Question

I'm a 80% free throw shooter.

You obviously don't believe me and say that I'm not that good, and you ask me to prove it. So I shoot 100 free throws and make 50 of them. Can you say with some level of certainty that I'm not a 80% free throw shooter? Why or why not?

What if I only shot 10 free throws and made 5. How is that different that above?

Answer 1

Answer:

In the event that somebody says that they're a 80% free toss shooter,

at that point for 100 free tosses we anticipate that them should make around (100*0.8)

i.e.,

= 80 free tosses

Standard deviation = √100*0.8*0.2

= √16

= 4 (from as far as possible hypothesis for estimations of n >= 30)

We can test the case of 80% free tosses utilizing theory testing which is given as follows

Null hypothesis

Ho : p = 0.8 versus

Alternative hypothesis

Ha : p < 0.8

Now to give test statistic

= 50 - 80 / 4

test statistic = - 7.5

p-estimation of this uneven i.e., one sided z test from the standard z tables is given as

P(z < - 7.5) ~ 0

Since this is around 0 i.e., p value is o, we can dismiss i.e., reject null hypothesis Ho and reason that the individual is certainly not a 80% free toss shooter.

Here we can say that for n = 10 free tosses, the example is little for us to make ends and we can't utilize the normal distribution to test and make ends.