# Hypothesis testing to provide evidence

"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:

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

• $H_0$: $p \leq 0.1$. May 2 '14 at 23:40
• @EricTowers would the following formula correctly work even though I am not really given a standard deviation? May 2 '14 at 23:50
• 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). May 3 '14 at 1:34
• The formula you posted would be for a z-test of a population mean, not a population proportion.
– jsk
May 3 '14 at 5:10

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).