This is another hypothesis test. This time the claim made by the research involved corresponds to the alternative hypothesis.
Maybe the data this problem talks about is old. Can it really be 55% watching network news? What about all those people who only watch podcasts or only read google news?
Problem adapted from Larson/Faber’s Elementary Statistics
When you are doing a hypothesis test how do you decide which form to use? Say we are going to test the population proportion .27. Which of the three possibilities do we choose?
Part of what makes this hard to figure out is that “the claim” stated in a problem can correspond to either 
If you claim the population proportion “is smaller than 27%” or “is less than 27%” then you would use the form
and your claim corresponds to the alternative hypothesis.
If you claim the population proportion “is greater than 27%” or “is more than 27%” then you would use the form
and your claim corresponds to the alternative hypothesis.
If you claim the population proportion “differs from 27%” or “is not equal to 27%” then you would use this form
and your claim corresponds to the alternative hypothesis.
If you claim the population proportion “is at most 27%” you will use
since the alternative hypothesis to “is at most 27%” would be “is more than 27%”.
If you claim a population proportion “is at least 27%” you will use
since the alternative hypothesis to “is at least 27%” would be “is less than 27%”.
Sometimes these last two cases are written differently by some books. The claim “is at most 27%” is written using the null hypothesis 
Here’s another example of a hypothesis test. Again you tell the type of test (right-tailed or left-tailed or two-tailed) from the form of the alternative hypothesis.
Notice in this one we got a fairly big p-value compared to the level of significance we were using. So we didn’t even come close to rejecting the null hypothesis this time.
Problem adapted from Larson/Farber’s Elementary Statistics
Here is an example of a two tailed hypothesis test.
For a two-tailed test you have to find the z-value and then take the p-value to be twice the area of the tail you get. Since for a two-tailed test the alternative hypothesis is 
Hmm… even if USA Today is right I’m beginning to wonder under what conditions people did see an extraterrestrial. Late at night I bet…
Problem adapted from Larson/Farber’s Elementary Statistics
When you do a hypothesis test, you use a sample to come up with a test statistic (z-value). Then you use the z-value to come up with a p-value, where the p-value is the area of the “tail(s)” involved.
Now the book says that you decide the result of the hypothesis test based on the size of the p-value (page 438). The smaller the p-value the more evidence against the null hypothesis you have. This is true if you are not given a level of significance (ie no 
But what happens if the problem says to use 1% or 5% level of significance (
This just means that when you are done you compare the p-value to this
If 
If 
Example (Using a level of significance in hypothesis test):
As an example suppose you are using a level of significance
and your p-value is
. Then reject the null hypothesis and say the result is significant.
Or suppose your level of significance is
and your p-value is
. Then you do not have enough evidence to reject the null hypothesis and say the result is not significant.
So the upshot is compare the p-value to the level of significance (
This problem shows an example of a hypothesis test. This one is a right tailed test, which you can tell from the form of the alternative hypothesis.
Note that if you are not using a level of significance to decide whether to reject or not, then you wind up with a p-value and make some conclusion about how much evidence there is against the null hypothesis based on the size of the p-value. The smaller the p-value the less likely you are to believe in the null hypothesis.
Problem adapted from Larson/Farber’s Elementary Statistics
