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

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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.

---

This structured presentation facilitates understanding of hypothesis testing using t-values, sample variability, and practical applications in evaluating behavioral studies.
Transcribed Image Text:Certainly! Below is the transcription of the image suitable for an educational website: --- **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. --- This structured presentation facilitates understanding of hypothesis testing using t-values, sample variability, and practical applications in evaluating behavioral studies.
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