# hypothesis testing

#### lredingt

##### New member
I am preparing for mba school in the spring and am refreshing my memory. I was looking at this business hypothesis problem and am having problems figuring out all the parts of the equation for pvalue approach.

with the formula z=(xbar - mu)/ (standard deviation/sqrt n)

I am seeing xbar = 352/400 mu=.9 and sqrt n = 400
where do i put the significance level and how do I find the standard deviation?

I am returning back to school after MANY years and have lost all my knowledge from disuse. I would appreciate anyone's help with this. It is probably really simple and I am not seeing it.

An automobile dealership has as one of its performance goals that the proportion of its automobiles sold that are deemed “good value for the money” by the purchasers be at least .90. For a random sample of 400 automobiles sold over the past six months, 352 were deemed by the purchasers to be “good value for the money.” Does this sample data provide evidence that the dealership is not meeting its performance goal? Either use the p-value approach to hypothesis testing or use the significance level approach with ? = .05.

#### galactus

##### Super Moderator
Staff member
Hypothesis testing for proportions:

$$\displaystyle z=\frac{\hat{p}-p}{\sqrt{\frac{pq}{n}}}$$

$$\displaystyle H_{0}\geq .90 \;\ \text{claim}$$

$$\displaystyle H_{a}: p<.9$$

$$\displaystyle z=\frac{.88-.9}{\sqrt{\frac{(-9)(-1)}{400}}} \;\ = \;\ -1.\overline{3}$$

With a .05 alpha level, the rejection region is a left tail test with critical region z=-1.65.

Our value of -1.33... is not in the rejection region. Fail to reject the null hypothesis.

The p-value is .0912. Since it is greater than the alpha level of .05, then we fail to reject.

What does this say about the dealers claim?. Does it hold water?

#### lredingt

##### New member
I thought the p and q of the standard deviation formula would be .5 and .5 because the probability of a "good value' or not is a 50-50 chance. Where do the -9 and -1 come from.