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C D ng cengage.com/static/nb/ui/index.html?nbld 497996&nbNodelda; 176563379&elsBN-9; MIND TAP The t Test for Two Related Samples Aplia a Due on Apr at SAM cesr Attempts Keep the Highest: /10 3. A two-tailed hypothesis test for a measures design Previous studies have shown that playing video games can increase visual peroeption abilities on tasks presented in the gaming zone of the screen (within s degrees of the center). A graduate student is interested in whether playing video games increases peripheral visual perception abilities or decreases attention to peripheral regions because of focus on the gaming zone. For his study, he selects a random sample of 81 adults. The subjects complete a difficult spatial peroeption task to determine baseline levels of their abilities. After playing an action video game (a first-person combat s for 1 hour a day over 10 days, they complete the difficult perception task for a second time. Before playing the action video game, the mean score in their accuracy on the spatial task was 0.31. After playing th on video game, the mean score was o.35. The mean of the differences between each person's pre- and post- sco es was 0.04, with a standard deviation of the differences equal to 0.08. The graduate student has no presupposed assumptions about whether playing video games increases peripheral visual perception abilities or decreases attention to peripheral regions because of focus on the gaming zone, so he formulates the null and alternative hypotheses as: 1: 0 He uses a repeated-measures t test. Because the sample size is large, if the null hypothesis is true as an equality, the test statistic follows a t-distribution with n 1-81 1 80 degrees of freedom.Explanation / Answer
This is a paired t test.
Resons: There are counts of data which is paired. Because, same adults's accuracy on a spatial task were measured before and after playing video games.
This is an experiment, and therefore, data is randomized. Accuracy score of one player is independent of another, therefore, the independence assumption also holds true. Moreover, there is no reason to beileve that the data do not follow normalization condition.
The critical t is +-1.99 (the test is two -tailed).
The standard error, SE=sd/sqrt n, where, sd is standard deviation of difference, and n is sample size.
=0.08/sqrt 81=0.009
Test statistic: t=(dbar-0)/SE
=0.04/0.009
=4.44
The test statistic falls in critical region. (Observed t> critical t). Rejected (reject H0, if observed t >critical t), can conclude.
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