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.

(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.

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

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

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

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

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

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