# Math Help - hypothesis and standardized test statistic

1. ## hypothesis and standardized test statistic

having a really hard time on this, had to miss two classes last week and now i have no idea what i'm doing. I checked my book but i think i'm missing something. can anyone help? step by step help is greatly appreciated

A producer of various kinds of batteries has been producing "D" size batteries with a life
expectancy of 87 hours. Due to an improved production process, management believes that there has
been an increase in the life expectancy of their "D" size batteries. A sample of 36 batteries showed an
average life of 88.5 hours. Assume from past information that it is known that the standard deviation of
the population is 9 hours.
a. Give the null and the alternative hypotheses.
b. Compute the standardized test statistic.
c. At 1% (α = .01) significance level test management's belief. State your conclusion

2. I would try

$\displaystyle H_0: \mu > 87$

$\displaystyle H_A: \mu \leq 87$

You have $\displaystyle n=36, \mu_0 = 88.5 , \sigma = 9$

Then apply a Z-test as the standard deviation is known.

What will your test statistic be?