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Single Sample t Test,
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Goal(s): Gain expertise with hypothesis testing (comparing the p-value with the alpha level) for the single sample t test. Notice the possibility of taking sample size into consideration, such that for a sample size of 30 or more, a Z test might be used even when the population standard deviation and distribution shape are unknown; consult with your instructor regarding best practices. Recognize that if the result is considered "statistically significant," then the null hypothesis is rejected.
How: For each scenario presented, compare the p-value with the alpha level, and decide whether to reject the null hypothesis. Make 30 quick decisions, with immediate feedback.
Site: P2L.io
About
About
For this activity, the terms "Null Hypothesis Distribution" and "Ho: Null Distribution" are both used to indicate a distribution of sample means as specified by the null hypothesis.
t test and p value
t test and p value
The t test specifies the number of estimated standard errors between the sample mean and the null hypothesis specified mean.
The closer the sample mean is to the middle of the Null Hypothesis Distribution, the smaller the resulting t test statistic. For a t test equaling zero, the sample mean occurred in the exact center of the Null Hypothesis Distribution.
High Probability. Assuming that the Null Hypothesis Distribution exists, there will be many sample means occurring in the middle of the distribution. Thus the probability of getting a sample mean drawn from the middle of the Null Hypothesis Distribution is high.
The further the sample mean is from the middle of the Null Hypothesis Distribution, the larger the resulting t test statistic.
Low Probability. At the edges of the Null Hypothesis distribution there are very few sample means occurring. Thus the probability of getting a sample mean deep in the tails of the distribution is quite low. It doesn't happen very often.
The t test can be used when the standard deviation must be estimated, as long as the parent population is at least roughly normally distributed. Hypothesis testing involves working with a distribution of sample means, and according to the Central Limit Theorem, that distribution more closely approximates the normal distribution as sample size increases. Likewise, our estimate of the population standard deviation becomes more accurate as sample size increases. Thus, based on the above two observations, there is some consensus to allow for the use of the Z test (in place of the t test) once the sample size is at least 30. In this game, the Z test will be reported for sample sizes of n ≥ 30.
One-tail vs Two-tail Hypothesis Test: The P-value
One-tail vs Two-tail Hypothesis Test: The P-value
For a two-tail hypothesis test, the the further the sample mean goes into the tails of the Null Hypothesis Distribution, the lower the p-value.
However, for a one-tail hypothesis test, we must further take into consideration the null hypothesis. Does the null hypothesis state either:
Sample Mean >= Pop. Mean, or
Sample Mean <= Pop. Mean?
Only if the sample mean goes in the opposite direction of what null hypothesis specifies will the p-value be low.
Alpha Level & Hypothesis Testing
Alpha Level & Hypothesis Testing
While our decision could involve comparing the t test to the appropriate t critical cutoffs, there is no need to do so in this case. We are given the p-value, which is sufficient to make the decision regarding whether to reject the null hypothesis.
The report will either provide "p-value (1-tailed)" for a one-tailed hypothesis or "p-value (2-tailed)" for a two-tail hypothesis. Our decision criterion, referred to as our alpha level, is set at .05. If the probability of the observed sample mean is .05 or less, then we consider the Null Hypothesis Distribution a "poor fit" and reject the null hypothesis.
Reject the null hypothesis when p ≤ .05.
Game
Optional: Earning Class Credit
To earn credit for this activity:
Click the 'Accommodations' button on the game menu.
Using the number pad (in the Accommodation dialog box), type the passcode provided by your instructor.
Click the 'Continue' button. Doing so will return you back to the game menu.
Then click 'Start' to begin the game.
When you complete the task with a score of 85% or greater, you will be given a completion code. To view this completion code, click on the 'Completion Code' button.
To get credit for having completed the activity, provide the completion code as your answer (e.g., to a quiz question). If the completion code is not yet available (e.g., performance was less than 85%), then click the 'Continue' button to re-do the activity.
Accommodations include:
Screen Reader (click the 'Screen Reader' button)
Unlimited decision time (e.g., Click the 'Accommodations' button, then type #17 by itself or at the end of a passcode. Click 'Continue').
Please notify your instructor if requesting these accommodations.
Instructors can modify games and set up quizzes rather easily. Check out game modifications.
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