AP Stat - Chapters 1-4 - Multiple Choice - Cumulative Test

IQs among undergraduates at Mountain Tech are approximately Normally distributed. The mean undergraduate IQ is 110. About 95% of undergraduates have IQs between 100 and 120. The standard deviation of these IQs is about a. 15. b. 10. c. 25. d. 20. e. 5.

e (empirical rule - 68-95-99.7, 100 and 120 are 2 Sx away from mean)

The scores on a university examination are Normally distributed with a mean of 62 and a standard deviation of 11. If the bottom 5% of students will fail the course, what is the lowest mark that a student can have and still be awarded a passing grade? a. 43 b. 57 c. 40 d. 62 e. 44

e (use table, look up z-score for 0.05 and then calculate x using z = (x-mean)/Sx)

(using a dot plot) the IQR for the number of AP courses is

find Q1 and Q3, IQR = Q3-Q1, DON'T INCLUDE MEDIAN WHILE FINDING Q1 AND Q3

linear relationship between height and age at certain age, relationship represented by y hat = 64.93 + 0.63x, y is the height and x is the age loretta is 20 months old and is 80 centimeters tall, what is her residual

2.47, why is she wearing a hat

what percent of the variation in yield can be explained by the LSRL using minitab

PERCENT OF THE VARIATION = r² (%)

the median age of five elephants at a certain zoo is 30 years, one of the elephants, whose age is 50 years, is transferred to a different zoo, the median age of the remaining four elephants is (40, 30, 25, less than 30, cannot be determined from the info given)

cannot be determined from the info given (M=30, 5 total, x y 30 z 50 or x y 30 50 z)

the following histogram represents the distribution of acceptance rates (% accepted) among 25 business schools in 1997, what % of schools have an acceptance rate above 40%

know how to read a histogram (variable vs. freq, fraction -> %)

(using table) the proportion of registered democrats that are male

male (that are democrats)/democrats (total)

A distrib of scores is approx normal with a mean of 78 and a stand dev of 8.6, which of the following equation can be used to find the score x above with 33% of the scores fall

0.44 = (x-78)/8.6

the variance of 16 people's weights (in pounds) is computed to be 29.16, the stand dev of these measurements is

5.4 (stand dev² = variance)

linear relationship between height and age at certain age, relationship represented by y hat = 64.93 + 0.63x, y is the height and x is the age joseph is 22.5 months old, what is his predicted height

79.11

(using a dot plot) the median number of AP courses taken by Mr. Williams students is

find the middle number

the first sentence a novel has 62 words, the five number summary for the lengths of the words is 1,2,3.5,6,12, according to the ___________ rule for identifying outliers, does this distrib have any outliers (no there are no outliers, yes there is at least one high outlier but no low outliers, yes there is at least one low outlier but no high outliers yes there is at least one high and one low outlier, not enough info)

(outlier if) 1.5 x IQR (above Q3 or below Q1, includes the number it equal when 1.5 x IQR added or subtracted from Q3 or Q1), (5 number summary (think boxplot): min, Q1, median (M), Q3, max), yes there is at least one high outlier but no low outliers

The time to complete a standardized exam is approximately Normal with a mean of 70 minutes and a standard deviation of 10 minutes. How much time should be given to complete the exam so that 80% of the students will complete the exam in the time given? a. 78.4 minutes b. 61.6 minutes c. 79.8 minutes d. 92.8 minutes e. 84 minutes

a

Birthweights at a local hospital have a Normal distribution with a mean of 110 oz. and a standard deviation of 15 oz. Using the Empirical Rule, the percent of infants with birthweights under 95 oz. is about a. 16% b. 2.5%. c. 32%. d. 84%. e. 68%.

a, empirical rule (68-95-99.7 rule) - percent of data w/in 1 Sx, 2 Sx, 3 Sx (draw curve with labels)

at a large airport, data were recorded for one month on how many baggage items were unloaded from each flight upon arrival as well as a time required to deliver all the baggage items on the flight to the baggage claim area a scatter plot of the two variables indicated a strong positive linear association between the variables which of the following statements is a correct interpretation of the word strong in the description of the association a. a least squares model predicts that the more baggage items that are unloaded from a flight the greater the time required to deliver the items to the baggage claim area b. the actual time required to deliver all the items to the baggage claim area based on the number of models unloaded will be very close to the time predicted by a least squares model c. the time required to deliver an item to the baggage claim area is relatively constant regardless of the number baggage claim items unloaded from a flight d. the variability in the time required to deliver all items to the baggage claim area is about the same for all flights regardless of the number of items unloaded from a flight e. the time required to unload baggage items from a flight is related to the time required to deliver the items to the baggage claim area

b

the least-squares regression line is the line that a. minimizes the sum of the distances between the actual UV values and the predicted UV values b. minimizes the sum of the squared residuals between the actual yield and the predicted yield c. minimizes the sum of the distances between the actual yield and the predicted UV d. minimizes the sum of the squared residuals between the actual UV reading and the predicted UV values e. minimizes the perpendicular distance between to the regression line and each data point

b

Suppose each employee in the company receives a $3,000 raise for next year (each employee's salary is increased by $3,000). Use Scenario 2-1. The z-scores of the salaries for the employees will a. be multiplied by $3,000. b. be unchanged. c. increase by square root $3,000 d. increase by $3,000. e. decrease by $3,000.

b (add/subtract - doesn't change shape or spread (range, IQR, stand dev), +/- # to locations - mean, median, quartiles, %iles, mult/divide - everything change (x or /) besides the shape, changes - center, location, spread), (z-score -> how many stand dev away from the mean, z = (x-mean)/stand dev)

which of the following statements are true about the least-squares regression line (could be multiple answers) a. the distinction between explan and resp variables is not essential b. the line always passes through the point (x bar, y bar) c. the LSRL is resistant to outliers

b, LSRL - line that makes the sum of the squared residuals as small as possible, non resistant to outliers, residual = y - y hat (why is she wearing a hat) - the difference between the actual and the predicted values of y, the distinction between explan and resp is essential regarding the LSRL b/c it will change the shape of the entire graph

Entomologist Heinz Kaefer has a colony of bongo spiders in his lab. There are 1000 adult spiders in the colony, and their weights are Normally distributed with mean 11 grams and standard deviation 2 grams. About how many spiders are there in the colony which weigh more than 12 grams? a. 840 b. 690 c. 309 d. 160 e. 117

c

A soft-drink machine can be regulated so that it discharges a mean of ? oz. per cup. If the ounces of fill are Normally distributed with a standard deviation of 0.4 oz., what value should ? be set at so that 98% of 6-oz. cups will not overflow? a. 6.60 b. 6.00 c. 5.18 d. 6.82 e. 6.18

c (find z-score for 98%, use z = (x-mean)/Sx to solve for mean where x = 6 oz)

A company produces packets of soap powder labeled "Giant Size 32 Ounces." The actual weight of soap powder in a box has a Normal distribution with a mean of 33 oz. and a standard deviation of 0.8 oz. What proportion of packets are underweight (i.e., weigh less than 32 oz.)? a. 0.1587. b. 0.2119. c. 0.1056. d. 0.8413. e. 0.1151.

c (proportion = percent, find percent by calculating z-score w equation then looking at the table)

there is a + correlation between the size of a hospital and the median number of days that patients remain in the hospital, does this mean that you can shorten a hospital stay by choosing to go to a smaller hospital a. no a neg correlation would allow that conclusion but r is pos b. yes the data show that stays are shorter in smaller hospitals c. no the + correlation is prob explained by the fact that seriously ill people go to large hospitals d. yes the correlation can't just be an accident e. yes but only if r is very close to 1

c, association/correlation does NOT imply causation, larger hospitals have more resources

a survey typically records many variables of interest to the researcher omvp;ved, below are some of the variab.es from a survey conducted by the U.S. Postal Service, which of the variables is categorical (county of residence, number of people living in household, total household income, age of respondent, number of rooms)

county of residence (categorial - categories, qualities)

the height of 3-year-old boys is approx normally distrib, duncan and shane are 3-y-o boys, duncan is 32.0 in tall and is at the 32nd %ile of the distrib, shane is 34.0 in and is at the 62nd %ile of the distrib, which of the following is closest to the mean of the height distrib a. 36.53 inches b. 32.79 inches c. 33.00 inches d. 33.21 inches e. 32.50 inches

d (make stand dev equal to each other and solve for mean because already have x value and can calculate z-score, Sx is the only thing we don't have)

A candy company produces individually wrapped candies. The quality control manager for the company believes that the weight of the candies is approximately normally distributed with mean 720 milligrams (mg). If the manager's belief is correct, which of the following intervals of weights will contain the largest proportion of the candies in the distribution of weights? a. 680 mg to 720 mg b. 620 mg to 660 mg c. 740 mg to 780 mg d. 700 mg to 740 mg e. 660 mg to 700 mg

d (mean in middle because most data centered around the mean)

if another data point were added with coordinates (x,y) the correlation would

decrease, increase, stay the same, cannot be determined without recalculating the correlation (correlation (r) - the strength and direction of the linear (not curved) relationship, r between -1 and 1, as r approx zero, the correlation is stronger)

(using table) the proportion of males that are registered as democrats

democrat (that are males)/male (total)

based on the boxplot, which of the following statements is true (maximum salary is about _________, the minimum salary is about __________, the range of the middle half of the salaries is about ___________, 25% of the employees make more than _________)

dots are outliers, where starts is minimum, first vertical line is Q1, second vertical line is median (Q2), third vertical line is Q3, where line ends is maximum, range of middle half is the IQR, between each quartile represents 25% of the data, include the outliers in minimum and maximum

A sample was taken of the salaries of 20 employees of a large company. The following are the salaries (in thousands of dollars) for this year. For convenience, the data are ordered. Suppose each employee in the company receives a $3,000 raise for next year (each employee's salary is increased by $3,000). Use Scenario 2-1. The interquartile range of the salaries for the employees will a. be multiplied by $3,000. b. decrease by $3,000. c. increase by $3,000. d. increase by square root of $3,000 e. be unchanged

e (add/subtract - doesn't change shape or spread (range, IQR, stand dev), +/- # to locations - mean, median, quartiles, %iles, mult/divide - everything change (x or /) besides the shape, changes - center, location, spread)

The distribution of heights of 6-year-old girls is approximately normally distributed with a mean of 46.0 inches and a standard deviation of 2.7 inches. Aliyaah is 6 years old, and her height is 0.96 standard deviation above the mean. Her friend Jayne is also 6 years old and is at the 93rd percentile of the height distribution. At what percentile is Aliyaah's height, and how does her height compare to Jayne's height? a. Aliyaah's height is at the 67th percentile of the distribution, and she is shorter than Jayne. b. Aliyaah's height is at the 17th percentile of the distribution, and she is shorter than Jayne. c. Aliyaah's height is at the 83rd percentile of the distribution, and she is taller than Jayne. d. Aliyaah's height is at the 67th percentile of the distribution, and she is taller than Jayne. e. Aliyaah's height is at the 83rd percentile of the distribution, and she is shorter than Jayne.

e, to find percent below when z is not exactly 1, 2, 3..., use table - numbers in big section of table are proportions (that can be turned into %) of data that is below that z-score (%ile - % below a data value)

The Normal curve below describes the death rates per 100,000 people in developed countries in the 1990's. The mean and standard deviation of this distribution are approximately

mean - estimate by looking where the peak is (because it is normal), stand dev -

you want to use numerical summaries to describe a distribution that is strongly skewed to the left, which combination of measure of center and spread would be the best to use (mean and IQR, mean and stand dev, median and range, median and stand dev, median and IQR)

median and IQR (it is skewed, don't use mean or stand dev b/c they are for symmetric data)

what is true of the correlation, r (can be multiple answers) a. it is a resistant measure of association b. if r is the correlation between X and Y, then - r is the correlation between Y and X c. correlation implies causation

none of them are true, it is not resistant to the pull of outliers b/c line wants to be as close to all points as possible

(using a residual plot) which of the following statements are true, what is true about residual plots

nonlinear relationship if the pattern is a curved pattern, linear if the pattern is uniformly scattered, watch wording with underestimating/overestimating, know when the number decreases/increases

which of the following graphs accurately represents the distrib for political party registration for each gender

other variable (x) vs. relative freq (y), other variable -> gender, segmented bar chart - segments for diff variables, diff variable in this case is political party, need to look at data and compare to graph

in a large set of data that are approx normally distrib r is value with z-score -1.00 s is value of Q1 t is value of 20th percentile what is the correct order from least to greatest for the values of r, s, and t

r, t, s

what is the avg error when predicting the yield, using the LSRL using minitab

stand dev of resid is the avg error of ________-- when using LSRL to predict ______________

(using table) the percentage of the proportion of males that are registered as democrats is part of (the marginal distrib of political party registration, the marginal distrib of gender, the conditional distrib of gender among democrats, the conditional distrib of political party registration among males, the conditional distrib of males within gender)

the conditional distrib of political party registration among males (marginal freq - the totals of each row and column, marginal distrib - the collection of all the marginal freq for ONE variable, conditional distrib - describes the relationship between TWO categorical variables, NUMERATOR (y) AMONG DENOMINATOR (x) (y/x))

a set of data has a mean that is much smaller than the median, which of the following statements is most consistent with this info (distrib is symmetric, bimodal, skewed right, skewed left, the data set probably has a few high outliers)

the distrib is skewed left (mean chases the tail, hand holds direction of skew)

which of the following statements is NOT true (in a symmetric distrib the mean and median are equal, 50% of the scores in a distrib are between the first and third quartiles, in a symmetric distrib the median is halfway between the first and third quartiles, the median is always greater than the mean, the range is the difference between the largest and the smallest observation in the data set)

the median is always greater than the mean

a researcher wishes to determine whether the rate of water flow over an experimental soil bed can be used to predict the amount of soil washed away, the explanatory variable is

the rate of water flow (x)

what is the correlation using minitab

turn r² from a percent to a decimal, take the square root, the sign (+/-) is the sign of the slope

what is the equation of the LSRL using minitab

y hat = a + bx