# Difficult Single Sample Hypotheses Test

• Mar 23rd 2011, 05:08 PM
Champ83
Difficult Single Sample Hypotheses Test
It is believed that 1.333% of all the TV's manufactured by a company are defective. Suppose that a random sample of 800 new TV's manufactured by this company has 16 defectives.

Test, at 5% significance level, to see if the data provide enough evidence to conclude that the true defective rate is different from 1.333%. Don't forget to state the null and the alternative hypotheses.

Also, what type of error might you have made in reaching your decision? Finally, compute the p-value for your test and use this p-value to decide if
H0 can be rejected when alpha=0.2 (instead of 0.05).

I've made several attempts and could not figured it out. Is there anyone who can show me how to do this question?

Thanks.

• Mar 23rd 2011, 07:21 PM
theodds
See AP Statistics Tutorial: Hypothesis Test for a Proportion

If you reject then you are risking a type I error, while if you fail to reject you are risking a type II error.
• Mar 23rd 2011, 10:00 PM
matheagle
Most likely, they are using the central Limit Theorem here, on this binomial distribution.
BUt with p near zero, the Poisson may be more appropriate.

$\displaystyle H_o:p=.01333$ vs. $\displaystyle H_a:p\ne .01333$

test stat is $\displaystyle Z^*={\hat p-p_o\over \sqrt{p_oq_o/n}}$

where $\displaystyle \hat p={16\over 800}$

p-value is $\displaystyle 2P(Z>|Z^*|)$