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Questions and Answers
What are the two specific test statistics used for hypothesis testing concerning means?
What are the two specific test statistics used for hypothesis testing concerning means?
z-test and t-test
If the sample size is large where $n \geq 30$ and the population standard deviation ($\sigma$) is known, you should use t-test.
If the sample size is large where $n \geq 30$ and the population standard deviation ($\sigma$) is known, you should use t-test.
False (B)
In the formula for the z-value, what does $\bar{x}$ represent?
In the formula for the z-value, what does $\bar{x}$ represent?
sample mean
In the formula for the z-value, what does $\mu$ represent?
In the formula for the z-value, what does $\mu$ represent?
The t-test is used when $n < 30$, the population is normal or nearly normal, and sample standard deviation (s) is known.
The t-test is used when $n < 30$, the population is normal or nearly normal, and sample standard deviation (s) is known.
What is the formula for degrees of freedom?
What is the formula for degrees of freedom?
In the Zcom formula, what does $\hat{p}$ represent?
In the Zcom formula, what does $\hat{p}$ represent?
In the Zcom formula, what does $p$ represent?
In the Zcom formula, what does $p$ represent?
Flashcards
When do you use a z-test?
When do you use a z-test?
A test used when the sample size (n) is large (≥ 30) and the population standard deviation (σ) is known.
When do you use a t-test?
When do you use a t-test?
A test used when the sample size (n) is small (< 30), the population is normal or nearly normal, and the population standard deviation (s) is unknown.
What is x̄?
What is x̄?
Sample mean
What is μ?
What is μ?
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What is n?
What is n?
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What is σ?
What is σ?
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What is s?
What is s?
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Formula for degrees of freedom (df)
Formula for degrees of freedom (df)
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What is p̂?
What is p̂?
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What is p?
What is p?
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Study Notes
- Two test statistics are used for hypothesis testing concerning means: z-test and t-test.
Z-test
- Use the z-test if the sample size n ≥ 30 and the population standard deviation (σ) is known.
- The formula for finding the z-value is:
- Variable definitions:
- x = sample mean
- μ = population mean
- n = sample size
- σ = population standard deviation
T-test
- Use the t-test if n < 30, the population is normal or nearly normal, and the sample standard deviation (s) is unknown.
- The formula for the t-value is:
- Variable definitions:
- x = sample mean
- μ = population mean
- n = sample size
- s = population standard deviation
- The degrees of freedom is n - 1 or df = n - 1.
Decision Making for Hypothesis Testing
- Reject H₀ ("Sufficient"):
- When H₀ is rejected, there is sufficient evidence at the alpha level of significance to reject the claim.
- Fail to Reject H₀ ("Insufficient"):
- When H₀ is not rejected, there is insufficient evidence at the alpha level of significance to reject the claim.
- Hₐ ("Support"):
- If there is sufficient evidence at the alpha level of significance to support the claim
- If there is insufficient evidence at the alpha level of significance to support the claim
Z-test Statistic for Proportion
- z-test statistic for proportion:
- Zcom =
- Variable definitions:
- Zcom = the z-test statistic for proportion
- p̂ = the sample proportion
- p = the hypothesized value of the population proportion
- n = the sample size or the number of observations in the sample
- q = 1 - p
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