stats 1 – Flashcard
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census
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collection of data from every member in the population
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statistical significance is achieved when
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we get a result that is very unlikely to occur by chance
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formula calculation
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least important factor to consider when conducting a statistical analysis of data?
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parameter vs. statistic
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a numerical measurement describing some characteristic of a population vs. a numerical measurement describing some characteristic of a sample
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discrete data
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number of possible values is countable
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When a car is randomly selected, it is found to have a weight of 1873.6 kg discrete or continuous?
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continuous
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discrete or continuous? When a bus is randomly selected, it is found to have a weight of 1876 kg
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continuous
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continuous data
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infinite amount of possible values or decimals
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nominal level
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characterized by data that consist of names, labels, or categories only, and the data cannot be arranged in an ordering scheme
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ordinal level
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involves data that can be arranged in some order, but differences between data values either cannot be determined or are meaningless
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interval level
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involves data that can be arranged in order and the difference between any two data values is meaningful. However, there is no natural zero starting point
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natural zero starting point
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where none of the quantity is present
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ratio level
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the interval level with the additional property that there is also a natural zero starting point (where zero indicates that none of the quantity is present); for values at this level, differences and ratios are meaningful
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what level of measurement? temp. are: 62, 66, 70, 74, 78
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interval
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what level of measurement? favorite films, type of restaurants
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nominal
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what level of measurement? ratings of hotels on a scale of 0-4 stars
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ordinal
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what level of measurement? blood levels of low, medium, and high
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ordinal
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what level of measurement? number of houses people own
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ratio
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what level of measurement? length of the side of a square in cm
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ratio
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What level of measurement? What is wrong In a survey, the favorite foods of respondents are identified as 100 for italian food, 200 for mexican food, 300 for chinese food, and 400 for anything else. The average (mean) is calculated for 628 respondents and the result is 256.1 .
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nominal. numbers are insignificant, so mean is useless
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What level of measurement? what is wrong In a set of data, car rankings are represented as 100 for first, 200 for second, and 300 for third. The average (mean) of the 664 car rankings is 231.2 .
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ordinal. data shouldnt be used to calculate an average
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observational vs. experiment
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dont modify vs. apply some treatment then observe its effects
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What is the difference between a random sample and a simple random sample?
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With a random sample, each individual has the same chance of being selected. With a simple random sample, all samples of the same size have the same chance of being selected.
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systematic sampling
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Select some starting point and then select every kth element in the population.
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stratified sampling
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Subdivide the population into at least two different subgroups that share the same characteristics, then draw a sample from each subgroup
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cluster sampling
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Divide the population area into sections (or clusters). Then randomly select some of those clusters. Now choose all members from selected clusters
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convenience sampling
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Use results that are easy to get
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multistage sampling
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Collect data by using some combination of the basic sampling methods
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3 very important considerations in the design of experiments are the following:
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1. Use randomization to assign subjects to different groups. 2. Use replication by repeating the experiment on enough subjects so that effects of treatment or other factors can be clearly seen 3. Control the effects of variables by using such techniques as blinding and a completely randomized experimental design.
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confounding
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occurs in an experiment when the experimenter is not able to distinguish between the effects of different factors
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placebo effect
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which occurs when an untreated subject reports improvement in symptoms
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What type of sampling? A woman is selected by a marketing company to participate in a paid focus group. The company says that the woman was selected because she was randomly chosen from all women in her tax bracket.
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stratified
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What type of sampling? In a poll conducted by a certain research center, 796 adults were called after their telephone numbers were randomly generated by a computer, and 7 % were able to correctly identify the president.
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random
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what type of sampling? A man experienced a tax audit. The tax department claimed that the man was audited because he was randomly selected from all the taxpayers
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random
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what type of sampling? To determine customer opinion of their food quality, General Foods randomly selects 40 city blocks during a certain week and surveys all homes within the city blocks
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cluster
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Determine whether the sample described below is a simple random sample. A quality control engineer selects every 15,000th light bulb that is produced.
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The sample is not a simple random sample because every sample of the same size does not have the same chance of being selected
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Determine whether the sample described below is a simple random sample. In order to test for a difference in the way that workers and non-workers purchase magazines, a research institution polls exactly 945 adult workers and 945 adult non-workers randomly selected from adults in the United States.
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The sample is not a simple random sample because every sample of size 1890 does not have the same chance of being selected
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Determine whether the sample described below is a simple random sample. In the last year, 112,472 adults got married in a county. A researcher plans to conduct a survey of 700 of those newlyweds. After obtaining a list of those who got married, he numbers the list from 1 to 112, 472, and then he uses a computer to randomly generate 700 numbers between 1 and 112,472. His sample consists of the newlyweds corresponding to the selected numbers.
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The sample is a simple random sample because every sample of size 700 has the same chance of being selected.
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Determine whether the sample described below is a simple random sample. According to a lottery commission, names of potential lottery winners are selected from a variety of different sources. Names from the list are randomly selected in a way that is equivalent to writing the names on slips of paper, mixing them in a bowl, and selecting the required number of potential lottery winners.
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The sample is a simple random sample because every sample of the same size has the same chance of being selected
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class width
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is the difference between two consecutive lower class limits or two consecutive lower class boundaries
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in a pareto chart, the bars are arranged
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in descending order according to frequencies
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what type of sampling? To determine customer opinion of their food quality, General Foods randomly selects 40 city blocks during a certain week and surveys all homes within the city blocks
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cluster
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In a symmetric and bell-shaped distribution
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the mean, median, and mode are the same
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empirical rule
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· About 68% of all values fall within 1 standard deviation of the mean. · About 95% of all values fall within 2 standard deviations of the mean. · About 99.7% of all values fall within 3 standard deviations of the mean.
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range
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very sensitive to extreme values
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range rule of thumb estimates standard deviation as
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s= range/4
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If your score on your next statistics test is converted to a z score, which of these z scores would you prefer: -2.00, -1.00, 0, 1.00, 2.00? Why?
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The z score of 2.00 is most preferable because it is 2.00 standard deviations above the mean and would correspond to the highest of the five different possible test scores.
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z score
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the number of standard deviations that a given value x is above or below the mean (x- mean)/ standard deviation
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Whenever a data value is less than the mean, the corresponding z-score is
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negative
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In a market research survey of 2977 motorists, 215 said that they made an obscene gesture in the previous month. If 45 of the surveyed motorists are randomly selected without replacement, what is the probability that none of them made an obscene gesture in the previous month? Should the 5% guideline be applied in this case
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.0343. 5% guideline should be applied. 45/2977 x 100--> 1.5% --> guideline should be applied (2762/2977) ^45 --> .0343
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Determine the written description of the complement of the given event. When 15 computers are received, at least one of them is defective.
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None of them are free of defects
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When five cell phones are shipped, none of them are defective. What is the written complement?
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At least one of them are defective
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4 requirements of binomial
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1. has a fixed number of trials 2. trials must be independent 3. outcomes into 2 categories (successes, failures) 4. probability of success remains the same throughout
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coefficient of variance formula
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(s/mean) x 100 --> for sample (population standard deviance/mean) x 100 --> for population
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formula using mean, probability (successes), and number of trials
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n x p = mean
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formula for p (successes) and q (failures)
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1= p + q
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range rule of thumb
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s= range/4
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variance
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square root of ((n x summation x^2) - summation (x)^2 ) / n (n-1)
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z-score
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z-score= (x-mean)/ standard deviation
