Statistics Cheat Sheet: Key Concepts and Formulas
Find the probability that exactly four of the sampled people own a tablet computer. We input 15 for n, .3 for p, and 4 for x = binompdf(15,.3,4) 15 is sample size .30=30% || To compute P(x), select poissonpdf and enter the values for λt and x separated by commas and press ENTER. || To compute P(Less than or equal to x), select poissoncdf and enter the values for λt and x separated by commas and press ENTER. || Let A and B be events with P(A) = 0.7, P(B) = 0.4, and P(B|A) = 0.2. Find P(A and B). = .14 || A fair coin is tossed four times. What is the probability that the sequence of tosses is HHHT? = .0625 || If P(A) = 0.21, P(B) = 0.81, and P(A and B) = 0.45, find P(A or B). = .57 || A student takes a true-false test that has 14 questions and guesses randomly at each answer. Let X be the number of questions answered correctly. Find P(Fewer than 4) = .0287 || The Australian sheep dog is a breed renowned for its intelligence and work ethic. It is estimated that 35% of adult Australian sheep dogs weigh 65 pounds or more. A sample of 11 adult dogs is studied. What is the mean number of dogs who weigh 65 lb or more? = 3.85 || Normal distributions have one mode. Normal distributions are symmetric around the mode. || The mean and median of a normal distribution are both equal to the mode. In other words, the mean, median, and mode of a normal distribution are all the same. The normal distribution follows the Empirical Rule || we found the area between z = −1.45 and z = 0.42. Find this area by using technology. normalcdf command. We enter the left endpoint of the interval (−1.45), the right endpoint (0.42), the mean (0), and the standard deviation (1) || we found the area to the right of z = −0.58 normalcdf command. We enter the left endpoint of the interval (−0.58). Since there is no right endpoint, we enter 1E99. Then we enter the mean (0) and the standard deviation (1) NORMALCDF(-.58,1E99,0,1) || we found the z-score that has an area of 0.26 to its left. The z-score is found by using the invNorm command. We enter the area to the left (.26), the mean (0), and the standard deviation (1) INVNORM(.26,0,1) || z-score that has an area of 0.68 to its right = 1-.68= INVNORM(.32,0,1) || Let x be a value from a normal distribution with mean μ and standard deviation σ. The z-score of x is z= (x-μ)/σ || IQ scores have a mean of 100 and a standard deviation of 15. Use technology to find the 90th percentile of IQ scores; in other words, find the IQ score that separates the upper 10% from the lower 90%. INVNORM(.90,100,15) || finding the area to the right of x = 280 with μ = 272 and σ = 9 = NORMALCDF(280,1E99,272,9) || finding the normal value that has an area of 0.98 to its left, where μ = 100 and σ = 15 INVNORM(.98,100,15) ||
A sample of size 50 will be drawn from a population with mean 10 and standard deviation 8.
Find the probability that x will be between 8 and 11 = normalcdf(8,11,10, 8/√(50))
Correlation coeffecient = Linreg on calc then r=coefficient. || When we are given the value of the explanatory variable, we can use the least-squares regression line to predict the value of the outcome variable. || The least-squares regression line passes through the point of averages || The least-squares regression line DOES NOT predict the result of changing the value of the explanatory variable. || Least Squares Regression Line ŷ = b0 + b1x. b1=slope b0=y intercept || Do not use the least-squares regression line to make predictions for x-values that are outside the range of the data. The linear relationship may not hold there. || Given a point (x, y) on a scatterplot, and the least-squares regression line ŷ = b0 + b1x, the residual for the point (x, y) is the difference between the observed value y and the predicted value ŷ. Residual = y − ŷ || When a residual plot exhibits no noticeable pattern, the least-squares line may be used to describe the relationship between the variables. || When a scatterplot contains outliers: 1) Compute the least-squares regression line both with and without each outlier to determine which outliers are influential. 2)Report the equations of the least-squares regression line both with and without each influential point. || The coefficient of determination is r², the square of the correlation coefficient r. || The coefficient of determination r² measures the proportion of the variation in the outcome variable that is explained by the least-squares regression line. The larger the value of r², the closer the predictions made by the least-squares regression line are to the actual values, on average. To compute the coefficient of determination, first compute the correlation coefficient r, then square it to obtain r². || The closer r² is to 0, the closer the predictions made by the least-squares regression line are to the actual values, on average= FALSE || Bivariate data are data that consist of ordered pairs. A scatterplot provides a good graphical summary for bivariate data. When large values of one variable are associated with large values of the other, the variables are said to have a positive association. When large values of one variable are associated with small values of the other, the variables are said to have a negative association. When the points on a scatterplot tend to cluster around a straight line, the relationship is said to be linear. || The correlation coefficient r measures the strength of a linear relationship. The value of r is always between −1 and 1. || A plot of residuals versus values of the explanatory variable is called a residual plot. When a residual plot has no apparent pattern, a linear model is appropriate. The correlation coefficient can be misleading in this regard, because the correlation may be large even when the relationship is not linear. || The least-squares regression line should be used for predictions only for values of x that lie within the range of the data used to compute the equation of the least-squares line. Making predictions outside the range of the data is called extrapolation, and such predictions are generally unreliable. || The probability of an event is the proportion of times the event occurs in the long run, as a probability experiment is repeated over and over again. || A sample space contains all the possible outcomes of a probability experiment. || An event is an outcome or a collection of outcomes from a sample space. || An unusual event is one whose probability is small= P<.05 the=””>Empirical Method consists of repeating an experiment a large number of times, and using the proportion of times an outcome occurs to approximate the probability of the outcome. || General addition rule P(A or B) = P(A) + P(B) − P(A and B) || Two events are said to be mutually exclusive if it is impossible for both events to occur. || Addition rule for mutually exclusive events P(A or B) = P(A) + P(B) || If A is any event, the complement of A is the event that A does not occur. The complement of A is denoted Ac. || Two events are independent if the occurrence of one does not affect the probability that the other event occurs. || General Multiplication Rule P(A and B) = P(A)P(B | A) or P(A and B) = P(B)P(A | B) || Multiplication Rule for Independent Events P(A and B) = P(A)P(B) || A random variable is a numerical outcome of a probability experiment. || Discrete random variables are random variables whose possible values can be listed. The list may be infinite — for example, the list of all whole numbers. || Continuous random variables are random variables that can take on any value in an interval. The possible values of a continuous variable are not restricted to any list. || Computing the mean and standard deviation of a discrete random variable ti-84 input L1 and L2 and do 1-VAR stats || Binomial Distribution – fixed number of trials are conducted, only two possible outcomes – Success or Failure ||