Null distribution and null hypothesis testing

Question 1

What is normal distribution?

Answer 1

Real-world data is often normally ditributed
aka a bull curve
a continuous distribution

Many statistical problems are easier to solve if we assume that the daa is normally distributed

Normal distributions arise during sampling because of the central limit theorem.

Question 2

Why does normal distribution play a central role in statistics?

Answer 2

The normal distribution plays a central role in statistics for three reasons….
- The normal distribution describes the probability distribution of a continuous numerical variable.
- It is symmetric around the mean.
- The further values are from the mean, the lower the probability of observations.
- Normal distribution = more POWERful stats
- The central limit theorem says thatthe sampling distribution of the mean will always be normally distributed, as long as the sample size is large enough.

Question 3

Testing the hypothesis

Answer 3

• We need to define the beak length at which we would reject the null hypothesis
• This threshold is called the critical value. Beyond this value, we reject the null hypothesis
• We can reject the H0 if the beak length is within the extreme 5% of long beaks measured

Question 4

What is the Z statistic formula?

Answer 4

Z calculates how many standard deviations a particular value is away from the mean.
If variable x is normally distributed with mean (μ) and variance (2σ, otherwise written as: σ2), then we can rearrange the equation to calculate the standard normal deviates to identify the limits that contain 95% of observations for any normal distribution (i.e. with any mean and variance).