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### 42 Cards in this Set

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 Rejecting Ho when it’s actually true: Type I error Ho can only be what 3 symbols? (≥, =, or ≤) The smallest significance level at which the null hypothesis will not be rejected: The p-value Scientific method-based means for using sample data to evaluate conjectures about a population: Hypothesis Testing What happens if p-value < α ? Then we reject the null hypothesis Sample statistic used to decide whether to reject or fail to reject the null hypothesis: Test statistic This is equivalent to a claim that the difference between the observations and the hypothesized value are due to random variation: Ho: the null hypothesis The probability of committing a type I error: The level of significance (denoted by α) Failing to reject Ho when it’s actually false: Type II error What type of probability distribution is the p-value? A conditional probability distribution The set of all values which would cause you to reject the null hypothesis, Ho: Critical region What happens if p-value > α? Then we do not reject the null hypothesis What is Ha? The alternative hypothesis that tells us what type of test we are using. Can be (>, ≠, or <) A statement based upon the null hypothesis. It is either "reject the null hypothesis" or "fail to reject the null hypothesis": Decision Rule A test of whether the population mean is different from the hypothetical mean: 2-tailed test This is equivalent to a claim that the difference between the observations and the hypothesized value are systematic (i.e., due to something other than random variation): Ha: the alternate hypothesis Why are p-values preferred? 1) They allow anyone to select their own significance level a. 2) They provide a measure of the strength of the evidence the sample data provides against the null hypothesis (smaller p-value – stronger evidence against Ho). 3) They are usually reported by computer packages. When the null hypothesis is true, but the sample information has resulted in the rejection of the null, a ____ has been made. Type I Error What happens if the level of significance (a) is made smaller? The critical (rejection) region becomes larger. The maximum probability of a Type I error that the decision maker will tolerate: Level of significance What increases the chances of making a Type I Error? Increasing the signficance level (i.e. from .01 to .05) The values that mark the boundaries of the critical region: Critical values If the level of significance of a hypothesis test is increased from .01 to .05, the probability of a Type II error Will be decreased Claim that the difference between the observations and the hypothesized value are systematic and caused by something other than random variation: Ha - the alternate hypothesis Hypothesis test for which sample results that are only sufficiently less than the conjectured value of the parameter: Lower-tailed test The smaller the _____ the greater evidence against ____. P-value, Ho List the 6 steps in Hypothesis Testing: 1) State the null and alternative hypotheses. 2) Select your test statistic. 3) State the level of significance a, and find the critical values/p-value. 4) Calculate the test statistic. 5) Decide whether to reject or not reject the null hypothesis. 6) Interpret your results. As z gets larger, ___ gets smaller. P-value What is the z-value for a two-tailed hypothesis test on a population mean when alpha is 5%? 1.96 The power of a statistical test is the probability of rejecting the null hypothesis when it is _______. When you increase alpha, the power of the test will _______. False, increase The quantity (1 - alpha) is called: The confidence coefficient For a given level of significance, if the sample size is increased, the probability of committing a Type II error will ____. Decrease In testing for differences between the means of two related populations the null hypothesis states that: The population mean difference is equal to 0 When testing for a difference in two population means from small samples, a pooled variance must be computed when ___________. Variances are assumed to be equal The point that divides the non-reject region from the rejection region: Critical value When will we use the z test? 1) The population is normally distributed. 2) The population standard deviation is known. 3) The population standard deviation is not known, but the sample size n>30 (in this case we will use Sx). As the number of ____ increase(s), the shape of the t distribution approaches the standard normal distribution. Degrees of freedom A random sample of 10 observations is selected from the first normal population and 8 from the second normal population. For a one-tailed test of hypothesis (.01 significance level) to determine if there is a difference in the population means, the degrees of freedom are n1 + n2 - 2 = 10 + 8 - 2 =16 What assumptions are necessary for a two-sample hypothesis test about the difference between two LARGE SAMPLE means? 1) The two populations must be independent (unrelated). 2) The samples must be large enough so that the distribution of the sample means follows the normal distribution (i.e. n1>30, n2>30). "Before" and "after" samples often characterized by a measurement: Dependent (matched) samples What assumptions are required when testing a hypothesis about the difference between two SAMPLE SAMPLE means? 1) The sample populations follow the normal distribution. 2) The two samples are from independent populations. 3) The standard deviations of the two populations are EQUAL. Which selection on your TI-83 would be used to answer the question “How much more do Lamborghini owners spend per year on maintenance than Subaru owners?” 2-SampTInterval This is unpaired numeric data