A sample of 10 seeds are tested to see if the proportion of seeds that germinates one winter has reduced from the usual value of 0.85. Find the critical region for a one-tailed test using a 5% significance level.
Answer: $\displaystyle x\leq6$
A sample of 10 seeds are tested to see if the proportion of seeds that germinates one winter has reduced from the usual value of 0.85. Find the critical region for a one-tailed test using a 5% significance level.
Answer: $\displaystyle x\leq6$
since n=10 is small you must use the binomial distribution and not approximate this via a normal
$\displaystyle H_0=.85$ vs $\displaystyle H_a<.85$
I doubt we will get exactly .05
$\displaystyle \alpha=P(X\le c)$ where X is a binomial rv with n=10 and p=.85
DARN close............. $\displaystyle P(X\le 6)\approx$ .049969798878515
at http://stattrek.com/Tables/Binomial.aspx
and u still have an inferior duck
Thanks for the reply, I had posted this before seeing it.
Another which I don't understand:
'My research shows that 3 out of 10 children say their favourite colour is red' announced the professor but Miss Smith believed that the proportion was much higher. She asked 6 students, 3 of whom had red as their favourite. She uses a 5% significance level.
a) Test Miss Smith's belief on the basis of this sample (a: He belief at the 5% significance level is unfounded.)
b) She decides to use a larger sample of 20 students. Find how many must choose red as their favourite colour for Miss Smith to have a significant result. (answer: 12)
Edit: I'll get round to updating the avatar soon...
$\displaystyle H_0=.3$ vs $\displaystyle H_a>.3$
Here Our rv X is binomial with n=6 and we assume p=.3 to obtain alpha.
$\displaystyle \alpha=P(X\ge c)$
If she observes 3 I would calculate the p-value as
$\displaystyle P(X\ge 3)\approx .25569$ which is not significant at alpha equal to .05.
As for n=20 I still would use the binomial and not approximate this with a normal.
and I don't see x=12 as the answer here...
If X is Bin(n=20, p=.3), then $\displaystyle P(X\ge 12)\approx 0.00513816153512103$