T-Test on Calculator Ti-84 Without Standard Deviaiton

What is a t-test?

A t-test is a statistical test that determines whether there is a significant difference between the means of two groups. It's commonly used in research to compare sample means to a population mean or to compare two sample means.

The t-test uses a t-distribution to calculate the probability that the difference between the sample means is due to chance. The test has three main types:

• One-sample t-test: Compares a sample mean to a known population mean
• Independent samples t-test: Compares means of two independent groups
• Paired t-test: Compares means of related samples (matched pairs)

When you don't have standard deviation values, you'll need to calculate them from your sample data first.

When to use a t-test

You should use a t-test when:

• Your sample size is small (typically n < 30)
• Your data is approximately normally distributed
• You don't know the population standard deviation
• You want to compare means of two groups

Common applications include:

• Comparing test scores of two teaching methods
• Testing whether a new drug has a different effect than a placebo
• Analyzing whether a marketing campaign increased sales

Performing a t-test without standard deviation

When you don't have standard deviation values, you'll need to calculate them from your sample data. Here's the process:

1. Calculate the mean of each sample
2. Calculate the standard deviation of each sample
3. Enter these values into the t-test formula

Once you have the standard deviations, you can perform the t-test using the appropriate formula for your test type.

Step-by-step on TI-84

Here's how to perform a t-test on your TI-84 when you don't have standard deviation values:

1. Enter your data into the calculator:
   • Press STAT then EDIT
   • Enter your data in L1 and L2
2. Calculate the sample means:
   • Press STAT then CALC
   • Select 1-Var Stats
   • Enter L1 for List and calculate for the first sample
   • Repeat for L2
3. Calculate the standard deviations:
   • Use the same 1-Var Stats function
   • Note the σx value for each sample
4. Perform the t-test:
   • Press STAT then TESTS
   • Select the appropriate test type (A for two-sample, B for one-sample)
   • Enter the required values including the standard deviations
   • Press ENTER to get the results

Worked example

Let's perform a two-sample t-test comparing the test scores of two teaching methods with sample sizes of 15 each.

1. Enter the data into L1 and L2
2. Calculate statistics for L1:
   • Mean: 72.4
   • Standard deviation: 8.1
3. Calculate statistics for L2:
   • Mean: 68.9
   • Standard deviation: 7.5
4. Perform the t-test:
   • Test type: Two-sample t-test
   • Data: L1, L2
   • Frequency: 1
   • Pool?: No
   • Enter the standard deviations
5. Results:
   • t = 2.34
   • p = 0.032
   • df = 26

Since p = 0.032 < 0.05, we reject the null hypothesis and conclude there is a statistically significant difference between the two teaching methods.

Interpreting results

When you perform a t-test, you'll get several key results:

• t-value: The calculated t-statistic
• p-value: The probability of observing the data if the null hypothesis is true
• Degrees of freedom: The number of independent pieces of information in your data

Interpretation guidelines:

• If p < 0.05, you reject the null hypothesis (there is a significant difference)
• If p ≥ 0.05, you fail to reject the null hypothesis (no significant difference)
• A larger absolute t-value indicates a greater difference between groups