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7.2 Hypothesis Testing for the Mean (Large Samples)

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- Key Concepts:
- Hypothesis Testing (P-value Approach)
- Critical Values and Rejection Regions
- Hypothesis Testing (Critical-Value Approach)

- So how do we calculate the P-value of a test?
- Recall: The P-value of a hypothesis test is the probability of obtaining a sample statistic with a value as extreme as or more extreme thanthe one determined from the sample data.
- When we test for one population mean, we use the standardized version of the sample mean as our sample (or test) statistic.

- Practice finding P-values:
#2 p. 389 (left-tailed test)

#6 (two-tailed test)

- Recall: The P-value of a hypothesis test is the probability of obtaining a sample statistic with a value as extreme as or more extreme thanthe one determined from the sample data.

- We are finally ready to conduct a hypothesis test for the mean using P-values! Guidelines are provided on page 381 (Using P-Values for a z-Test for the Mean µ).
#34 p. 391 (Sprinkler System)

#38 p. 392 (Salaries)

- If the P-value of a test is difficult to calculate, we can use what’s known as the critical-value approach.
- A rejection region of the sampling distribution is the range of values for which the null hypothesis is not probable.
- A critical value separates the rejection region from the nonrejection region.
- Practice finding critical values and rejection regions
#16 p. 390

#20

- Practice finding critical values and rejection regions

- How do we decide whether or not to reject the null hypothesis when we’re working with critical values and rejection regions?
- If our test statistic falls within the rejection region, we reject Ho. Otherwise, we do not reject Ho.

- Guidelines are provided on page 386 (Using Rejection Regions for a z-Test for µ).
#40 p. 392 (Caffeine Content in Coffee)

#42 p. 393 (Sodium Content in Cereal)