Applet Exploration

Section 19.3 Applet Exploration

In this exploration, you will have the opportunity to explore how different factors impact the p-value of a two-sample t-test.

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Exercises Guess the p-value

You can use the embedded applet below, or open it in a separate window/tab for a larger view.

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1. First Guess.

Press the Draw New Samples button to generate data from two populations. Based on the resulting data, enter a guess for the p-value for a two-sample \(t\)-test on these data and then press Check Guess.

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How close was your guess? Were you surprised by the actual value? In what way? How might you guess differently the next time?

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Solution.

Answers will vary.

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2. Second Guess.

Press the Draw New Samples button, enter your guess for the value of the p-value for these data and press Enter. Describe how close you were and what adjustments you might make in your thinking.

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Solution.

Answers will vary.

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3. Practice with 10 Samples.

Repeat this process for a total of 10 pairs of samples (you do not need to record your results but you should try to learn from the reveal of the actual values as you make your guesses). Do you think your guessing ability improved by the last guess? Explain.

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Solution.

Answers will vary.

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4. Effect of Population Mean Difference.

Now check the Edit population parameters box and press Draw New Samples. Press Check Guess and now use the slider to create a larger and larger difference between the two population means. How does this impact the p-value?

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Solution.

The greater the difference between the population means, the smaller the p-value.

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