section 9.1 and 9.2 hypothesis testing

• a hypothesis is a claim about a population parameter, such as a population portion or population mean 
• in this chapter, the null hypothesis will always include the condition of equality, just ass the null hypothesis for the gender choice 
• it is useful to give names to the three different types of alternative hypotheses 
• the first form ("less than") leads to what is called a left-tailed  hypothesis test, because it requires testing whether the population parameter lies to the left (lower values) of the claimed value 
• Similarly, the second form 
• null alternatives hypothesis - the null hypothesis, or H0 is the starting assumption for a hypothesis test. For the types of hypothesis always 
• in each case, identify the population
• solution (cont) 
• identifying hypothesis 
• in each case, identify the population parameter about which a claim is made, state the null and alternative hypothesis for a hypothesis test, and indicate whether the hypothesis test will be left-tailed, right tailed, or two tailed 
• two possible outcomes of a hypothesis test 
• there are two possible outcomes to a hypothesis test 
• reject the null hypothesis
• the null hypothesis is that the proportion of femal zebras is the accepted population proportion 
• do not reject the null hypothesis, in which case we lack evidence to support the biogist claim 
• drawing a conclusion from a hypothesis test 
• we will look at trwo ways to make the decision about rejecting or not rejecting the null hypothesis 
• statistical significance 
• if the probability of a particular result is 0.05 or less, we say that the result is statistically significant at the 0.05 or less, we say that the result is statistically significant at the 0.05 level; 
• we decide 
• if the chance 
• consider 
• p calues is a short for probability value; 
• the p valu for a hypothesis test of a claim about a population parameter is the probability of selecting a sample at least as extreme as the observed sample, assuming that the null hypothesis is true;
• a small p value ( such as less than or equal to 0.05) indicates that the sample 
• you suspect that a coin may have a bias toward landing tails more often 
• your 100 coin tosses represent a random sample size n=100, and the result of 40 heads is the sample  proportion at least as 
• the hypothesis test process 
• formulate the null and alternative hypotheses each of which must make a claim about a population parameter, such as a population mean 
• the hypothesis test process 
• step 3: determine the likelihood of observing a sample statistic (mean or proportion) at least as extreme as the one you found under the assumption 
• in the united states the average car is driven about 12000 miles each year. The owner of a large rental car company suspects that for his fleet, the mean distance is greater than 12000 miles each year. He selects a random sample of n= 225 cars from his fleet and finds that the mean annual mileage for this sample is x bar =12375 
• the p-value of 0.01 tells us that the result is significant
• In American courts of law, the fundemental principle is that a defendant is presumed innocent 
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