Solution To Psyc 354 Homework 7 Excel Homework 770 Pts Possi

Solution To Psyc 354 Homework 7excel Homework 770 Pts Possible

Research Question: A clinical psychologist is treating 25 patients with clinical depression. She wants to find out whether these patients score differently than the general population on an emotional response scale with a population mean μ = 9.5. She is only interested in whether there is a difference, but not in the direction of the difference at this point. Open the “Data Set 7” attachment under the “Excel Homework 7” header located in the Assignment Instructions folder and perform a single-sample t-test to evaluate this hypothesis.

1. State the null and alternative (research) hypothesis in symbolic form. Remember that your hypothesis should include evaluators such as =, ≠, or a combination of these.
2. Remember that we are only doing 2-tailed t-tests at this point.
3. Fill in the cells for the degrees of freedom and μ, which are already known. These will be used in formulas as shown in this week’s presentation.
4. Compute the standard deviation of the sample (s) using the steps shown in this module/week’s presentation.
5. Fill in the sample mean (M), using the AVERAGE function for the raw scores on the left.
6. Test our hypothesis at the .01 level of significance. Enter the alpha value in the appropriate cell.
7. Find the critical t value for our test, based on the alpha level, using the TINV function as shown in this module/week’s presentation. Remember that we are running a two-tailed test, so no change to the alpha level is needed.
8. Compute the sample t score using the steps gone over in this week’s presentation.
9. Fill in the critical p-value based on your alpha level.
10. Compute your sample’s p-value (based on your sample’s t score) by using the TDIST function as shown in this module/week’s presentation.
11. Answer the 2 questions underneath the second table directly in Data Set 7, after each question as indicated. (Questions = 3.5 points each for a total of 7 pts.)

Paper For Above instruction

The hypothesis testing process in psychological research provides a rigorous framework to evaluate whether observed data support a specific research hypothesis. In this case, a clinical psychologist seeks to determine if patients suffering from clinical depression exhibit different emotional responses compared to the broader population. The population mean μ is known to be 9.5, and the sample consists of 25 depressed patients. The primary goal is to perform a single-sample t-test to evaluate the null hypothesis that the sample's mean emotional response is equal to the population mean, against the alternative hypothesis that it is not equal, reflecting a two-tailed test approach.

Formulating the hypotheses entails defining the null hypothesis (H₀) as the population mean being equal to 9.5, and the alternative hypothesis (H₁) as the population mean not equal to 9.5. Symbolically, these are expressed as H₀: μ = 9.5 and H₁: μ ≠ 9.5. This setup aligns with the research question, aiming to detect any deviation—whether higher or lower—of the sample mean from the population mean.

Critical to the analysis are known constants: the degrees of freedom (df) and the population mean (μ). For a sample of 25 individuals, df will be calculated as n - 1, equaling 24. The population mean μ remains at 9.5. These figures are input into the Excel spreadsheet formulas to facilitate subsequent calculations such as standard deviation, t-statistics, and p-values.

The sample standard deviation (s) is calculated using the sample data by following standard formulas—computing the square root of the variance, which is the average squared deviations from the sample mean. This process involves computing the differences between each raw score and the sample mean, squaring these differences, summing all squared deviations, dividing by n - 1 (for an unbiased estimate), and taking the square root.

Once the standard deviation is calculated, the sample mean (M) is determined using the AVERAGE function applied to the raw scores data. The mean provides a point estimate of the central tendency of the sample, critical for calculating the t-statistic.

Statistical significance is tested at the α = 0.01 level, which is input into the corresponding cell within the Excel worksheet. This alpha level indicates that there is a 1% risk of rejecting the null hypothesis when it is true, controlling for Type I error.

The critical t value for a two-tailed test at the 0.01 significance level is obtained using the TINV function. This function considers the degrees of freedom and the alpha level to determine the threshold t value beyond which results are considered statistically significant. Because it is a two-tailed test, the total alpha is split equally between the two tails.

The computed t score for the sample is obtained using the standard formula: (M - μ) divided by (s / √n). This t score indicates how many standard errors the sample mean is from the population mean. The sign of this t-value tells us the direction of the deviation, although for the two-tailed test, the critical value is symmetrical.

Based on the alpha level set at 0.01, the critical p-value associated with the test indicates the threshold below which the observed data are deemed significantly different from the null hypothesis. The exact p-value corresponding to the calculated t score is derived using the TDIST function, which computes the probability of obtaining a t statistic as extreme or more extreme, considering the degrees of freedom.

Finally, the researcher must interpret the results by comparing the calculated p-value to the significance level. If the p-value is less than 0.01, the null hypothesis is rejected, suggesting that the depressed patients’ emotional responses differ significantly from the general population. Conversely, if the p-value exceeds 0.01, there is not enough evidence to reject the null, indicating no statistically significant difference was detected.

References

• Field, A. (2013). Discovering Statistics Using IBM SPSS Statistics. Sage Publications.
• Gravetter, F. J., & Wallnau, L. B. (2016). Statistics for The Behavioral Sciences. Cengage Learning.
• Laerd Statistics. (2017). One-sample t-test. https://statistics.laerd.com/statistical-guides/one-sample-t-test-statistical-guide.php
• Howell, D. C. (2013). Statistical Methods for Psychology. Cengage Learning.
• Tabachnick, B. G., & Fidell, L. S. (2013). Using Multivariate Statistics. Pearson Education.
• Keselman, H. J. (2018). Statistical Methods in Psychology. Routledge.
• Wilkinson, L., & Task Force on Statistical Inference. (1999). The t test: An analysis of its misuse. The American Statistician, 53(3), 177-182.
• Gelman, A., & Hill, J. (2006). Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press.
• King, R., & Minium, E. (2007). Statistical Resources: The t Test. https://rao2000.wixsite.com/rao2000/single-post/2017/03/28/statistical-resources-the-t-test
• McDonald, J. H. (2014). Handbook of Biological Statistics. Sparky House Publishing.