TI 89 for Statistics > TI 89 Hypothesis Testing

## TI 89 Hypothesis Testing Overview

The TI 89 takes away the tedium of the calculations, allowing you to concentrate on the meaning of the testing. You will usually be working on your

**alternate hypothesis**. For example, you think that average weights have gone up or down and you want to test your new hypothesis. It’s important that you understand and can state the null hypothesis, because otherwise the results (even from a calculator), have no meaning.

**Contents**:

## TI 89 Hypothesis Testing on a Mean

**Example problem:** Fifty years ago, middle school students at a local school had a mean height (μ) of 5ft 4 inches with a standard deviation (Ïƒ) of 2.4 inches. You want to test the hypothesis that the mean has increased over the last 50 years. You take a random sample of 30 students and find their mean is 65.11 with a standard deviation of 2.26569. At an alpha level of α = 0.05, can you conclude that their mean height has increase based on this information?

**Step 1:** Press APPS and scroll to the **Stats/List Editor**. Press ENTER.

If you don’t see the Stats/List editor, you need to download it to your calculator from here. You’ll need the original cable that came with the TI 89.

**Step 2:** Write out the hypothesis. The null hypothesis is Î¼ = 64. The alternate hypothesis (the one you are testing) is μ > 64.

**Step 3:** Press 2nd F1 1. Make sure the data entry method says “Stats.” Press ENTER.

**Step 4:** Enter the following values: μ_{0} = 64, σ = 2.4, x = 65.1, n = 30. Scroll down to **Alternate Hyp** and choose **Hyp: μ > μ _{o}**.

**Step 5:** Press ENTER and read the results. The p value is **0.00603**. This is smaller than the alpha level of 0.05, so you reject the null hypothesis and accept the alternate hypothesis: the mean has increased over the last 50 years.

## TI 89 Hypothesis Testing: Large Sample Proportions

Note: the statistics flash app (free from TI.com) is required for this how to.

**Hypothesis tests** are tests of significance: they tell you what your results mean; a result of p = 0.15 or p = 0.012 has no meaning unless you have something to compare it to. For large sample **hypothesis testing**, you can use a normal approximation to the binomial. To test whether your sample size is large enough, n Ã— p and n Ã— (1 – p) must be greater than 10.

**Example problem**: 62% of students agree with a recent tuition increase. Test the claim that more than 62% of students would be in favor of the tuition increase today, at a significance level of 0.05. You have a sample of 260 students, and 69.4% of them would be in favor.

**Step 1:** State the hypothesis and the alternate hypothesis. The hypothesis is stated in the question: 62% of students agreed with the tuition increase so H_{o} is p = 0.62. The alternate hypothesis (the one we want to test) is that more than 62% would vote for it: H_{1} is p > 0.62.

**Step 2:** Make sure you can use the normal approximation to the binomial: n Ã— p = 260 Ã— .694 = **180 > 10** and n Ã— (1 – p) = **98.8 > 10**.

**Step 3:** Press APPS, scroll to the **Stats/List Editor** and press ENTER.

**Step 4:** Press 2nd F1 5. This brings you to the 1-proportion z-test screen.

**Step 5:** Enter 0.62 into the **p0** box.

**Step 6:** Press the scroll down key and enter 180 in the successes box (this is n Ã— p, 260 Ã— .694 or the number of students who agreed in the latest sampling).

**Step 7:** Scroll down and enter 260 into the **n** box.

**Step 8:** Scroll down and hit the right scroll key to bring up a list of options. Scroll down to **prop>p _{0}**. Press ENTER.

**Step 9:** Scroll down to “Results.” Use the scroll keys to select “Calculate.” Press ENTER.

**Step 10: **Read the results: The P-Value given by the results screen is **0.008152**. This is smaller than your alpha level (0.05) so there is is strong evidence that the new proportion will be larger than 63%, so you reject the null hypothesis and accept the alternate hypothesis.

That’s how to perform TI 89 hypothesis testing!

**Tip #1**: If you get a domain error, you may need to clear the data in your list editor. Press Esc, F1, 8 and try the steps again.

**Tip #2**: Choosing “Draw” instead of “Calculate” in Step 9 will give you a nifty graph of your result instead of a calculations screen. This is handy if you need to visualize something to learn it!

**Warning**: This calculation is for a one-tailed test (greater than). If you have a two-tailed test or a one-tailed test (less than) you’ll need to change the option in Step 8 to **propâ‰ p** (two-tailed test) or **prop<p** (one-tailed test, less than). Unsure? See One Tailed Test or Two.

Lost your guidebook? You can download a new one from the TI website here.