0
$\begingroup$

"A battery manufacturer randomly selects 100 nickel plates for test cells, cycles them a number of times, and determines that 14 of the plates have blistered. Does this provide compelling evidence for concluding that more than 10% of all plates blister under such circumstances? State and test the appropriate hypotheses using a significance level of α=0.05."

In the following question I'm trying to set up my answer as follows but don't really know what to do afterwards.

$H_0: p= 0.1 vs. H_a: p> .1$

I can't really tell what formula I should be using after setting that portion of the problem up however. There is no standard deviation given so I'm not sure. I was thinking of trying the following formla:

$z = \frac{x - \mu}{s/ \sqrt{n}}$

$\endgroup$
4
  • $\begingroup$ $H_0$: $p \leq 0.1$. $\endgroup$ May 2 '14 at 23:40
  • $\begingroup$ @EricTowers would the following formula correctly work even though I am not really given a standard deviation? $\endgroup$
    – Valrok
    May 2 '14 at 23:50
  • $\begingroup$ this is a duplicate of math.stackexchange.com/questions/773786/…, but I'm posting an answer because the answer at the other question is not very informative (even if accurate). $\endgroup$ May 3 '14 at 1:34
  • $\begingroup$ The formula you posted would be for a z-test of a population mean, not a population proportion. $\endgroup$
    – jsk
    May 3 '14 at 5:10
0
$\begingroup$

Hint: the number of batteries that "blister" in your sample of 100 batteries is well-approximated by a binomial distribution with $n=100$ and $p$ equal to the probability that a given battery blisters. (I say "approximated" because I'm assuming the batteries are chosen independently from an "infinite" population.)

To test the null hypothesis that $p\leq 0.1$, you should calculate the probability of getting 14 or more "blistered" batteries under the assumption that $p=0.1$. This is called the $p$-value. If $p<\alpha=0.05$, you reject the null hypothesis.

To calculate this $p$-value, you want to calculate $P(X\geq 14)$ assuming $X$ has the binomial distribution with $p=0.1$ and $n=100$. You can calculate this probability in several ways: using a binomial distribution table, or using the normal approximation to the binomial (perhaps with the continuity correction).

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.