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Previous studies have shown that playing video games can increase visual perception abilities on tasks presented in the gaming zone of (within 5 degrees of the center). A graduate student is interested in whether playing video games increases peripheral visual perception decreases attention to peripheral regions because of focus on the gaming zone. For his study, he selects a random sample of 64 adults. T complete a difficult spatial perception task to determine baseline levels of their abilities. After playing an action video game (a first-persor simulation) 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 0.42. After playing the action video game,

Previous studies have shown that playing video games can increase visual perception abilities on tasks presented in the gaming zone of (within 5 degrees of the center). A graduate student is interested in whether playing video games increases peripheral visual perception decreases attention to peripheral regions because of focus on the gaming zone. For his study, he selects a random sample of 64 adults. T complete a difficult spatial perception task to determine baseline levels of their abilities. After playing an action video game (a first-persor simulation) 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 0.42. After playing the action video game,

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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This is a ______ test. Use the Distributions tool to find the critical score(s) for the level of significance α = 0.01. The critical score(s) (the value(s) for t that separate(s) the tail(s) from the main body of the distribution, forming the critical region) is/are ______. To calculate the test statistic, you first need to calculate the estimated standard error under the assumption that the null hypothesis is true. The estimated standard error is ______. The test statistic is t = ______. Use the tool to evaluate the null hypothesis. (Note: You can place the purple line on your t statistic to tell whether it lies within or outside the critical region. It's possible that this line may not rest exactly on the t statistic, but you will be able to tell whether it lies within or outside the critical region.) The t statistic ______ in the critical region for a two-tailed hypothesis test. Therefore, the null hypothesis is ______. The graduate student ______ conclude that playing video games alters peripheral visual perception. The graduate student repeats his study with another random sample of the same size. This time, instead of the treatment being playing the combat simulation video game, the treatment is playing a soccer video game. Suppose the results are very similar. After playing a soccer video game, the mean score was still 0.5 lower, but this time the standard deviation of the difference was 1.8 (vs. the original standard deviation of 2.4). This means ______ has the more consistent treatment effect. This difference in the standard deviation also means that a 95% confidence interval of the mean difference would be ______ for the original study, when the treatment was playing the combat simulation video game, than the 95% confidence interval of the mean difference for the second study, when the treatment was playing a soccer video game. Finally, this difference in the standard deviation means that when the graduate student conducts a hypothesis test testing whether the mean difference is zero for the second study, he will be ______ likely to reject the null hypothesis than he was for the hypothesis test you completed previously for the original study.
Transcribed Image Text:This is a ______ test. Use the Distributions tool to find the critical score(s) for the level of significance α = 0.01. The critical score(s) (the value(s) for t that separate(s) the tail(s) from the main body of the distribution, forming the critical region) is/are ______. To calculate the test statistic, you first need to calculate the estimated standard error under the assumption that the null hypothesis is true. The estimated standard error is ______. The test statistic is t = ______. Use the tool to evaluate the null hypothesis. (Note: You can place the purple line on your t statistic to tell whether it lies within or outside the critical region. It's possible that this line may not rest exactly on the t statistic, but you will be able to tell whether it lies within or outside the critical region.) The t statistic ______ in the critical region for a two-tailed hypothesis test. Therefore, the null hypothesis is ______. The graduate student ______ conclude that playing video games alters peripheral visual perception. The graduate student repeats his study with another random sample of the same size. This time, instead of the treatment being playing the combat simulation video game, the treatment is playing a soccer video game. Suppose the results are very similar. After playing a soccer video game, the mean score was still 0.5 lower, but this time the standard deviation of the difference was 1.8 (vs. the original standard deviation of 2.4). This means ______ has the more consistent treatment effect. This difference in the standard deviation also means that a 95% confidence interval of the mean difference would be ______ for the original study, when the treatment was playing the combat simulation video game, than the 95% confidence interval of the mean difference for the second study, when the treatment was playing a soccer video game. Finally, this difference in the standard deviation means that when the graduate student conducts a hypothesis test testing whether the mean difference is zero for the second study, he will be ______ likely to reject the null hypothesis than he was for the hypothesis test you completed previously for the original study.
