# Thread: hypothesis testing

1. ## hypothesis testing

hi i need help!

A manufacturing company makes spray paint. The drying time
of the paint, in seconds, is known to be approximately normally distributed, with
mean 90. The people in the research division of the company want to put a new
chemical ingredient in the paint, which they hope will reduce the drying time.
In order to investigate this, they make some paint with the new ingredient and
spray it on 15 surfaces, then record the 15 drying times, in seconds. The sample
mean of these times is 86 and the sample standard deviation is 4.5.
Perform an appropriate hypothesis test, at the 5% level of significance, to see
whether there is evidence that the new ingredient reduces the drying time.

could sum1 please explain 2 me how to go about this question. thank you

2. ## Check your notes

(Assuming you are a first year at QMUL too) Look at the example from our last statistics lecture as it follows exactly the same process, but with mew=90, standard deviation 4.5.

3. Your hypotheses are

$\displaystyle H_0:\mu=90$ vs. $\displaystyle H_a:\mu<90$

where $\displaystyle \mu$ is the mean drying time for the NEW spray.

Your test statistic is $\displaystyle {\bar x- \mu_0\over s/\sqrt{n}}={86-90\over 4.5/\sqrt{15}}$.

The rejection region (of $\displaystyle H_0$) is $\displaystyle (-\infty, t_{14,.05})$.

NOW, if your test statistic falls in the rejection region you reject $\displaystyle H_0$

and you accept $\displaystyle H_a$ at $\displaystyle \alpha=.05$.