Hypothesis test

Dhriti grows tomatoes. Over a period of time, she has found that there is a probability 0.3
of a ripe tomato having a diameter greater than 4 cm. She decides to try a new fertiliser. In
a random sample of 40 ripe tomatoes, 18 have a diameter greater than 4 cm. Dhriti claims
that the new fertiliser has increased the probability of a ripe tomato being greater than
4 cm in diameter.
Test Dhriti’s claim at the 5% level of significance. State your hypotheses clearly.

H₀: p = 0.3
H₁: p > 0.3

Why is the next line

P(X>= 18) NOT P(X<=18)

thanks

Reply 1

Thrug

0.3*40 = 12.

So 18 is larger than expected so you are looking for 18 or even greater than 18.

If you had an answer smaller than 12 it would be 'less than or equal to'.

(edited 12 years ago)

why?

Original post by jsmith6131

why?

What does H1 say?

It basically says if p =/= 0.3, then it must be >0.3 because there were so many large tomatoes.

What we require, is the probability of getting 'as bad or worse' as this. That means 18 tomatoes or even more than 18. If the probability of that is so small (under 5%) then it can be said it is so rare that chances are, p>0.3 and we take H1.

The result can be thought of as a 'rare outlier' if you will. And we need the probability of it being even rarer or just as rare as that. So if it is under the expected value we look to less than, but when it is more than the expected value we are looking at more than.