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| 5187072821 | 1. With a random sample from a population for which the variance is known, which of the following would enable use of the normal distribution to compute the probability of obtaining a specific value of the mean from the sample? a. a sample size of 30 or more b. the empirical rule c. the central limit theorem d. both a & b e. both a & c | E | 0 | |
| 5187074728 | 2. A relative frequency distribution differs from a simple frequency distribution by including: a. the cumulative number of observations that are less than or greater than a particular value b. the cumulative percentage of observations that are less than or greater than a particular value c. the percentage of the total number of observations represented by the number of observations in the category d. the percentage of the number of observations in the category represented by the total number of observations e. none of the above | C | 1 | |
| 5187103734 | 3. The standard error of a statistic is defined as the: a. standard deviation of the statistic's sampling distribution b. variance of the statistic's sampling distribution c. mean deviation of the sample d. variance of the sample e. sum of the squared deviations of the population | A | 2 | |
| 5187110980 | 4. The properties of the mean include: a. the sum of the squared deviations of each value about the mean is less than the sum of the squared deviations about any other number b. the sum of deviations of each value about the mean is zero c. Σ(x-μ)^2 = a minimum d. Σ(x-μ) = 0 e. all of the above | E | 3 | |
| 5187124870 | z-score | z= (x ̅- μ)/(σ/√n) | 4 | |
| 5187126317 | t-statistic | t=(x ̅- μ)/(s/√n) | 5 | |
| 5187130693 | Mean | μ= Σx/N x ̅=Σx/n | 6 | |
| 5187132274 | Variance | σ^2=(Σ〖(x-μ)〗^2)/N s^2=(Σ〖(x-x ̅)〗^2)/(n-1) | 7 | |
| 5187138193 | Standard error | s/√n σ/√n | 8 | |
| 5187140689 | Confidence interval | x ̅± t (s/√n) x ̅± z (σ/√n) | 9 | |
| 5187158038 | = (p-Π)/√((Π(1-Π))/n); | Test statistic for a single sample hypothesis test for proportions (z) | 10 | |
| 5187179017 | = (x ̅1- x ̅2)/√(((s_1^2)/n_1 +(s_2^2)/n_2 )) | Test statistic for comparing two means with unequal variances (t) | 11 | |
| 5187188078 | = (x ̅_1- x ̅_2)/√(s_p^2 (1/n_1 +1/n_2 )) | Test statistic for equal comparing two means with equal but unknown variances (pooled t) | 12 | |
| 5187200393 | =((n_1-1) s_1^2+(n_2-1) s_2^2)/(n_1+n_2-2) | Variance of a pooled t (equal but unknown variances) (s_p^2) | 13 | |
| 5187213739 | A function that assigns a numerical value to each outcome in an experiment whose results depend to some extent on chance A rule (or function) that assigns unique real numbers to each outcome in a sample space of an experiment A quantity resulting from an experiment that, by chance, can assume different values | Random variable | 14 | |
| 5187226092 | Has a probabilistic component associated with the process of determining its value The specific outcome of a trail is not known or cannot be determined exactly in advance | Properties of a random variable | 15 | |
| 5187229326 | A random variable that can assume only certain clearly separated values; it is usually the result of counting something | Discrete random variable | 16 | |
| 5187231532 | Can assume an infinite number of values within a given range; it is usually the result of some type of measurement | Continuous random variable | 17 | |
| 5187236438 | A sample selected so that each item or person in the population has the same chance of being included | Simple sample | 18 | |
| 5187239422 | A random sample for which a rule or system is utilized to select the observations to be included in the sample, generally from a list of members of the population | Systematic sample | 19 | |
| 5187243370 | A population is first divided into non-overlapping subgroups, called______, & then a simple random sample is selected from each _______; useful when a population can be clearly divided in groups based on some characteristics | Stratified sample | 20 | |
| 5187248515 | The # of cases selected within each group should be proportional to the percentage of the group in the entire population Expect each group to have different characteristics than other groups (variation in the data will be between groups rather than within groups) | Properties of a stratified sample | 21 | |
| 5187252345 | A population is divided into clusters using naturally occurring geographic or other boundaries; then, clusters are randomly selected and a sample is collected by randomly selecting from each cluster | Cluster sample | 22 | |
| 5187262203 | Population is so large or dispersed for simple random sampling Expect each group to have very similar characteristics to any other group (most variation in the data will be within groups rather than between them) | Properties of a cluster sample | 23 | |
| 5187276766 | Accuracy of an estimate indicates the lack of bias or systematic error in the statistic's representation of the population parameter | Biased vs. unbiased estimators | 24 | |
| 5187283785 | Little systemic error; accurate | Unbiased estimate | 25 | |
| 5187286350 | Large systemic error; inaccurate | Biased estimate | 26 | |
| 5187303186 | z= (x ̅_1- x ̅_2)/√((σ_1^2)/n_1 +(σ_2^2)/n_2 ) | Comparing 2 means Equal variances with sigma known n >= 30 | 27 | |
| 5187315424 | t= (x ̅_1- x ̅_2)/√(s_p^2 1/n_1 +1/n_2 ) s_p^2=((n_1-1) s_1^2+(n_2-1) s_2^2)/(n_1+n_2-2) | Comparing 2 means Equal but unknown variances | 28 | |
| 5187321243 | t=(x ̅_1- x ̅_2)/√(((s_1^2)/n_1 +(s_2^2)/n_2 )) df=([(〖(s_1^2)/n_1 )+((s_2^2)/n_2 )]〗^2)/(〖((s_1^2)/n_1 )〗^2/(n_1-1)+〖((s_2^2)/n_2 )〗^2/(n_2-1)) | Comparing 2 means Unequal & unknown variances | 29 | |
| 5187365734 | For a symmetrical, bell-shaped frequency distribution, i. Approx. x of the observations will lie within plus and minus one SD of the mean; ii. About y of observations will lie within plus or minus 2 SD of the mean; iii. z will lie within plus or minus 3 SD of the mean | Empirical rule x = 68% y = 95% z = 99.7% | 30 | |
| 5187372392 | The statistic, computed from sample information, that estimates a population parameter Conveys nothing about the precision of the estimate | Point estimate | 31 | |
| 5187378666 | Should be provided with the point estimate | Standard error | 32 | |
| 5187388144 | Interval estimates | x ̅± z (σ/√n) | 33 | |
| 5187405305 | Should be included with interval estimates | Level of confidence | 34 | |
| 5187407063 | When to use z-score | When you know σ AND n ≥ 30 Know that population is normally distributed | 35 | |
| 5187410802 | When to use t-statistic | When you don't know σ OR n < 30 Must assume population is normally distributed | 36 | |
| 5187426535 | Differences in the appearance of normal distribution & t-distribution | T distribution is more spread out and flatter at the center than the standard normal distribution | 37 | |
| 5187447276 | Impact of not having a normally distributed population in hypothesis testing | Does not matter if the population is not normally distributed Central limit theorem is used & we want n >= 30 | 38 | |
| 5187454206 | The hypothesized value of μ will not lie within the calculated confidence interval | Rejection of the null hypothesis | 39 | |
| 5187456527 | The hypothesized value of μ will lie within the calculated confidence interval | Non-rejection of the null hypothesis | 40 | |
| 5187460211 | The error of rejecting the null hypothesis when it is true | Type I error | 41 | |
| 5187462653 | The error of failing to reject the null hypothesis when it is false | Type II error | 42 | |
| 5187466779 | The probability distribution of the statistic (i.e., all possible values of the statistic & their probabilities) derived from a large number of samples of the same size taken from the same population Uses experiments | Empirical sampling distribution | 43 | |
| 5187476646 | The probability distribution of the statistic derived from a formula Uses formulas & theory | Theoretical sampling distribution | 44 | |
| 5187481320 | Appropriate distribution for testing hypotheses about two independent populations having the same mean | *Practically always use t z-score (normal distribution): When n > 30, σ is known, &equal variances t-statistic (t-distribution): When σs are equal but unknown When σs are unequal & unknown | 45 | |
| 5187514669 | a. Total area under the curve (or the area between the curve & the x-axis) will always be equal to 1 b. Symmetric around the middle c. The area between the mean and any ordinate (observation), which is specified as a distance from the mean in terms of standard deviation units, is constant d. There is a family of normal curves; a normal curve is fully defined when both its mean and variance are specified e. Bell-shaped f. Asymptotic: curve never actually touches x-axis g. Location of a normal distribution is determined by the mean h. Mean, median, and mode are equal | Characteristics of normal distributions | 46 | |
| 5187526978 | The distribution of values taken by the statistic in a large number of samples from the same population The distribution of all possible values of the statistic computed from samples of the same size | Sampling distribution | 47 | |
| 5187538253 | As the sample size n for a random sample increases, the sampling distribution statistics from the sample will approach a normal distribution and will equal the respective population parameters | Central limit theorem | 48 |
