AP Statistics Semester One Review

Ms. Adkins picked up 12 items in the grocery store with a mean cost of $ 3.25 . Then she added an apple pie that costs $ 6.50 . What is the new mean for all 13 items ?

$ 3.50

Population: all Dallas residents. Sample: the 850 people who respond.

A candidate for mayor of Dallas wants to know what proportion of city residents support his candidacy. His staff calls 1,000 people chosen at random from the city telephone directory and 850 of them respond. What are the population and the sample in this example?

0.08192

A college basketball player makes 80% of her free throws. Suppose this probability is the same for each free throw she attempts, and free throw attempts are independent. What is the probability that she makes all of her first four free throws and then misses her fifth attempt this season?

0.40

A cumulative relative frequency graph for the 48 racers who finished the grucling 50km cross-country ski race at the 2010 Vancouver Olympics is given below. approximately what proportion of the racers finished the race in more than 2.20 hours?

The proportion of males who said they would contribute to an environmental organization is higher than the proportion of females who said they would contribute such an organization.

A sample of 250 high school students were asked, "Il you had $1000 to contribute to one kind of charitable organization, which type of organization would you choose? Here is a two-way table that displays data on gender and response to this question. which of the following conclusions scems to be supported by the data?

a sample chosen in such a way that every set of n units in the population has an equal chance to be the sample that is actually selected.

A simple random sample of size n is defined to be

1/6

An event A will occur with probability 0.5. An event B will occur with probability 0.6. The probability that both A and B will occur is 0.1. Which of the following is the conditional probability of A, given B?

factors and experimental units

An experiment was conducted by some students to explore the nature of the relationship between a person's heart rate (measured in beats per minute) and the frequency at which that person stepped up and down on steps of various heights. Three rates of stepping and two different step heights were used. A subject performed the activity (stepping at one of the three stepping rates at one of the two possible heights) for three minutes. Heart rate was then measured anthe end of this period. The variables "stepping rate" and "step height" are the factors. levels. controls. experimental units. response variables.

0.9375

Flip a coin four times. If Z = the number of heads in four flips, then the probability distribution of Z is given in the table below. What is the probability of at least one tail?

mean= A; median= B

For the density curve shown, which letters correspond to the locations of the mean and median of the distribution?

0.614

Forrest has determined that if he gets to the bus stop at 7:30 am, there is a 0.15 probability that he misses the bus. If he arrives at the bus stop three consecutive days at 7:30, what is the approximate probability that he catches the bus all three days?

The mean and median must be approximately equal.

If a distribution is approximately symmetric, which of the following is true?

0.85

In the Florida scratch-card lottery, the numbers and values of prizes awarded for every 100,000 cards sold are What is the expected payoff per card?

75%

Mrs. Abbey collects health data of many women|in each of several small countries. One of the variables measured for each woman in the study is her weight in pounds. The following list gives the five-number summary for the weights of adult women in one of the countries. Country A: 92, 110, 120, 160,240 About what percent of Country A women weigh between 110 and 240 pounds?

0.32

Mrs. Heart asked 100 randomly selected adult Americans if they thought that women should be allowed to go into combat situations. Here are the results, classified by the gender of the subject. Which of the following is the probability of a "Yes" answer, given that the person was Female?

stratified random sample

Mrs. Kerns plan to give a math achievement test to samples of 15-year-old students from both the U.S. and Korea in order to compare mathematics knowledge in the two countries. In each country, she will randomly select 300 students from low-income families, 400 students from middle-income families, and 200 students from high-income families. The sample from Korea is a (a) systematic random sample. (b) simple random sample. (c) convenience sample. (d) voluntary response sample. (e) stratified random sample.

0.030

Of people who died in the United States in a recent year, 86% were white, 12% were black, and 2% were Asian. (We will ignore the small number of deaths among other races.) Diabetes caused 2.8% of deaths among whites, 4.4% among blacks, and 3.5% among Asians. What is the probability that a randomly chosen death was due to disabilities?

0.526

People with type O-negative blood are universal donors. That is, any patient can receive a transfusion of O-negative blood. Only 7.2% of the American population has O-negative blood. If 10 Americans are randomly selected, what is the probability that at least 1 of them is a universal donor?

the mean

Suppose a data set consists of 25 positive integers. If every value in the data set is multiplied by negative 2, which of the following values would be negative? (a) the range (b) the IQR (c) the standard deviation (d) the mean (e) None of the choices provided would have a negative value.

0.8704

Suppose that 40% of the cars in a certain town are white. A person stands at an intersection waiting for a white car. Let X = the number of cars that must drive by until à white one drives by. P(X < 5) =

5

The 16th percentile in a Normal distribution is 25 If the mean is 30, what is the best estimate of the standard deviation?

