Introduction

This document provides a comprehensive guide on how to perform hypothesis testing using a TI-84 calculator. It covers both z-test and t-test methods, suitable for different scenarios depending on whether the population standard deviation is known.

Preliminaries

  • Null hypothesis (\(H_0\)): The statement that the parameter of the population is equal to a specified value.
  • Alternative hypothesis (\(H_a\)): The statement that the parameter is different from the specified value.
  • Significance level (\(\alpha\)): Commonly set at 0.05.
  • Test type: One-tailed or two-tailed depending on the hypothesis.

Example 1: Z-Test for the Mean

Scenario

Test if the average IQ of a group is more than the population mean of 100. Assume the population standard deviation is known to be 15. A sample of 50 individuals has a mean IQ of 104.

Steps on TI-84

Step 1: Configure the Test

  • Press STAT.
  • Right arrow to TESTS.
  • Choose 1:Z-Test....

Step 2: Input the Data

  • For Stats, input:
    • \(\mu_0\): 100
    • \(\sigma\): 15
    • \(\bar{x}\): 104
    • n: 50
  • Choose >μ_0 for a two-tailed test.

Step 3: Calculate and Interpret

  • Scroll to Calculate and press ENTER.
  • The calculator will provide the z-statistic and p-value.
  • Interpret the p-value relative to \(\alpha = 0.05\).

Example 2: T-Test for the Mean

Scenario

Evaluate whether the mean height of a sample of 25 students is different from the known average of 68 inches. The sample has a mean height of 66 inches with a standard deviation of 3.5 inches.

Steps on TI-84

Step 1: Configure the Test

  • Press STAT.
  • Right arrow to TESTS.
  • Choose 2:T-Test....

Step 2: Input the Data

  • For Stats, input:
    • \(\mu_0\): 68
    • \(\bar{x}\): 66
    • Sx: 3.5
    • n: 25
  • Choose ≠μ_0 for a two-tailed test.

Step 3: Calculate and Interpret

  • Scroll to Calculate and press ENTER.
  • The calculator will provide the t-statistic, p-value, and degrees of freedom.
  • Interpret the p-value relative to \(\alpha = 0.05\).

Conclusion

These examples demonstrate how to conduct a z-test and a t-test on the TI-84 calculator, depending on whether the population standard deviation is known. Follow these steps to test different hypotheses regarding population means using your calculator.