Certainly! Here is a transcription and detailed explanation suitable for an educational website: --- ### 6. A Two-Tailed Hypothesis Test for a Repeated-Measures Research Design **Research Context** Previous studies have shown that playing video games can enhance visual perception abilities on tasks within the gaming zone of the screen (within 5 degrees of the center). A graduate student is investigating whether playing video games enhances peripheral visual perception abilities or decreases attention to peripheral regions due to focus on the gaming area. For this study, a random sample of 64 adults participated. Subjects initially completed a challenging spatial perception task to establish baseline abilities. Following this, they played an action video game (first-person combat simulation) for 1 hour daily over 10 days. They then completed the spatial perception task again. **Baseline and Post-Test Results** Before playing the video game, the mean score on the spatial task was 0.42. After engaging with the video game, the mean score was -0.08. The mean of the differences between each individual’s scores from pre- to post-test was 0.5, with a standard deviation of 2.4. **Hypotheses** The student forms the hypotheses as follows, without presupposing whether gaming increases or decreases peripheral perception skills: - Null Hypothesis (H₀): μₜ = 0 - Alternative Hypothesis (H₁): μₜ ≠ 0 **Analysis** A repeated-measures t-test is used. With a large sample size, if H₀ is true, the test statistic follows a t-distribution with n - 1 = 64 - 1 = 63 degrees of freedom. **Graphical Representation** Below the text is a diagram showing a symmetrical t-Distribution curve centered at 0, indicating the range for the test statistic values. This graph illustrates where critical values fall under the curve's tails, determining the statistical significance. **Procedure** 1. **Type of Test**: Use the Distributions tool to find the critical score(s) for the significance level α = 0.01. 2. **Critical Values**: Determine the critical score(s) where the distribution’s tails separate from the main body, forming the critical region. 3. **Test Statistic**: Calculate the test statistic by finding the estimated standard error under the assumption that H₀ is true. Compute the estimated standard error as follows: \( \text{Estimated Standard Error}
Transcribed Image Text:Certainly! Here is a transcription and detailed explanation suitable for an educational website: --- ### 6. A Two-Tailed Hypothesis Test for a Repeated-Measures Research Design **Research Context** Previous studies have shown that playing video games can enhance visual perception abilities on tasks within the gaming zone of the screen (within 5 degrees of the center). A graduate student is investigating whether playing video games enhances peripheral visual perception abilities or decreases attention to peripheral regions due to focus on the gaming area. For this study, a random sample of 64 adults participated. Subjects initially completed a challenging spatial perception task to establish baseline abilities. Following this, they played an action video game (first-person combat simulation) for 1 hour daily over 10 days. They then completed the spatial perception task again. **Baseline and Post-Test Results** Before playing the video game, the mean score on the spatial task was 0.42. After engaging with the video game, the mean score was -0.08. The mean of the differences between each individual’s scores from pre- to post-test was 0.5, with a standard deviation of 2.4. **Hypotheses** The student forms the hypotheses as follows, without presupposing whether gaming increases or decreases peripheral perception skills: - Null Hypothesis (H₀): μₜ = 0 - Alternative Hypothesis (H₁): μₜ ≠ 0 **Analysis** A repeated-measures t-test is used. With a large sample size, if H₀ is true, the test statistic follows a t-distribution with n - 1 = 64 - 1 = 63 degrees of freedom. **Graphical Representation** Below the text is a diagram showing a symmetrical t-Distribution curve centered at 0, indicating the range for the test statistic values. This graph illustrates where critical values fall under the curve's tails, determining the statistical significance. **Procedure** 1. **Type of Test**: Use the Distributions tool to find the critical score(s) for the significance level α = 0.01. 2. **Critical Values**: Determine the critical score(s) where the distribution’s tails separate from the main body, forming the critical region. 3. **Test Statistic**: Calculate the test statistic by finding the estimated standard error under the assumption that H₀ is true. Compute the estimated standard error as follows: \( \text{Estimated Standard Error}
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