7.2 Hypothesis Testing for the Mean ( known)

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

7.2 Hypothesis Testing for the Mean ( known)

• 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 than the 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:

#10 p. 373 (left-tailed test)

#14 (two-tailed test)

7.2 Hypothesis Testing for the Mean ( known)

• We are finally ready to conduct a hypothesis test for the mean using P-values! Guidelines are provided on page 365 (Using P-Values for a z-Test for the Mean µ ( known)).

#32 p. 375 (Sprinkler System)

#36 p. 375 (Salaries)

7.2 Hypothesis Testing for the Mean ( known)

• 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

#22 p. 374

#24

7.2 Hypothesis Testing for the Mean ( known)

• 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 370 Using Rejection Regions for a z-Test for a Mean µ ( known)

#38 p. 376 (Electricity Consumption)

#39 p. 376 (Fast Food)