QUIZ 2

finding least squares regression line

- by hand (when info is given) 1. find b1 = r times Sy / Sx 2. plug given numbers into the formula and solve 3. then find b0 = line over y - b1 times X 4. solve and plug those answers into the equation of y = b1x+b0 - using StatCrunch 1. stat 2. regression -> simple linear 3. plug in x and y variable 4. compute and answer will be shown in the line with y = ___ + ____x

if r = ___, then a perfect negative linear relation exists between the two qualitative variables

-1

standard deviation

1. press [STAT] and then select 1:Edit 2. once the data is entered, hit [STAT] and then go to the CALC menu (at the top of the screen). Finally, select 1-var-stats and then press [ENTER] twice 3.term-10 select Sx (stands for sample standard deviation) and the symbol σ I (stands for population standard deviation)

scatter graph

example: r = -0.049 -> dots scattered everywhere r = -1 -> dots in a even straight line, not on top of each other r = -0.810 -> dots scatted in a line but not consistent, on top each other

interpret slope

for every increase in adults having ____, the median income increases by ___ on average

interpreting two probabilities

if 100 of something were sampled with replacement, one would expect about ___ of something to the something and about ___ of the something. the blank answers come from you solving the probability, make sure to multipy the answer to 100 for a whole #, not decimal

find the sum of squared residuals of least square

in StatCrunch: 1. stat 2. regression -> simple linear 3. plug in x and y values 4. answer found in error (ss)

the standard deviation ____ and the interquartile range ____. what property does it illustrate?

increases, is not affected (should be the answer most of the time but may be different) illustrates resistance

why does it not make sense to interpret y intercept

it does not make sense to interpret y intercept because x value of 0 is outside the scope of the model

E^c

Complement of event E for example: S = 1,2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 event E = 4, 5 ,6 ,7 ,8 answer will be E^c = {1, 2, 3, 9, 10, 11, 12}

determine cost of lbs for trail mix

lbs(cost)... add all up. get the total and divide it by total lbs to get the cost

listing outcomes of F or G

list all the numbers given for event F and G for example: S =2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13 F = 2, 3, 4, 5, 6, 7 G = 6, 7, 8, 9 F or G = 2, 3, 4, 5, 6, 7, 8, 9

finding lower and upper fence

lower = Q1 - 1.5 (IQR) upper = Q3 + 1.5 (IQR)

find midpoint for L1 if needed by

lower limit - upper limit / by 2 round if needed

measure of central tendency best describes the weight of the​ candy

mean

the standard deviation is used in conjunction with the ___ to numerically describe distributions that are bell shaped. the ___ measures the center of the​ distribution, while the standard deviation measures the ___ of the distribution.

mean, mean, spread

measure of central tendency best describes the​ "center" of the​ distribution

median

five number summary

minimum, Q1, median, Q3, maximum Q1 = first line of the box median = middle line in the box Q3 = last line of the box

finding linear correlation coefficient between ____ and ___

on StatCrunch: 1. stat 2. regression -> simple linear 3. plug in x and y variable 4. compute and R (correlation coefficient) is the answer

finding the probability if P(E) = 0.35 and P(F) = 0.40, and P(E and F) = 0.05

plug into its formula of P(E) + P(F) - P(E and F) and solve 0.35 + 0.40 - 0.05 = 0.7

___ divide data sets in forths.

quartiles

If E and F are disjoint events, then P(E or F) =

P(E) + P(F)

If E and F are not disjoint events, then P(E or F) =

P(E) + P(F) - P(E and F)

find Q1, Q2 and Q3

Q1 = add two middle numbers of top section then divide by 2 Q2 = add both middle number of whole list then divide by 2 Q3 = add two middle number of bottom section then divide by 2

finding IQR

Q3-Q1

finding find P(F or G) using general addition rule

S =2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13 F = 2, 3, 4, 5, 6, 7 -> 6/12 = 0.5 G = 6, 7, 8, 9 -> 4/12 = 0.333 P(E and F) = 6, 7 -> 2/12 = 0.167 P(E) + P(F) - P(E and F) -> 0.5 + 0.333 - 0.167 = plug into calculator to get answer which will be 0.666

