Hypothesis Testing for a mean - large samples
Hypothesis testing with one mean on the TI-83 - Large and small samples
Hypothesis testing with one mean with the TI-83 is easy and practical. The tests can be done with either just summary stats or the raw data. The TI-83 uses the p-value method of hypothesis testing.
Recall in hypothesis testing you need to
- Decide on a claim and hypothesis
- Create the null and alternative hypothesis
- Select a significance level according to the seriousness of a type I error
You still need to do these things with a calculator - however it will do nearly all the rest. Here is an example (#8 p. 373)
A New York Times article noted that the mean life span for 35 male symphony conductors was 73.4 years, in contrast to the mean of 69.5 years for the general population. Assuming the 35 males have life spans with a standard deviation of 8.7 years, use a 0.05 level of significance to test the claim that male symphony conductors have a mean life span that is different from 69.5 years
To do the test: do the following
- Hit STAT, use the left arrow to highlight TESTS - here is the screen you should see
Since this is a sample size larger than 30, we use the normal distribution
,
73.4 for 
, 8.7 for 
and
35 for n. Here is your screen
)
Here is the screen
Recall that since this is the p-value method, you can compare the p-value against the level of significance (in this case 0.05). Since the p-value is in the critical region, you would reject the null hypothesis in this case!
EXAMPLE WITH DATA:
Here are 10 values from a population with unknown mean but known standard deviation of 2.5
66.71 66.27 62.81 66.92 62.91 71.42 67.39 65.81 62.81 63.79
Since the standard deviation of the population is known, we use the normal distribution. We are to test the claim that the mean is different from 67.25 at the 0.05 significance level. Here is the set up
In this case Hit STAT and use the arrow keys to highlight TESTS, then once again select Z-Test. But this time use the arrow keys and enter to highlight Data. Your screen should look as follows:
Now enter the appropriate values for the fixed mean, the standard deviation and the List where the data is located. Your screen should look as follows:
Now make sure the alternative hypothesis is as you want it and highlight Calculate and hit enter. Did you get these results?
Since the p-value is in the critical region - we reject the null hypothesis
You can draw the distribution as well
Hit STAT, use arrows to highlight TESTS
Select Z-Test, but this time highlight the word Draw at the bottom of the screen:
Hit enter to get the curve drawn with shaded critical regions:
