What is a one-sample?z-test?

• A?one-sample?z-test?is used to?test the mean (μ)?of a?normally distributed?population
  • You use a?z-test when the?population variance (σ2) is known

What are the steps for performing a one-sample?z-test on my GDC?

• STEP 1:?Write the hypotheses
  • H_0?:?μ?=?μ₀
    • Clearly state that?μ?represents the?population mean
    • μ_{0 ?}is the?assumed population mean

• • For a?one-tailed?test H_1?:?μ?<?μ_0?or H_1?:?μ?>?μ₀
  • For a?two-tailed?test: H_1?:?μ?≠?μ₀
    • The alternative hypothesis will depend on what is being tested

• STEP 2:?Enter the data?into your GDC and choose the?one-sample?z-test
  • If you have the raw data
    • Enter the data as a list
    • Enter the value of?σ
  • If you have summary statistics
  • Your GDC will give you the?p-value
• STEP 3:?Decide?whether there is?evidence to reject the null hypothesis
  • If the?p-value < significance level then reject H₀
• STEP 4:?Write your conclusion
  • If you?reject H₀-?then there is?evidence?to suggest that...
    • The mean has decreased (for H_1?:?μ?<?μ₀)
    • The mean has increased (for H_1?:?μ?>?μ₀)
    • The mean has changed (for H_1?:?μ?≠?μ₀)
  • If you?accept H-_0?then there is?insufficient evidence?to reject the null hypothesis which suggests that...
    • The mean has not decreased (for H_1?:?μ?<?μ₀)
    • The mean has not increased (for H_1?:?μ?>?μ₀)
    • The mean has not changed (for H_1?:?μ?≠?μ₀)

How do I find the?p-value for a one-sample?z-test using a normal distribution?

How do I find the critical value and critical region for a one-sample z-test?

Exam Tip

What is a one-sample?t-test?

• A?one-sample?t-test?is used to?test the mean (μ)?of a?normally distributed?population
  • You use a?t-test when the?population variance (σ2) is unknownt-distributions are similar to normal distributions
• • • As the sample size gets larger the?t-distribution tends towards the standard normal distribution
• You won’t be expected to find the critical value
  • The?p-value can be found using the test function on your GDC

What are the steps for performing a one-sample?t-test on my GDC?

• STEP 1:?Write the hypotheses
  • H_0?:?μ?=?μ₀
    • Clearly state that?μ?represents the?population mean
    • μ_{0 ?}is the?assumed population mean

• • For a?one-tailed?test H_1?:?μ?<?μ_0?or H_1?:?μ?>?μ₀
  • For a?two-tailed?test: H_1?:?μ?≠?μ₀
    • The alternative hypothesis will depend on what is being tested

• STEP 2:?Enter the data?into your GDC and choose the?one-sample?t-test
  • If you have the raw data
    • Enter the data as a list
  • If you have summary statistics
  • Your GDC will give you the?p-value
• STEP 3:?Decide?whether there is?evidence to reject the null hypothesis
  • If the?p-value < significance level then reject H₀
• STEP 4:?Write your conclusion
  • If you?reject H₀-?then there is?evidence?to suggest that...
    • The mean has decreased (for H_1?:?μ?<?μ₀)
    • The mean has increased (for H_1?:?μ?>?μ₀)
    • The mean has changed (for H_1?:?μ?≠?μ₀)
  • If you?accept H-₀then there is?insufficient evidence?to reject the null hypothesis which suggests that...
    • The mean has not decreased (for H_1?:?μ?<?μ₀)
    • The mean has not increased (for H_1?:?μ?>?μ₀)
    • The mean has not changed (for H_1?:?μ?≠?μ₀)