Find the t value that forms the boundary of the critical region in the right-hand tail for a one-tailed test with an alpha of .01 for each of the following sample sizes. (Assume this is a one sample t-test) 2.764 a. n=10 b. n=20 2.528 c. n=30 2.457
Find the t value that forms the boundary of the critical region in the right-hand tail for a one-tailed test with an alpha of .01 for each of the following sample sizes. (Assume this is a one sample t-test) 2.764 a. n=10 b. n=20 2.528 c. n=30 2.457
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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**Statistical Analysis: Critical Regions and Hypothesis Testing**
2. **Finding the Critical Region Boundary for a One-Tailed Test with Alpha = 0.01**
For each sample size, determine the t value for a one sample t-test:
a. n = 10: t = 2.764
b. n = 20: t = 2.528
c. n = 30: t = 2.457
3. **Evaluating the Effect of a Treatment**
A sample of n = 6 is obtained from a population with a mean of μ = 80. After administering treatment, the sample mean is M = 72. Analyze with the following variances:
a. If sample variance is s² = 54, assess if the treatment has a significant effect using a two-tailed test with alpha = 0.5.
b. If sample variance is s² = 150, assess if the treatment has a significant effect using a two-tailed test with alpha = 0.5.
c. Compare your results for parts a and b to evaluate the impact of score variability on hypothesis testing outcomes.
4. **Impact of Calorie Content Posting on Menu Items in Fast-Food Restaurants**
**Study Findings:**
Researchers, including Elbel, Gyamfi, and Kersh (2011), investigated whether displaying calorie content influenced customer choices. Their findings suggested no significant change in behavior. Data showed:
- Before labeling, the average calorie count was M = 786 with s = 85 in a sample of n = 100 (children and adolescents).
- After labeling, the average was M = 772 with s = 91 in a similar sample.
Use a two-tailed test with alpha = 0.05 to determine if there is a significant difference in calorie consumption before and after the labeling mandate.
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This structured presentation facilitates understanding of hypothesis testing using t-values, sample variability, and practical applications in evaluating behavioral studies.
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