Question

10) A consumer product magazine recently ran a story concerning the increasing prices of digital cameras. The story stated that digital camera prices dipped a couple of years ago, but are now beginning to increase in price because of added features. According to the story, the average price of all digital cameras a couple of years ago was $215.00. A random sample of cameras was recently taken and entered into a spreadsheet. It was desired to test to determine if that average price of all digital cameras is now more than $215.00. What null and alternative hypothesis should be tested?

Answer 1

Null hypothesis :
`\mu \leq 215`

Alternative hypothesis:
`\mu >215`

Explanation:

A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".

The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".

The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".

On this case they try to proof that due to the time, the average price for all digital camera has increased. So this needs to be on the alternative hypothesis. And the complement of the alternative hypothesis would be on the null hypothesis.

Null hypothesis :
`\mu \leq 215`

Alternative hypothesis:
`\mu >215`

Other important thing is that on the alternative hypothesis we never can have the symbol equal.

Other way to create the hypothesis is with the equal sign on the null hypothesis (but that's not the best way to do it):

Null hypothesis :
`\mu = 215`

Alternative hypothesis:
`\mu >215`