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Single Sample t Test,
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Goal(s): Increased experience with the single sample t test. Gain expertise with how to interpret the "Sig. (2-tailed)," depending upon whether it is a one-tail or two-tail hypothesis 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. Recognize that if the result is considered "statistically significant," then the null hypothesis is rejected. Become familiar with interpreting statistical results as they might be produced by a software program (e.g., SPSS).
How: For each scenario presented, take into consideration whether it is a one-tail or two-tail hypothesis test. Evaluate the "Sig. (2-tailed)" result, 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 (or even further away) 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
For this game, the statistical software will always assume a two-tail test. Many statistical software programs take this approach (e.g., SPSS). What does it mean? You, the end user, must take into consideration whether it is a one-tailed or two-tailed hypothesis test.
If a two-tailed test, then...
Reject the null hypothesis when the 'Sig. (2-tailed)' ≤ .05
If a one-tailed test (e.g., "Null Hyp: Sample Mean <= Pop. Mean"), then...
Retain the null hypothesis if the results are consistent with the null hypothesis
Otherwise, reject the null hypothesis:
If 'Sig. (2-tailed)' ≤ (2 x alpha level).
For a one-tailed test, with the sample mean in the direction opposite of that predicted by the null hypothesis, with a Sig. (2-tailed) of .09, and an alpha level of .05, we would reject the null hypothesis.Which can also be stated as: reject the null if ('Sig. (2-tailed)' / 2) ≤ .05.
That is to say, for a one-tailed hypothesis, if the results are consistent with the null hypothesis, then retain it. Otherwise, compare the 'Sig. (2-tailed)' to a value that that is double the alpha level (e.g., 2 * .05 = .10); for an alpha of .05, reject the null if the 'Sig. (2-tailed)' ≤ .10. Alternatively, one could halve the 'Sig. (2-tailed)' and compare it to the alpha level (e.g., .05). Mathematically, these two methods will give the same result, so pick whichever approach you find easier to apply.
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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