35%

The density curve shown takes the value 0.5 on the interval 0 ≤ x ≤ 2 and takes the value 0 everywhere else. What percent of the observations lie between 0.5 and 1.2?

0.1056

The weight of written reports produced in a certain department has a Normal distribution with a mean of 60 grams and a standard deviation of 12 grams. What is the probability that the next report will weigh less than 45 grams?

matched pairs experiment

To test the effects of a new fertilizer, 100 plots were divided in half. Fertilizer A is randomly applied to one half of each plot. and B to the other. This is

0.84

What is the probability that a randomly selected subject in the study is Male or answered "No"?

assigns labels that place each individual into a particular group, called a category.

categorical variable

gives the percent or proportion of individuals that have a specific value for one categorical variable among individuals who share the same value of another categorical variable (the condition).

conditional relative frequency

the median of the data values that are to the left of the median in the ordered list.

first quartile

the minimum, the first quartile , the median, the third quartile , and the maximum.

five number summary

shows the number of individuals having each value.[

frequency table

shows each interval of values as a bar. The heights of the bars show the frequencies or relative frequencies of values in each interval.

histogram

mean p-hat= 0.27 standard deviation p-hat= 0.0888

if you select a simple random sample of 25 Americans and let - the proportion in the sample who get 30 minu of exercise at least five days per week, what are the values of the mean and standard deviation of the sampling distribution of p-hat?

an object described in a set of data. Individuals can be people, animals, or things.

individual

symmetric, single-peaked, bell-shaped density curve

normal distribution

a scatterplot of the ordered pair (data value, expected z-score) for each of the individuals in a quantitative data set. That is, the x-coordinate of each point is the actual data value and the y-coordinate is the expected z-score corresponding to the percentile of that data value in a standard Normal distribution

normal probability plot

a number that describes some characteristic of a population.

parameter

the value with p% of observations less than or equal to it.

percentile

shows each category as a slice of the "pie." The areas of the slices are proportional to the category frequencies or relative frequencies.

pie chart

At the beginning of the school year , Mrs. Mallon from Discovery High School asks every student in her classes to fill out a survey that asks for their age , gender how long they have lived at their current address , their favorite school subject , and whether they plan to go to college after high school Which of the following best describes the variables that are being measured ?

3 categorical variables , 2 quantitative ( continuous ) variables

The number of copies made each day typically varies by about 24 copies from the mean

A small company estimating its photocopying expenses finds that the mean/number of copies made per day for the past 12 months is 258 copies per day with a standard deviation of 24 copies per day. Which of the following is a correct interpretation of standard deviation?

0.03

A study of 240 randomly selected residents of a subtropical resort city with 82,000 residents found that 5.4% of them had been exposed to the mosquito-borne virus that causes Dengue fever. Suppose the actual percentage of people in the city who have been exposed to the virus is 3%. Let j= the proportion of residents who have been exposed in a random sample of 240. What is the mean up of p?

whether there is an association between sex and starting salary among graduates of this nursing school

A survey is to be administered to recent graduates of a certain nursing school in order to compare the starting salaries of women and men. For a random sample of graduates, three variables are to be recorded: sex, starting salary, and area of specialization. Which of the following best describes a conclusion that can be drawn from this study?

mean= 26.25 standard deviation= 1.75

A vending machine operator has determined that the number of candy bars sold per week by a certain machine is a random variable with mean 125 and standard deviation 7. His profit on each bar sold is $0.25, and it costs him S5.00 per week to maintain the machine and rent the space for it. Which of the following gives the correct

if you flip 3 coins 5000 times, the percentage of time you get three heads will be very close 12.5%.

If you flip three coins, the probability of getting three heads is 0.125. Which of the following statements follows from this? A) If you flip three coins 1000 times, you will get three heads exactly 125 times. B) If you flip 3 coins 10 times and never get three heads, the probability of getting three heads in the next set of 10 flips is slightly greater than 0.125. C) If you have 20 sets of three coin flips, then at least one set of flips will be three heads. D) if you flip 3 coins 5000 times, the percentage of time you get three heads will be very close 12.5%. E) If you get 3 heads two times in a row, the probability of getting 3 heads again on the next toss of 3 coins is nearly zero.

2011, because the standardized score is greater than in 1965.

In 1965, the mcan price of a new car was S2,650 and the standard deviation was 51,000. In 2011, the mean was $30,500 and the standard deviation was $9,000. If a Ford Mustang cost $2,300 in 1965 and $28,000 in 2011, in which year was it more expensive relative to other cars? (a) 1965, because the standardized score is greater than in 2011. (b) 1965, because the standard deviation is smaller. (c) 2011, because the standardized score is greater than in 1965. (d) 2011, because $28,000 is greater than $2,300. (e) We cannot compare the two prices, because we don't know if the prices for each year are Normally distributed.

0.8340

Sule's job is just a few bus stops away from his house. While it can be faster to take the bus to work, it's more variable, because of variations in traffic. He estimates that the commute time to work by bus is approximately Normally distributed with a mean of 12 minutes and a standard deviation of 4 minutes. The commute time if he walks to work is also approximately Normally distributed with a mean of 16 minutes with a standard deviation I minute. What is the probability that the bus will be faster than walking?

skewed to the right with a mean of zero and a standard deviation of one

The distribution of the time it takes for different people to solve a certain crossword puzzle is skewed to the right, with a mean of 30 minutes and a standard deviation of 15 minutes. The distribution of z-scores for those times is (a) Normally distributed, with mean 30 and standard deviation 15. (b) skewed to the right, with mean 30 and standard deviation 15. (c) Normally distributed, with mean 0 and standard deviation 1. (d) skewed to the right, with mean 0 and standard deviation 1. (e)skewed to the right, but the mean and standard deviation cannot be determined without more information.

knowing a students gender is helpful for predicting their current emotion

The mosaic plot displays the distribution of emotion by gender for the random sample of 50 students . Which of the following is the best evidence that there is an association between gender and emotion ?

experiments can give better evidence of causation.

The most important advantage of experiments over observational studies is that A) experiments are usually easier to carry out. B) experiments can give better evidence of causation. C) confounding cannot happen in experiments. D) an observational study cannot have a response variable. E) observational studies cannot use random samples.

There are 10 states that have designated a pine as their state tree.

The pie chart describes the distribution of state tree types for the 50 states in the United States. The category "Other" include all trees that are the state tree for two or fewer states. Which of the following conclusions can we draw from this chart?

creates approvimately equal groups for comparison.

The principle reason for the use of random assignment in designing experiments is that it

the distribution of values taken by a statistic in all possible samples of the same sample size from the same population

The sampling distribution of a statistic is

12

The states differ greatly in the kinds of severe weather that afflict them . The histogram below shows the distribution of average annual property damage caused by tornadoes over the period of 50 years in the United States .

not mutually exclusive or independent

The two-way table below gives information on the performers in the New York Philharmonic Orchestra, categorized by section (type of instrument) and gender. You select one musician from this group at random. Which of the following statements is true about the events "Plays a woodwind" and "Male?"

the proportion of adult male Labrador Retrievers that weigh less than 80 pounds is approximately equal to the proportion that weigh more 94 pounds.

The weights of adult male Labrador Retrievers are approximately Normally distributed ith dtriean of 87 pounds and a standard deviation of 8 pounds. Which of the following statements is true? (a) About 95% of adult male Labrador Retrievers weigh between 79 and 95 pounds. 62 (b) The median weight of adult male Labrador Retrievers is more than 87 pounds. (c) the proportion of adult male Labrador Retrievers that weigh less than 80 pounds is approximately equal to the proportion that weigh more 94 pounds. (d) Almost all adult male Labrador retrievers weight more than 79 pounds. (e) The standardized weights of 80-pound and 94-pound adult male Labrador Retrievers are roughly equal.

57.1 % , conditional

What percentage of males felt tired ? Is this a marginal , conditional , or joint distribution value ?

0.28- invNorm(0.61, 30, 15, L)= 34.1899 34.12-30/15= 0.28

Which of the following is closest to the 61st percentile of the standard Normal distribution?

the response of randomly selected people to the question, "What is your favorite TV sit-com?"

Which of the following is not a random variable? a. the number of heads in ten tosses of a fair coin b. the number of passengers in cars passing through a toll booth c. the age of the driver in cars passing through a toll booth d. the response of randomly selected people to the question, "What is your favorite TV sit-com?" e. the response of randomly selected people to the question, "How many hours of sleep did you get last night?'

The area underneath the curve is equal to 1.

Which of the following is true about all Normal distributions? (a) There is no area under the curve for z-scores greater than 3.49. (b) The area underneath the curve is equal to 1. (c) The points at which the curvature changes from "up" to "down" (the points of inflection) are at the first and third quartiles of the distribution. (d) About 68% of the values of the variable are more than one standard deviation away from the mean. (e) The mean is usually greater than the median.

c. Y has a binomial distribution with n = 40 observations and probability of success p = 0.5, provided that after selecting a card it is replaced in the deck and the deck is shuffled well before the next card is selected.

You select 40 cards from a standard deck of 52 cards. Let Y = the number of red cards (hearts or diamonds) in the 40 cards selected. Which of the following best describes this setting? a. Y has a binomial distribution with n = 40 observations and probability of success p = 0.5. b. Y has a binomial distribution with n = 40 observations and probability of success p = 0.5, provided the deck is shuffled well. c. Y has a binomial distribution with n = 40 observations and probability of success p = 0.5, provided that after selecting a card it is replaced in the deck and the deck is shuffled well before the next card is selected. d. Y has a geometric distribution with n = 40 observations and probability of success p = 0.5. e. Y has a geometric distribution with-n - 52 observations and probability of success p = 0.5.

eliminate a possible source of bias

a double blind experiment was conducted to evaluate the effectiveness of the Salk polio vaccine. the purpose of keeping the diagnosing physicians ignorant of the treatment status of the experimental subjects was to

biased, overstating the effectiveness of the diet.

a news release for a diet product company reports: "we have good news for the 65 million americans on a dire" the study showed that people who lose weight can keep it off. the sample consisted of twenty graduates of the company's program who endorsed it in commercials. The results of the study are probably (a) biased, overstating the effectiveness of the diet. (b) biased, understating the effectiveness of the diet. (c) unbiased because these are nationally recognized individuals. (d) unbiased, but they could be more accurate. A larger sample size should be used. (e) unbiased, because this is a prospective study.

6.16

a worn out bottling machine does not properly apply caps to 5% of the bottles it fills. In a production run of 800 bottles, what is the standard deviation for the number of bottles with improperly applied caps?

between two variables if knowing the value of one variable helps us predict the value of the other. If knowing the value of one variable does not help us predict the value of the other, then there is no association between the variables.

association

shows each category as a bar. The heights of the bars show the category frequencies or relative frequencies.

bar graph

a visual representation of the five-number summary.

boxplot

A quantitative variable that can take any value in an interval on the number line is a

continuous variable

plots a point corresponding to the percentile of a given value in a distribution of quantitative data. Consecutive points are then connected with a line segment to form the graph.

cumulative relative frequency graph

models the distribution of a quantitative variable with a curve that

density curve

A quantitative variable that takes a fixed set of possible values with gaps between them is a

discrete variable

tells us what values the variable takes and how often it takes those values

distribution

shows each data value as a dot above its location on a number line

dotplot

the distance between the first and third quartiles of a distribution

interquartile range

unbiased

is a statistic used to estimate a parameter is such that the mean of its sampling distribution is equal to the true value of the parameter being estimated, what is the statistic said to be?

gives the percent or proportion of individuals that have a specific value for one categorical variable and a specific value for another categorical variable.

joint relative frequency

gives the percent or proportion of individuals that have a specific value for one categorical variable.

marginal relative frequency

the average of all the individual data values. To find the mean, add all the values and divide by the total number of data values.

mean

the point at which the curve would balance if made of solid material.

mean of a density curve

the midpoint of a distribution, the number such that about half the observations are smaller and about half are larger.

median

he equal-areas point, the point that divides the area under the curve in half.

median of a density curve

a modified segmented bar graph in which the width of each rectangle is proportional to the number of individuals in the corresponding category.

mosaic plot

takes number values that are quantities—counts or measurements

quantitative variable

divide the ordered data set into four groups having roughly the same number of values

quartiles

the distance between the minimum value and the maximum value

range

shows the proportion or percent of individuals having each value.

relative frequency table

A statistical measure isn't sensitive to extreme values

resistant

displays the distribution of a categorical variable as segments of a rectangle, with the area of each segment proportional to the percent of individuals in the corresponding category

segmented bar graph

displays the distribution of a categorical variable for each value of another categorical variable. The bars are grouped together based on the values of one of the categorical variables and placed side by side.

side-by-side bat graph

if the left side of the graph is much longer than the right side.

skewed to the left

if the right side of the graph is much longer than the left side.

skewed to the right

0.6

special 20-sided die is constructed so that cach face has one of the following numbers on it: i, 2, 3, от 4. The table below gives the probability of each value (with one value missing). what is the probability of rolling an odd number?

measures the typical distance of the values in a distribution from the mean

standard deviation

tells us how many standard deviations from the mean the value falls, and in what direction

standardized score(z-score)

a number that describes some characteristic of a sample.

statistic

the science and art of collecting, analyzing, and drawing conclusions from data.

statistics

shows each data value separated into two parts: a stem, which consists of all but the final digit, and a leaf, the final digit. The stems are ordered from lowest to highest and arranged in a vertical column. The leaves are arranged in increasing order out from the appropriate stems.

stemplot

variances of the sampling distributions will be nearly the same if we sample the same number of residents from each state

suppose we want to compare the proportion of Texas residents (population 26 million) and the proportion of Wyoming residents(population 526 thousand) whol have purchased items through online auction sites we would like to select samples from each state in such a way that the sampling distributions have roughly equal variances.

if the right side of the graph (containing the half of observations with the largest values) is approximately a mirror image of the left side.

symmetric

a distribution of sample data

the distribution of values from a single sample of size n from a population is

the median of the data values that are to the right of the median in the ordered list.

third quartile

is a table of counts that summarizes data on the relationship between two categorical variables for some group of individuals.

two-way table

an attribute that can take different values for different individuals.

variable