Question

Consider Firm A.
Firm A charges $ 500 for its product.
Firm A wants to know if its’ competitors, on average, charge a price lower than
$ 500.
So, they test the null hypothesis that the population mean price of the product
= $ 500 against the alternative hypothesis that it is less than $ 500.
They sample 256 other firms, and find the following sample statistics:
Sample Mean = $ 458
Sample Standard Deviation = $ 336
Test the null hypothesis, using an “alpha” = .05. Show your work.

Answer 1

We have the testing problem

We have the sample information

Since sample size is large enough ( n>30)we can use the normal test. (z-test)

The test statistic is given by

and we reject the null hypothesis for small values of calculated z under null hypothesis.

Here we have

So from standard normal table,

So the critical region of the test is reject null hypothesis if the calculated value

We have

So based on the sample information we reject the null hypothesis that the population mean price of the product
= $ 500 against the alternative hypothesis that it is less than $ 500

The p-value of the test is given by

Based on this p-value also we can conclude that since p-value is less than alpha=0.05, based on the sample information we reject the null hypothesis that the population mean price of the product
= $ 500 against the alternative hypothesis that it is less than $ 500