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42 Cards in this Set
- Front
- Back
Rejecting Ho when it’s actually true:
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Type I error
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Ho can only be what 3 symbols?
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(≥, =, or ≤)
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The smallest significance level at which the null hypothesis will not be rejected:
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The p-value
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Scientific method-based means for using sample data to evaluate conjectures about a population:
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Hypothesis Testing
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What happens if p-value < α ?
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Then we reject the null hypothesis
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Sample statistic used to decide whether to reject or fail to reject the null hypothesis:
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Test statistic
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This is equivalent to a claim that the difference between the observations and the hypothesized value are due to random variation:
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Ho: the null hypothesis
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The probability of committing a type I error:
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The level of significance (denoted by α)
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Failing to reject Ho when it’s actually false:
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Type II error
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What type of probability distribution is the p-value?
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A conditional probability distribution
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The set of all values which would cause you to reject the null hypothesis, Ho:
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Critical region
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What happens if p-value > α?
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Then we do not reject the null hypothesis
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What is Ha?
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The alternative hypothesis
that tells us what type of test we are using. Can be (>, ≠, or <) |
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A statement based upon the null hypothesis. It is either "reject the null hypothesis" or "fail to reject the null hypothesis":
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Decision Rule
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A test of whether the population mean is different from the hypothetical mean:
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2-tailed test
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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):
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Ha: the alternate hypothesis
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Why are p-values preferred?
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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. |
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When the null hypothesis is true, but the sample information has resulted in the rejection of the null, a ____ has been made.
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Type I Error
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What happens if the level of significance (a) is made smaller?
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The critical (rejection) region becomes larger.
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The maximum probability of a Type I error that the decision maker will tolerate:
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Level of significance
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What increases the chances of making a Type I Error?
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Increasing the signficance level (i.e. from .01 to .05)
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The values that mark the boundaries of the critical region:
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Critical values
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If the level of significance of a hypothesis test is increased from .01 to .05, the probability of a Type II error
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Will be decreased
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Claim that the difference between the observations and the hypothesized value are systematic and caused by something other than random variation:
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Ha - the alternate hypothesis
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Hypothesis test for which sample results that are only sufficiently less than the conjectured value of the parameter:
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Lower-tailed test
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The smaller the _____ the greater evidence against ____.
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P-value, Ho
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List the 6 steps in Hypothesis Testing:
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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. |
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As z gets larger, ___ gets smaller.
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P-value
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What is the z-value for a two-tailed hypothesis test on a population mean when alpha is 5%?
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1.96
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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 _______.
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False, increase
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The quantity (1 - alpha) is called:
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The confidence coefficient
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For a given level of significance, if the sample size is increased, the probability of committing a Type II error will ____.
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Decrease
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In testing for differences between the means of two related populations the null hypothesis states that:
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The population mean difference is equal to 0
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When testing for a difference in two population means from small samples, a pooled variance must be computed when ___________.
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Variances are assumed to be equal
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The point that divides the non-reject region from the rejection region:
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Critical value
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When will we use the z test?
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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). |
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As the number of ____ increase(s), the shape of the t distribution approaches the standard normal distribution.
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Degrees of freedom
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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
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n1 + n2 - 2 = 10 + 8 - 2 =16
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What assumptions are necessary for a two-sample hypothesis test about the difference between two LARGE SAMPLE means?
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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). |
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"Before" and "after" samples often characterized by a measurement:
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Dependent (matched) samples
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What assumptions are required when testing a hypothesis about the difference between two SAMPLE SAMPLE means?
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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. |
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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?”
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2-SampTInterval
This is unpaired numeric data |