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.

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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.

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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.

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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.