# Recognize elements of an hypothesis testing problem

Before the launch of a commercial product, a company makes a market survey to know the price that buyers are willing to pay. It is assumed that this price is normally distributed with a desviation of \$10. The marketing department informs that the public considers appropriate the price of \$30. To test this hypothesis against a price of \$40, a sample of 25 people is selected and adopted the following decision rule: if the sample mean is less than \$35, are considered it is appropriate to set a price of \$30. 1. Find the probability of committing an error of type 1. 2. Find the probability of committing an error of type 2. 3. Find de power. Let be$\alpha$the probabilityof committing an error of type 1 and$\beta$the probability of committing an error of type 2:$\alpha=P($accept$H_0/H_0$is false$)$and$\beta=P($refuse$H_0/H_0$is false$)$The problem is thatI can't find the hypothesis. My criterion is to define it as follows:$H_0: \mu = \$30$ -> null hypothesis

$H_1: \mu \not= \$30$-> alternative hypothesis This is ok?, but what can I do with the price of$\$40$?

And, whatis the sample mean?, I have to find it to calculate the $\alpha$. Or I have to suppose an $\alpha=0,01$?