hypothesis test on ti 84

Hypothesis Testing using the Z-Test on the TI-83 Plus, TI-84 Plus, TI-89, and Voyage 200

The TI-83 Plus and TI-84 Plus are optimized for performing many tasks in statistics, and one of their most powerful features is the ability to perform a variety of tests of statistical significance. With the statistics package installed, the TI-89, TI-92 Plus, and Voyage 200 also have much of this capability. This tutorial demonstrates how to use your graphing calculator to solve basic hypothesis testing problems such as the following using the Z-Test:

A researcher designs an experiment where a random sample of n = 50 high school seniors are given a pill to improve their concentration and problem solving skills. After being administered the pill, subjects take the SAT, and their scores on the SAT Math section are tabulated. The average score of student who took the pill is x̄ = 540. Given that the average score of all high school seniors on the SAT is μ = 510 with standard deviation σ = 100, is there statistically significant evidence that students who took the pill scored higher?

Before beginning the calculations, it is necessary to come up with specific hypotheses for the tests and choose a level of significance. In inferential statistics, there are two hypothesis, the null hypothesis, and the alternative hypothesis. The null hypothesis, denoted H₀, is always that the statistic measures of the treated group (in this case students given a pill) is the same as that for the general population. Since we are only interested in whether or not the pill has a positive effect, we are doing a one-tailed Z-Test, and our null hypothesis is:

H₀: μ <= μ₀

Where μ is the true mean (as opposed to sample mean) of scores of students in the treatment group. μ₀ refers to the known population mean, in this case 510. The alternative hypothesis H 1 is what we expect if the treatment does have an effect on the population, and is always the opposite of the alternative hypothesis. Our alternative hypothesis is:

H₁: μ > μ₀

Finally, we have to choose a level of significance (α) for our test. It is possible that even if the treatment has no effect, we could get a mean score of 540. This seems unlikely and the chances of this happening goes down with the more subjects in the study, but the purpose of hypothesis testing is first of all to avoid coming to the wrong conclusion. The level of significance is a threshold probability below which we say that we have found statistical evidence. It is considered good practice to choose this beforehand so that the statistician doesn’t change α after wards in order to “find” statistical evidence where there is none. For most problems, a level of significance is:

α = .05

This means that if we find there is less than a 5% chance that the sample mean is higher than 540 by chance alone, we will conclude statistical significance.

Performing a Z-Test on the TI-83 Plus and TI-84 Plus

From the home screen, press STAT ▶ ▶ to select the TESTS menu. “Z-Test” should already be selected, so press ENTER to be taken to the Z-Test menu.

Now select the desired settings and values. While it is possible to use a list to store a set of scores from which your calculator can determine the sample data, this problem doesn’t give individual scores, so make sure STATS is selected and press ENTER .

Enter the data given in the problem, μ₀ = 510, σ = 100, x̄ = 540, and n = 50. Finally, make sure to select >μ₀ for the alternative hypothesis.

There are now two options for the output of the Z-Test: “Calculate” displays the z-score (the number of standard deviations x̄ is above or below the mean) and then the corresponding p-value, the probability of getting such a sample by luck alone.

“Draw” draws a normal distribution graph and displays the z-score and p-value at the bottom of the screen.

We have z = 2.12 and p = .017 , which means that there is a 1.7% chance of seeing such a variation in sample mean by chance alone. Since p<α, we can conclude that there is significant evidence that the treatment group is different from the general population. Assuming good experimental practices, this implies (but does not prove) that taking the pill improves students' Math SAT scores. Note that this does not necessarily mean the pill improves concentration and problem solving skills as claimed-although these may be skills important for scoring higher on the Math SAT, this is a separate claim.

Performing a Z-Test on the TI-89, TI-92 Plus, and Voyage 200

Before you begin, it is necessary to have the proper software on your device. If you have a TI-89 Titanium or other newer calculator, then you should have a Stats/List Editor icon on your Apps screen. Otherwise, you should have a Stats/List Editor application in your Flash Apps folder. (Reached by pressing APPS then ENTER ). If you don’t have this software or you aren’t sure, you can download it here .

Once you are in the Stats/List Editor app, press 2nd F1 (F6) to enter the tests menu. Z-Test should already be selected, so press ENTER to confirm. You will be prompted for the data input method. Data uses a list containing the of scores from which your calculator can determine the sample data, this problem doesn’t give individual scores, so make sure STATS is selected and press ENTER .

Enter the data given in the problem, μ₀ = 510, σ = 100, x̄ = 540, and n = 50. Finally, make sure to select μ > μ₀ for the alternative hypothesis.

There are two options for the output of the Z-Test. Selecting “Results: Calculate” displays the z-score (the number of standard deviations x̄ is above or below the mean) and then the corresponding p-value, the probability of getting such a sample by luck alone.

“Results: Draw” draws a normal distribution graph and displays the z-score and p-value at the bottom of the screen.

We have z = 2.12 and p = .017 , which means that there is a 1.7% chance of seeing such a variation in sample mean by chance alone. Since p<α, we can conclude that there is significant evidence that the treatment group is different from the general population. As before, this implies (but does not prove) that taking the pill improves students' Math SAT scores.

