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stat I - exam III

When we conduct a formal statistical study to test a hypothesis, what are the names and the symbols for the two hypotheses we typically generate? Null hypothesis H0 and the alternative hypothesis H1
What is the type error and symbol for the probability we will reject the null hypothesis when it is actually true? Type I error: α
What is Type II error β? The probability we will accept the null hypothesis when the actual population mean is a different value (i.e. the null hypothesis is actually false).
How is α typically determined? It is selected by the person conducting the experiment / study.
Is it possible to determine β for all potential alternative distributions? We cannot determine β for all potential alternative distributions, because there are an infinite number of alternative distributions.
Is it possible to determine β is for a particular alternative distribution? We can determine β for a particular alternative distributions
What does a P-value represent? It is the probability, assuming that H 0 (null hypothesis) is true, of obtaining a test (i.e. sample) statistic that is that value or further away from the mean.
Can a P-value ever be negative? No a p-value cannot be negative because it represents a probability which cannot be less than 0
can a p-value ever be 1? Yes, a p-value can be 1. When x = μ , the p-value is 1
Can a p-value ever be greater than 1? No, it cannot be greater than 1, because it represents a probability. Probabilities cannot be greater than 1.
When testing a hypothesis with an unknown standard deviation, what is done? Same procedures as with known standard dev, but use t value instead of z.
If P <= α, the result is _______________ ______________ at the α level. statistically significant
When P < α do we reject or not reject the null hypothesis? We reject the null hypothesis If P < α
When testing a one sided hypothesis we follow same steps as two sided but we dont _______ divide α by 2. only one rejection region. must determine the direction of the rejection region.
If samples are taken from two different continuous random variable distributions and the means of those two samples are x1& x2 , then is x1 − x2 a random variable? Yes
Is the variance of x2 − x1 bigger or smaller than the variance for x2 or x1 ? The variance for x2 − x1 would be bigger than either one, provided both x2 or x1 are both greater than 0.
If we wish to test if the population means from two continuous random variable distributions are equal, then what null and alternative hypotheses should be write? H0: μ1−μ2=0
If we wish to test if the population means from two continuous random variable distributions are a specific difference apart from each other, then what null and alternative hypotheses should be write? H0: μ1−μ2=d Ha: μ1−μ2≠d where d = the specific difference
If we wish to compare the population proportions of two binomial random variable distributions, what sample statistics do we use to make the comparison? pˆ 1 a n d pˆ 2
What are the conditions necessary to have a valid large-sample inferences about p1 − p2 ? ● Both samples are representative of their populations ● The two samples are independent of each other ● np≥10 and n(1 − p)≥10 for both populations / samples ● The two populations are at least 20 times the size of their respective samples
For 96% confidence, what is the appropriate z-value to use: α=1−.96=.04; α2 =.02; zα2 =2.055;
If we wish to test if the population proportions from two binomial random variable distributions are equal, then what null and alternative hypotheses should be write? H0: p1−p2=0 H1: p1−p2≠0
If we don’t know the underlying σ1^2 and σ2^2 for the two continuous random variable distributions, but there is a set of sample data from each distribution, what sample statistics are used to estimate σ1^2 and σ2^2 in the formula for σ(x1−x2) ? s1^2 & s2^2
Created by: aiur100