Module 10 statistics (Questions and Answers A+ Graded 100% Verified)

Module 10 statistics (Questions and Answers A+ Graded 100% Verified) Standard error ANS: the result when the standard deviation of a statistic is estimated from the data t-distribution ANS: suppose that a SRS of size n is drawn from an N(µ,σ) population. Then the one-sample t statistic has the t distribution with n -1 degrees of freedom. There is a t distribution for every positive degrees of freedom k. All are symmetric distributions similar in shape to Normal distributions. The t(k) distribution approaches the N(0,1) distribution as k increases there is a different t distribution for _____ _______ _____ ANS: each sample size density curves of t(k) distributions are: ANS: -symmetric about 0 -bell shaped as degrees of freedom k increase, the t(k) density curve gets closer to the ? ANS: N(0,1) curve s will be closer to σ as _____ _____ increases ANS: sample size one-sample t confidence interval ANS: for a one-sample t confidence interval : ANS: the confidence level is exactly C when the population distribution is Normal and is approximately correct for large n in other cases in terms of a random variable T having the t(n-1) distribution, the P-value for a test of H0 against ANS: Ha: µ>µ0 is P(T> or = t) Ha: µ<µ0 is P(T< or = t) Ha: µ does not equal µ0 is 2P(T> or = the absolute value of t) matched pairs ANS: common comparative design in which subjects are first matched in pairs, and then within each pair, one subject is randomly assigned Treatment 1 and the other is assigned Treatment 2. alternatively, we can make two measurements or observations on each subject. one-sample procedures are used to analyze this data by first taking the differences within the subject to produce a single sample of differences key points about matched pairs ANS: 1. a matched pairs analysis is called for when subjects are matched in pairs or there are two measurements or observations on each individual and we want to examine the difference 2. for each pair or individual, use the difference between the two measurements as the data for your analysis 3. use the one-sample confidence interval and significance-testing procedures t procedures ANS: these procedures are relatively robust against non-normal populations. they are useful for non-normal data when 15 < n < 40 unless the data show outliers or strong skewness. when n> 40, these procedures can be used even for clearly skewed distributions conditions for one-sample t test ANS: 1. Simple Random Sample 2. population normal- check data plot single peaked with no outliers or n large What table should be used to find P-value for a one-sample inferential procedure on µ? ANS: the t table p-values obtained from the t-distribution table are always reported as an _______ ANS: interval p-values are exact if the population is ________ and __________ for non-normal populations with large n ANS: normal, approximate the most common use of a one-sample t procedure is to _______ ________ ______ ______ ANS: analyze matched pairs data reject H0 when p-value is smaller than ____ ANS: alpha robust procedures ANS: a statistical inference procedure is called robust if the required probability calculations are insensitive to violations of the assumptions made;confidence level or p-value does not change very much when conditions of procedure are not met guidelines for inference on a single mean ANS: -sample size less than 15: use t procedures if the data are close to the data are clearly non-normal or if outliers are present, do not use t -sample size of at least 15 and less than 40: the t procedures can be used except in the presence of outliers or strong skewness -large samples: the t procedures can be used even for clearly skewed distributions when the sample is large, roughly n > or = 40 are t procedures robust with respect to ANS: -lack of SRS? Never -lack of normality? Yes, but only IF data are not strongly skewed and have no outliers it is always better to use a value of the standard deviation that is a little ______ than what we expect than to use one that is smaller ANS: larger distribution-free inference procedure ANS: use this kind of procedure when doing an inference about the mean of a clearly non-Normal distribution based on a small sample (1 strategy) nonparametric procedures ANS: distribution-free procedures binomial distribution ANS: the distribution of the count X of successes in the binomial setting with parameters n and p. The parameter n is the number of observations, and p is the probability of a success on any one observation. the possible values of x are the whole numbers from 0 to n. As an abbreviation, we say that the distribution of X is B(n, p) sign test for matched pairs ANS: ignore pairs with difference 0; the number of trials n is the count of the remaining pairs. the test statistic is the count X of pairs with a positive difference. p-values for X are based on the binomial B(n, 1/2) distribution It is better to use a test that is powerful when we believe our assumptions are approximately satisfied than a less powerful test with _____ _________ ANS: fewer assumptions