S2 Hypothesis testing

Whats the reason for using -1.6449?

You've used it as well but rounded it to 1.65.

It's the z value for which H0 is rejected with a 5% significance level.

Right fair enough. Mind helping me with another question...


On average, 4 out of 5 new television sets of a particular brand are fault-free during the first year of purchase. A new design is marketed and a random sample of 20 sets is monitored by the manufactured over a period of a year. The number of fault-free sets during this period is 19.

A) test, at the 5% significance level, whether the proportion of fault-free sets of this new design is greater than 4 out of 5.

What i tried:

Ho: p=0.8
H1: p>0.8

My first question is how do you know what sort of distribution you have.
Anyway i thought it was binomial

X-B(20,0.8)
P(x>19) = i looked at the table in the book. I wasnt taught binomal at AS. N=20, p=0.8 and x =19? Value i got was 0.9885. Which is wrong as the answer is 0.0692.

Cheers

For what sort of distribution, look for a fixed number of trials and it'll be binomial. In this case you have 20 and it makes no sense to have more than 20 fault-free trials. Whereas if you thought it was Poisson and tried to adjust the rate to go from 4 out of 5 to 16 out of 20, you could get values greater than 20 and the test would be useless. And practice as many questions as you can until you get the hang of identifying it.

In your question you're not looking for $P (x > 19)$ but $P( x\ge 19)$. You're interested in the probability of getting what you got from the sample as well, rather than excluding it by finding P(x>...)

Yeah i wrote the bit about p( x greater than or equal to) on paper but forgot to type it out. That is my issue with this question im not to sure how you work that out? You cant use a normal i dont think as it doesnt satisfy it.

Binomial is fine, it looks like you've just misread the tables then.

Can you see why you use binomiial and how to get the correct value from the tables?

I swear the tables give you less than though. What i did was just go for n=20 p=0.8 x=19? That gave me 0.9885.

The formula sheet gives you cumulative probability, so when x=19 you're finding P(X less than or equal to 19) but you're interested in P(Greater than or equal to 19) so you'd have to rewrite that probability as something in terms of P(X less than or equal to ...).

What's in the blanks?

1-p(x< or equal to 18)?