You might also like:

• Transferring Spreadsheets Between Microsoft Excel and your TI-83+, TI-84+, TI-89, TI-92+, or Voyage 200
• How to Graph Equations on the TI-83 Plus and TI-84 Plus
• Video: Using Variables on Your TI Graphing Calculator

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When conducting a hypothesis test, one of the critical steps is calculating the test statistic. A powerful yet user-friendly tool, the TI-84 graphing calculator, can help you do this quickly and accurately. In this article, we will discuss how to calculate a test statistic on a TI-84 calculator.

Step-by-Step Instructions:

1. Turn on your TI-84 calculator.

2. Press the “STAT” button located on the left side of the calculator to access the statistical modes.

3. Select “TESTS” from the displayed menu using the right arrow key.

4. Choose the type of hypothesis test you would like to perform. The most common tests include:

– 1-PropZTest for a proportion

– 2-PropZTest for comparing proportions from two independent samples

– T-Test for comparing means from one sample (with unknown population standard deviation)

– 2-SampTTest for comparing means from two independent samples (with unknown population standard deviations)

5. Once you have selected your desired test, press Enter to access data input prompts.

6. Input the required data values by pressing the corresponding arrow keys and then entering each value followed by Enter.

For instance:

– For 1-sample tests: input sample size (n), sample mean or proportion (e.g., x̄ or p̂), null hypothesis value (μ₀ or p₀), and sample standard deviation (s) if needed

– For 2-sample tests: input sample sizes (n₁ and n₂), sample means or proportions (x̄₁ and x̄₂ or p̂₁ and p̂₂), hypothesized difference in population means or proportions (μ₁ – μ₂ or p₁ – p₂), and sample standard deviations if needed

7. Choose an alternative hypothesis for your test using the arrow keys: lower-tailed test (μ > μ₀ or p > p₀), upper-tailed test (μ < μ₀ or p < p₀), or two-tailed test (μ ≠ μ₀ or p ≠ p₀). Press Enter to confirm your selection.

8. Press the “CALCULATE” button (usually scrolling down will bring you to the ‘Calculate’ option) and press Enter. The calculator will now calculate the test statistic and display it on the screen, along with the corresponding P-value.

9. Interpret your results by comparing the P-value with your chosen significance level (e.g., α = 0.05). A smaller P-value indicates stronger evidence against the null hypothesis, while a larger P-value suggests insufficient evidence for rejecting the null hypothesis.

Conclusion :

Calculating a test statistic on a TI-84 calculator is a straightforward process that can help you streamline your statistical analyses. By following these simple steps, you can quickly and accurately evaluate your hypothesis tests, enhancing your understanding of complex statistical concepts and making informed decisions based on data.

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How to Perform a Paired Samples t-test on a TI-84 Calculator

A  paired samples t-test  is used to compare the means of two samples when each observation in one sample can be paired with an observation in the other sample.

This tutorial explains how to conduct a paired t-test on a TI-84 calculator.

Example: Paired samples t-test on a TI-84 Calculator

Researchers want to know if a new fuel treatment leads to a change in the average mpg of a certain car. To test this, they conduct an experiment in which they measure the mpg of 11 cars with and without the fuel treatment.

Since each car receives the treatment, we can conduct a paired t-test in which each car is paired with itself to determine if there is a difference in average mpg with and without the fuel treatment.

Perform the following steps to conduct a paired t-test on a TI-84 calculator.

Step 1: Input the data.

First, we will input the data values for both samples. Press   Stat   and then press   EDIT  . Enter the following values for the control group (no fuel treatment) in column L1 and the values for the treatment group variable (received fuel treatment) in column L2, followed by the difference between these two values in column L3.

Note:  At the top of the third column, highlight L3. Then press   2nd   and   1   to create L1, followed by a minus sign, then press  2nd   and   2   to create L2. Then press  Enter . Each of the values in column L3 will automatically populate using the formula L1-L2.

Step 2: Perform the paired t-test.

To perform the paired t-test, we will simply perform a t-test on column L3, which contains the values for the paired differences.

Press  Stat . Scroll over to TESTS . Scroll down to 2:T-Test and press ENTER .

The calculator will ask for the following information:

• Inpt:  Choose whether you are working with raw data (Data) or summary statistics (Stats). In this case, we will highlight Data and press  ENTER .
• μ 0 : The mean difference to be used in the null hypothesis. We will type 0 and press   ENTER .
• List: The list that contains the differences between the two samples. We will type L3 and press   ENTER . Note: To get L3 to appear, press  2nd  and then press  3 .
• Freq:  The frequency. Leave this set to 1.
• μ :The alternative hypothesis to be used. Since we are performing a two-tailed test, we will highlight  ≠ μ 0  and press  ENTER . This indicates that our alternative hypothesis is μ≠0. The other two options would be used for left-tailed tests (0) and right-tailed tests (>μ 0 ) .

Lastly, highlight Calculate and press  ENTER .

Step 3: Interpret the results.

Our calculator will automatically produce the results of the one-sample t-test:

Here is how to interpret the results:

• μ≠0 : This is the alternative hypothesis for the test.
• t=-1.8751 : This is the t test-statistic. 
• p=0.0903 : This is the p-value that corresponds to the test-statistic.
• x =-1.5455 . This is the mean difference of group 1 – group 2.
• s x =2.7336 . This is the standard deviation of the differences.
• n=11 : This is the total number of paired samples.

Because the p-value of the test (0.0903) is not less than 0.05, we fail to reject the null hypothesis.

This means we do not have sufficient evidence to say that there is any difference between the average mpg of the two groups. That is, we do not have sufficient evidence to say that the fuel treatment affects mpg.

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