hypothesis testing ti 84 plus

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.

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AP®︎/College Statistics

Course: ap®︎/college statistics   >   unit 11.

• When to use z or t statistics in significance tests
• Example calculating t statistic for a test about a mean
• Calculating the test statistic in a t test for a mean

Using TI calculator for P-value from t statistic

• Using a table to estimate P-value from t statistic
• Calculating the P-value in a t test for a mean
• Comparing P-value from t statistic to significance level
• Making conclusions in a t test for a mean
• Free response example: Significance test for a mean

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MathBootCamps

T-test for the mean using a ti83 or ti84 calculator (p-value method).

Do people tend to spend more than 2 hours on a computer every day? Can you say that the mean age of a college freshman in your state is not 18 years old? These are the types of questions that can be answered using collected data and a t-test for the mean. In this guide, you will see how you can use a TI83 or TI84 calculator to perform this test using the p-value method.

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We will use an example to see how this process works. For this example, assume that the requirements for a hypothesis test for the mean are met (randomly selected sample, independent observations, large population size).

Example: performing a t-test on the calculator

Suppose that a marketing firm believes that people who are planning to purchase a new TV spend more than 7 days researching their purchase. They conduct a survey of 32 people who had recently purchased a TV and found that the mean time spent researching the purchase was 7.8 days with a standard deviation of 3.9 days. At a significance level of 0.05, does this survey provide evidence to support the firm’s belief?

Step 1: Write the null and alternative hypotheses

The null hypothesis is the equality* statement using the same value:

Step 2: Calculate the p-value using your calculator and the correct test

1. Press [STAT] then go the the TESTS menu.

2. Select “2. T-test”. Make sure that you highlight Stats and press [ENTER] if your screen looks different from this.

3. Enter the values and select the correct tail for the test.

4. Highlight Calculate and press [ENTER].

Step 3: Compare the p-value to the significance level alpha and make your decision

To make the decision, use the decision rule:

In this problem:

Step 4: Interpret your decision in terms of the problem

So, we are saying that there is not enough evidence that the population mean is greater than 7. In context, we are saying:

This sample does not provide evidence that the mean time spent researching a new TV purchase is more than 7 days.

Although our sample mean was in fact larger than 7, it wasn’t quite enough to suggest that this is true for the entire population. Remember, in hypothesis testing, that is what we are trying to determine – is the sample enough to say that the hypothesis holds for the entire population?

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How to use TI-84 Plus to find critical value?

The TI-84 Plus is a popular graphing calculator that can be effectively used to find critical values in various statistical calculations and analyses. Understanding how to use this calculator correctly can save you time and effort in determining critical values for hypothesis testing, confidence intervals, and more. In this article, we will guide you step by step on how to use the TI-84 Plus to find critical values, ensuring accurate results for your statistical calculations.

Table of Contents

Step 1: Enter the Data

Before finding critical values, you must have your data ready.

Step 2: Choose the Appropriate Function

Depending on the type of analysis you are conducting, select the appropriate function. For example, to find a critical value for a hypothesis test based on a t-distribution, choose the “t-Test” function.

Step 3: Input the Required Information

Upon selecting the function, the calculator will prompt you to input specific information, such as sample size, mean, standard deviation, and degrees of freedom.

Step 4: Specify the Desired Significance Level

Next, specify the significance level (alpha) for the analysis. This value indicates the maximum probability of rejecting the null hypothesis when it is true. Commonly used significance levels are 0.05 and 0.01.

Step 5: Calculate the Critical Value

Once you have entered all the necessary information, the calculator will calculate and display the critical value based on the specified significance level and the given data.

Step 6: Interpret the Critical Value

Interpret the obtained critical value in the context of your analysis. It represents the threshold value at which you can confidently accept or reject a hypothesis or determine the bounds of a confidence interval.

1. Can the TI-84 Plus be used to find critical values for different distributions?

Yes, the TI-84 Plus provides functions to find critical values for various distributions such as the t-distribution, normal distribution, chi-square distribution, and more.

2. How can I find a critical value for a one-sample t-test?

Use the “t-Test” function on the TI-84 Plus, input the sample mean, standard deviation, sample size, and the desired significance level to obtain the critical value.

3. What if I want to find a critical value for a two-sample t-test?

The TI-84 Plus can also handle two-sample t-tests. Select the appropriate function, input the required information for both samples, and specify the significance level.

4. Can the TI-84 Plus calculate critical values for a chi-square test of independence?

Yes, the calculator offers functions for chi-square tests as well. Enter the observed frequencies, expected frequencies, and degrees of freedom to find the critical chi-square value.

5. What if I need to find a critical value for a confidence interval calculation?

When calculating confidence intervals, you can utilize the “invT” function on the TI-84 Plus. Input the desired confidence level and degrees of freedom to obtain the critical t-value.

6. Is it possible to find critical values for a proportion test using the TI-84 Plus?

Yes, the TI-84 Plus allows you to find the critical value for a proportion test. Input the sample proportion, sample size, and desired significance level to obtain the critical z-value.

7. How can I determine the critical value for a one-way ANOVA on the TI-84 Plus?

Use the “ANOVA” function on the calculator and input the necessary information, including the sample means and standard deviations for each group, to obtain the critical F-value.

8. Can I find the critical value for a two-way ANOVA on the TI-84 Plus?

Yes, the TI-84 Plus supports two-way ANOVA calculations. Select the function, input the required data for each group, and the calculator will display the critical F-value.

9. How do I know if my critical value is acceptable for my analysis?

Compare the obtained critical value with the test statistic value. If the test statistic falls beyond the critical value, you can reject the null hypothesis or consider the result statistically significant.

10. Is it possible to find critical values for a correlation analysis on the TI-84 Plus?

Unfortunately, the TI-84 Plus does not have built-in functions to find critical values for correlation analysis. However, it can calculate other relevant statistics such as correlation coefficient and p-value.

11. Can I find critical values for a linear regression on the TI-84 Plus?

The TI-84 Plus can perform linear regression analysis but does not provide direct functions for critical values in this context. However, the calculator can calculate other important regression statistics like coefficients, standard errors, and t-values.

12. How accurate are the critical values provided by the TI-84 Plus?

The critical values given by the TI-84 Plus are highly accurate and based on established mathematical formulas. However, always cross-verify them with the appropriate statistical tables or other reliable sources to ensure accuracy in your analysis.

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