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Section 9.5 Hypothesis Test for One Population Mean When is unknown When is unknown the sample standard deviation is used. Instead of the one mean z-test, the one mean t-test or more simply known as the t-test is used. The studentized version of is t x x 0 s n Also it will be important to estimate the p-value of the test for our three different alternative hypotheses P-value t0 Right tailed Test Z0 P-value P-value t0 t0 Two tailed Test t0 Left tailed Test In all three cases if the P value ,then the null hypothesis is rejected. Example Examples 9.106 Active management of labor (AML) is a group of interventions designed to help reduce the length of labor and the rate of cesarean deliveries. Physicians were interested in determining whether AML would translate into a reduced cost for delivery. According to the article published on this study, 200 AML deliveries had a mean cost of $2480 with a standard deviation of $776. At the time of the study, the average cost of having a baby in a U.S. hospital was $2528. At the 5% significance level, do the data provide sufficient evidence to conclude that, on average, AML reduces the cost of having a baby in a U.S. hospital? 9.104 According to the document Consumer Expenditures, a publication of the Bureau of Labor Statistics, the average consumer unit spent $1874 on apparel and services in 2006. The same year, 25 consumer units in the Northeast had the following annual expenditures, in dollars, on apparel and services. At the 5% significance level, do the data provide sufficient evidence to conclude that the 2006 mean annual expenditure on apparel and services for consumer units in the Northeast differed from the national mean of $1874. The sample mean and sample standard deviation of the data are $2060.76 and $350.90.