find P(F or G) by counting outcomes

S =2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13 (12 total) F or G = 2, 3, 4, 5, 6, 7, 8, 9 (8 total) P(F or G) = 8/12 =0.667

compute anf interpret interquartile range, IQR

the answer will be the interquartile range is ____ mpg. it is the range of the middle 50% of the observations in the data set

outliers

the number(s) greater than your upper fence

how to determine actual % of item

the total # given(but do not include the #wanted)/ overall total times 100 ^ for example: find weigh between 0.71 and 0.99 -> its all the numbers but 0.71 and 0.99 ​gram StatCrunch: 1. data 2. sort, column ascending 3. calculate for example: we have 50 total but there are 15 # between 5 and 15. therefore you calculate 15/50 x 100

variance

variance = (standard deviation)^2

sample standard deviation

(L1-u [amount from sample mean]^2L2 plugged into L4, L4 divided by L2

find the probability P(E^c) of P(E) = 0.46

1 - 0.46 = 0.54 as your answer

P(E^c)

1 - P(E) for example: S = 1,2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 event E = 4, 5 ,6 ,7 ,8 -> 7/12 = 0.583 will be the answer

find population mean or sample mean by

add all together and divide by the amount of # given

finding minimum score with a at least _ standard deviation, mean of _ and standard deviation of _

add the mean and at least standard deviation, then multiply by the standard deviation for example: at least = 2.5, mean = 100, standard deviation = 26 -> 100+2.5 x 26 = 165

side-by-side boxplots

answers = 1. Variable y — the interquartile range of variable y is larger than that of variable x. 2. Symmetric — the median is the center of the box and the left and right whiskers are about the same length. 3. depending on your graph, can be skewed left or right

knowing which number could be a probability of an event

any number except for a negative number and a whole number with decimals for example: 1, -0.53, 0.28, 0.01, 1.53, 0 -> the probability is 1, 0.28, 0.01, 0

sample arithmetic mean (statistic)

bar over x

probability that randomly selected family has income greater than $57,500

because median is 50, the probability is 0.5

shape of distribution on a box and whiskers graph

center = roughly symmetric box to the left = skewed right box to the right = skewed left

possible reasons for any outliers

data entry, a student with usually high income and a student providing false information (should be the first 3 answer choices)

finding P(E)

sample from 1-10 probability event E = {4, 5, 6} therefore, 3/10 = 0.3

graphs

skewed right = mean > median skewed left = mean < median symmetric = mean = median

sample space

spinner outcomes + card outcomes for example: SO = 1, 2, 3, 4, and CO is B and R -> 1B, 2B, 3B, 4B, 1R, 2R, 3R, 4R if # comes first, make sure to put the number first before the letter, if not it'll be wrong. vice versa

sample variance and standard deviation

s² and s

example: Scores of an IQ test have a​ bell-shaped distribution with a mean of 100 and a standard deviation of 15. Use the empirical rule to determine the following.

x = 100 s = 15 plug into empirical rule : x-3s, x-2s, x-s, x, x+s, x+2s, x+3s % = [0.15, 2.35, 13.5, 34, 34, 13.5, 2.35, 0.15]

sample mean

x times y / y total L1 X L2 / L2

finding ERA and which player is the best

x-μ/o = ERA x = lowest ERA μ = mean ERA o = standard deviation solve for each male and female, the person with higher year because of lower z-score

calculate lengths will bolt be destroyed

z will be less than or equal to standard deviation from the mean x < -z (standard deviation [# usually in decimals])+mean x > -z (standard deviation [# usually in decimals])+mean for example: bolts more than 4 standard deviation from mean, mean length of 14 cm with standard deviation of 0.05 cm 1. -4(0.05)+14 = 13.8 2. 4(0.05)+14 = 14.2 answer will be: a bolt will be destroyed if the length is less than 13.8 cm or greater than 14.2

the ___ represents the number of standard deviation an observation is from the mean.

z-score

the sum of the deviations about the mean always equals ___.

zero

population arithmetic mean (parameter)

μ (pronounced "mew")

population variance and standard deviation

σ² and σ² 1. find the mean 2. (#- mean)^2 + ... + (# - mean)^2 divide by total = population variance 3. square root population variance to get standard deviation #