QM 2 - CHAP 4

QM2 - CHAPTER 4

📌 Section A: One-Sample t-test

1. Define a one-sample t-test.
   Include when and why it is used, and provide a real-world example.

This test compares the sample mean to a known or hypothesis population mean. This tests whether sample mean is significantly different from population mean. There's only one group of participants. For example, is class A’s average exam score significantly different from the national average exam score. 

Used when you have one group and want to test how it compares to a benchmark.

2. List and explain the assumptions of a one-sample t-test.

• Scales of measurements - The DV should be interval or ratio. Continuous scale like height, weight and money. 

• Normality - data should be normality distributed. Forms a bell shape curve. 

• Population mean must be known or meaningful 

• Observations are independent - each participant score is not influenced by the others 

• Sample is randomly selected to generalize findings 

3. A researcher wants to test if students in their class watch more than the global average of 5 hours of Netflix per week.
   a. What test should they use?
   b. Formulate the null and alternative hypotheses.

• One sample t-test. 

• Null hypothesis (Ho) - there is no difference in hours spent each week watching Netflix in students samples with the global average. 

• Alternative hypothesis (H1) - there is a difference in hours spent each week watching Netflix in students samples with the global average. 

H₀: μ = 5 (no difference from global average)

H₁: μ ≠ 5 (significantly different from global average)

Based on the following SPSS output for a one-sample t-test, interpret the results:
Test Value = 5  

t(39) = 2.14, p = .039  

M = 5.56, SD = 1.10

4. a. Is the result significant?
   b. What does this mean in plain English?

• Yes, the result is significant (p < .05).

• The sample’s average Netflix time (M = 5.56) is significantly higher than the global average of 5 hours.

5. You conducted a one-sample t-test and got a non-significant result. What could this suggest about your sample compared to the population?

• The result is not significant (p > .05).

• There is no difference between the sample’s average and the global average.

• Sample mean is not statistically different from the population mean. 

• The sample might match the population 

• The sample size might be too small to detect a real difference.

6. Scenario: Do local students study significantly more than the global average of 2 hours per week?

One-Sample t-test Table

A one sample t-test was conducted to compare the hours spent each week studying in local students with the global average (2 hours per week). There is a significant difference between the hours spent each week studying in local students with the global average, t(39) = 3.66, p = 0.001. The local students' sample (M = 2.28, SD = 0.57) spent hours studying each week is significantly higher than the global average which is 2 hours per week.

📌 Section B: Paired-Samples t-test

6. Define a paired-samples t-test.
   When is it used? How is it different from an independent-samples t-test?

This test compares the means of two related measurements from the same group. This tests whether there is significant difference before and after intervention. Each participant provides 2 scores which are pre-test and post-test. This uses a within-subjects design where the same participants are measured multiple times. 

7. List and explain the assumptions of a paired-samples t-test.

• Scales of measurement - the DV should be measured at interval or ratio scale which is continuous. 

• Normality - the difference between the scores/data should be normally distributed 

• Observations are dependent - each pair of scores is from the same person or matched participants.

• Each pair is independent of other pairs. 

8. Imagine you're testing if a 4-week mindfulness app improves sleep quality in university students.
   a. What kind of design is this?
   b. What is IV and DV?
   c. What statistical test should you use?
   d. Write the null and alternative hypotheses.

• Within-subjects design 

• IV - mindfulness app , DV - sleep quality 

• Paired sample t-test 

• Null hypothesis (Ho) - there is no significant difference in sleep quality before and after the usage of the mindfulness apps between university students. 

• Alternative hypothesis (H1) - there is significant difference in sleep quality before and after the usage of the mindfulness app between university students. 

9. A researcher compared participants' anxiety before and after a therapy program. The SPSS output showed:
t(25) = -3.12, p = .005  

Pre-therapy M = 15.2, SD = 4.3  

Post-therapy M = 12.1, SD = 3.8

a. What test was used?
b. Is the result significant?
c. Interpret the result in one sentence.

• Paired sample t-test 

• Yes the results are significant, p = 0.005

• A paired sample t-test was conducted to test whether attending a therapy program is able to improve anxiety level. There is a significant difference in anxiety level before (M = 15.2, SD = 4.3) and after attending the therapy program (M = 12.1, SD = 3.8) , t(25) = -3.12, p = .005. Thus, the therapy program is effective in improving anxiety level. 

10. Scenario: A group of 30 students took a motivation test before and after attending a self-efficacy workshop. Did their motivation improve?

SPSS Output: Descriptive Statistics

SPSS Output: Paired-Samples Test

A paired sample t-test was conducted to test whether attending a self-efficacy workshop is able to improve students' motivation. There is a significant difference in sleep quality before (M = 3.10, SD = 0.52 ) and after attending the therapy program (M = 3.45, SD = 0.50) , t(5.27) = 29, p < 0.001. Thus, the self-efficacy workshop is effective in improving students' motivation level.