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Losing Confidence Testing my patience Tell me a tail Sample This Pot-pouri $100 $100 $100 $100 $100 $200 $200 $200 $200 $200 $300 $300 $300 $300 $300 $400 $400 $400 $400 $400 $500 $500 $500 $500 $500 Final Jeopardy For $100… This is half the width of the confidence interval. The Answer is… What is the margin of error? Final Jeopardy For $200… This is the probability that the true mean is captured by the confidence interval. The Answer is… What is the confidence level? Final Jeopardy For $300… The margin of error gets smaller as this gets larger. The Answer is… What is the sample size? Final Jeopardy For $400… If the standard deviations are unknown when finding the confidence interval for the difference between two groups, we would use this type of confidence interval. The Answer is… What is a two sample t-interval? Final Jeopardy For $500… This states that if x is from any distribution, the sample mean of x has an approximately normal distribution. The Answer is… What is the Central Limit Theorem? Final Jeopardy For $100… This is a statement of fact, equality, or of the status quo. The Answer is… What is the null hypothesis? Final Jeopardy For $200… This is the probability at which we consider something a rare event. The Answer is… What is the significance level? Final Jeopardy For $300… Reject the null hypothesis in favor of the alternative when this is less than the significance level. The Answer is… What is the p-value? Final Jeopardy For $400… This is the distance and direction, in terms of standard deviations, that a sample mean is from a hypothesized mean. The Answer is… What is the test statistic? Final Jeopardy For $500… This is the probability of a type I error. That is, the probability we reject the null hypothesis when it is in fact true. The Answer is… What is alpha, or the significance level? Final Jeopardy For $100… This is tail of the test that we would use if we believed the true mean would be larger than the hypothesized mean. The Answer is… What is a right tailed test? Final Jeopardy For $200… This is the area in the tail(s) that is beyond the critical values. The Answer is… What is the significance level or alpha? Final Jeopardy For $300… This is the area in the tail(s) beyond the value of the test statistic. The Answer is… What is the p-value? Final Jeopardy For $400… A confidence interval most closely relates to this type of test. The Answer is… What is a two-tailed test? Final Jeopardy For $500… This is the smallest significance level, alpha, at which we can reject the null hypothesis. The Answer is… What is the p-value? Final Jeopardy For $100… This is the standard deviation of the sample mean. The Answer is… What is the standard error or σ/(n)? Final Jeopardy For $200… This is the distribution we must use if the true standard deviation is unknown. The Answer is… What is the t-distribution? Final Jeopardy For $300… What is the expected value of the sample mean? The Answer is… What is the true mean? Final Jeopardy For $400… This is the error in using a statistic to estimate a parameter. The Answer is… What is sampling error? Final Jeopardy For $500… This parameter completely defines a t-distribution. Equivalently, this is the information we need to find probabilities for a t-distribution. The Answer is… What are degrees of freedom? Final Jeopardy For $100… We would use this type of hypothesis test to test for a difference between two groups with different, unknown standard deviations. The Answer is… What is a non-pooled two sample t-test? Final Jeopardy For $200… We would use this inferential procedure if we wanted a probable range for a value of the true mean. The Answer is… What is a confidence interval? Final Jeopardy For $300… For comparing two populations using a sample of size 50 from the first population and a sample of size 72 from the second, this is the number degrees of freedom that we would use to compare these two populations using the t distribution. The Answer is… What is 49? Final Jeopardy For $400… What is the value at the center of the confidence interval The Answer is… What is the sample mean? Final Jeopardy For $500… This is the pseudonym under which William Gosset published while working for the Guiness Brewery The Answer is… What is Student? Final Jeopardy FINAL JEOPARDY For $1000 and the game… For two populations we find two separate samples. For sample one, the sample size, mean and variance are 21, 51.48, and 121.22, respectively. For sample two, the sample size, mean and variance are 23, 41.52, and 294.1225, respectively. This is the test statistic and decision for a test that these populations have different means at =.05. The Answer is… What is t=2.31 and reject the null since critical value is 2.086? Final Jeopardy CONGRATULATIONS!!! Final Jeopardy