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STATISTICS 2005

Fundamentals of Statistics Section 95

TI-83 Instructions - Hypothesis Testing with one mean - large and small samples

Instructor: Pete Wildman

Fall Semester 1999

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

  1. Decide on a claim and hypothesis
  2. Create the null and alternative hypothesis
  3. 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

  1. Hit STAT, use the left arrow to highlight TESTS - here is the screen you should see

    2. Since this is a sample size larger than 30, we use the normal distribution

  2. Hit 1 for Z-Test. You will see this screen

  3. Now use the arrow keys and ENTER to make sure STATS is highlighted. Your screen should look as follows:

  4. Now enter the appropriate data 69.5 for , 73.4 for , 8.7 for and 35 for n. Here is your screen

  5. Now use the arrow keys and enter to highlight the appropriate null hypothesis (in this case )

    6. Here is the screen

  6. Finally highlight calculate and hit enter - here are your results:

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:

SMALL SAMPLES:

If the sample size is less than or equal to 30, and the distribution is approximately bell-shaped and the population standard deviation is not known, you use the T-test. Here is an example

(#8 p. 384): The expense of moving the storage yard for the Consolidated Delivery Service is justified only if it can be shown that the mean travel distance will be less than 214 miles. In trial runs of 12 delivery trucks, the mean and standard deviation are found to be 198 miles and 42 miles respectively. A the 0.01 level of significance, test the claim that the mean is less than 214 miles.

  1. Hit STAT, use the arrow keys to highlight TESTS and this time hit 2 for T-Test. Your screen should be as follows

    2.  

  2. Since this is a summary stats problem, make sure Stats is highlighted and enter the fixed mean, sample mean, standard deviation and sample size. Then highlight the appropriate alternative hypothesis. Do you have this screen:

  3. Now highlight calculate and hit enter. Did you get these results?

Since the p-value is not in the critical region, we fail to reject the null hypothesis. Once again you could draw the graph (in the same way as you did for the Z-Test), here are your results: