Intro to Statistics Final Exam Questions with Complete Solutions

Intro to Statistics Final Exam Questions with Complete Solutions Population a collection of persons, things, or objects under study. Sample selecting a portion (or subset) of the larger portion Parameter A numerical characteristic of the whole population that can be estimated by a statistic. Ex: we consider all math classes to be the population, so the average number of points earned per student over all math classes is a parameter. Statistic A number that represents a property of the sample. Ex: if we consider one math class to be the sample of the population of all the math classes, then the average number of points earned by a student in that one math class at the end of the term is an example of a statistic. Variable usually letters x and y, is a characteristic or measurement that can be determined for each number of the population Numerical variable: takes on a value with equal units such as weights in pounds and time in hours. Categorical variable: place the person or thing into a category (ex: party affiliation, gender, gpa). Data the actual values of the variable What are the levels of measurement? Nominal: no numerical value or order (names, labels, categories) Ordinal: usually no numerical value, but there is an order, however, the differences between the data are meaningless (small, medium, large) Interval: data can be ordered, and differences are meaningful Ratio: can be ordered, differences are meaningful, and zero corresponds to none of the values (0 is a measurement) simple random sample each sample of the sample size has an equal chance of being selected; simple random sample from the entire population Stratified Sampling Divide the entire population into distinct subgroups called strata. The strata are based on a specific characteristic such as age, income, education level, and so on. All members of a stratum share the specific characteristic. Draw random samples from each stratum. Cluster Sampling Divide the entire population into pre-existing segments or clusters. The clusters are often geographic. Make a random selection of clusters. Include every member of each selected cluster in the sample. Randomly select some cluster. Systematic Sampling randomly select a starting point and take every nth piece of data from a listing of the population Multistage Sampling Use a variety of sampling methods to create successively smaller groups at each stage. The final sample consists of clusters. Convenience Sampling Involves selecting participants who are readily available without any attempt to make the sample representative of a population. Midpoint A point that divides a segment into two congruent segments lower boundary + upper boundary __________________________________________________ = midpoint 2 Class Width the distance between lower (or upper) limits of consecutive classes largest data value - smallest data value ________________________________________________________ = class width desired number of classes Frequency Table efficiently displays data. Organizes data into classes and list the number of data points in each class; classes with 0 occurrences are also listed Class Limit First find class width, then add that to the smallest data value, and keep adding it until you get to the highest data value. (ex: if the smallest data value is 36, and the class width is 13, then you would add 13 to 36, and the upper class limit for that bin would be 48, and the lower class limit for the next bin would be 49) Class Boundaries Take class limits and do -.5 for the lower class limit and +.5 for the upper limit Frequency the number of times a value of the data occurs Cumulative frequency frequency of a class with added frequencies of classes before that one. (ex: if bin 1's frequency is 3, and bin 2's frequency is 2, then bin 1's cumulative frequency 3 and bin 2's cumulative frequency would be 5 because you added it with bin 1's frequency, and then you would add bin 2's frequency with bin 3's) Relative Frequency the ratio (fraction or