from 0.5." In that case, you should add the probability of getting 17 or fewer females to the probability of getting 17 or fewer males. This is called a two-tailed probability. If you do that with the chicken result, you get *P*=0.06, which is not quite significant.

## Michael Jordan Won't Accept the Null Hypothesis: ..

At this point, a word about error. **Type I error** is the false rejection of the null hypothesis and **type II error** is the false acceptance of the null hypothesis. As an aid memoir: think that our cynical society rejects before it accepts.