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The document you've uploaded includes questions about hypothesis testing, particularly focusing on t-tests using SPSS for various data sets. Here’s a summary of how to approach each question:

### Q1: One-sample t-test for Japanese car MPG

#### A. Hypotheses
- **Null Hypothesis (H0)**: The MPG for Japanese sedans is less than or equal to the MPG for American sedans.
  \[
  H_0: \mu \leq 26.5
  \]
- **Alternative Hypothesis (H1)**: The MPG for Japanese sedans is greater than the MPG for American sedans.
  \[
  H_1: \mu > 26.5
  \]

#### B. Sample Mean
You need to compute the mean for the given sample data of Japanese cars' MPG:

\[
M = \frac{34 + 30 + 32 + 35 + 34 + 28 + 34 + 29 + 30 + 33 + 37 + 32 + 29 + 34 + 24}{15}
\]
Calculate this value to two decimal points.

#### C. Standard Deviation (σ)
Use the standard deviation formula:
\[
\sigma = \sqrt{\frac{\sum (X - M)^2}{n-1}}
\]
Here, \(M\) is the sample mean you found, and \(X\) are the individual MPG values.

#### D. SPSS Output for t-statistic
Run the one-sample t-test in SPSS using the population mean (26.5) and report the t-statistic. Include the SPSS output screenshot in your final document.

#### E. P-value
Retrieve the p-value from the SPSS output to determine statistical significance.

#### F. Conclusion on Hypothesis
Based on the p-value, either reject or fail to reject the null hypothesis. Explain if the result supports the idea that Japanese sedans have significantly better fuel efficiency.

#### G. Interpretation
State whether Japanese sedans are statistically more fuel-efficient than American sedans based on the test.

---

### Q2: Two-sample t-test for Age Difference

#### A. Type of t-test
A **two-sample independent t-test** should be used, as you're comparing two independent groups (males and females).

#### B. Hypotheses
- **H0**: There is no significant difference in the average age between males and females.
- **H1**: There is a significant difference in the average age between males and females.

#### C-F. SPSS Analysis
- Perform the two-sample t-test in SPSS, paste the output, and calculate Cohen’s d for effect size.
- Report the t-statistic, degrees of freedom, p-value, and effect size.
- Make a decision on the null hypothesis and answer whether males and females differ significantly in age.

---

### Q3: Paired t-test for Memory Performance

#### A. Type of t-test
A **paired t-test** should be used, as you're comparing the memory performance of the same participants at two different times (Mem1 vs. Mem2).

#### B. Hypotheses
- **H0**: There is no significant change in memory performance from the first to the second testing session.
- **H1**: There is a significant change in memory performance.

#### C-F. SPSS Analysis
- Run the paired t-test in SPSS, paste the output, and calculate Cohen’s d for the effect size.
- Report the results in APA format, including t-statistic, degrees of freedom, p-value, and effect size.
- Make a conclusion based on the null hypothesis and the research question.

---

Would you like detailed step-by-step guidance for calculating specific values like the mean and standard deviation? Let me know!

### Related Questions:
1. How does a one-sample t-test differ from a two-sample t-test in terms of assumptions?
2. Why is it important to check if the data is normally distributed before running a t-test?
3. What does a p-value tell you about your hypothesis test result?
4. How can the effect size help interpret the results beyond the p-value?
5. What are the assumptions underlying a paired t-test?

**Tip:** Always check the assumptions of normality and independence before running a t-test to ensure valid results.

Perform a one-sample t-test using SPSS. Determine whether Japanese sedans have significantly higher MPG than American sedans with a comparison population mean of 26.5. Report sample mean, standard deviation, t-statistic, p-value, and conclude the hypothesis test.

Learn how to perform a one-sample t-test using SPSS to determine if Japanese sedans have significantly higher MPG compared to American sedans. This step-by-step guide includes calculating the sample mean, standard deviation, t-statistic, p-value, and interpreting the results.

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