Mid-term Statistics I
The following boxplot contains information about the length of time (in minutes) it took women participants to finish the marathon race at the 2012 London Olympics. What can be said about the shape of the distribution of women's running times for the marathon?
The distribution is right-skewed.
Find the probability that a male college student from the group chose "housework" as their most likely activity on Saturday mornings? (Round to the nearest thousandth)
0.156 [15/96=0.156]
Researchers conducted an experiment to determine if riding a bike to school improves attention span. What are the treatment and outcome variables?
The treatment variable is riding a bike to school. The outcome variable is the child's attention span.
The following list shows the age at appointment of U.S. Supreme Court Chief Justices appointed since 1900. Use the data to answer the question. Find the mean, rounding to the nearest tenth of a year, and interpret the mean in this context.
The typical age of a U.S. Supreme Court Chief Justice appointed since 1900 is 61.4.
Is the following an example of theoretical probability or empirical probability? A card player declares that there is a one in thirteen chance that the next card pulled from a well-shuffled, full deck will be a queen.
Theoretical
The ethnicity of the individual respondents in a political poll of a randomly selected group of adults is an example of what type of variable?
Categorical variable
For the pair of histograms below, determine which distribution has the larger standard deviation.
(i) has a larger standard deviation than (ii).
The data below are the number of hours worked (per week) and the final grades of 9 randomly selected students from a drama class. Calculate the linear correlation coefficient.
-0.991
Calculate the linear correlation coefficient for the data below. x: -1 1 8 5 3 2 4 6 7 0 y: 20 15 3 8 12 13 10 5 4 17
-0.995
You are dealt one card from a standard 52-card deck. Find the probability of being dealt an ace or a 9.
2/13
There were fifteen people who participated in the class between the ages of 25 and 45. Use the histogram to answer the question. How many participants had a heart rate between 120 and 130 bpm?
3
For what percentage of great lakes states would you expect the economic impact from fishing to be between $151.00 and $485.00 (in millions of dollars)?
95%
The mean can be thought of as the balancing point of a distribution. According to this description, at what value is the following distribution balanced?
About 30
Which of the following statements regarding the correlation coefficient is not true?
All of these are true statements.
The boxplots below represent movie runtimes (length of a movie in minutes) for movies that have been rated by the Motion Picture Association of America as R, PG-13, PG, and G. List ratings according to their median runtimes, from longest to shortest.
PG-13, R, PG, G
Which scatterplot below depicts a stronger linear relationship? Why?
Scatterplot (ii) shows a stronger linear relationship because it has less vertical variation between points.
Which of the following are mutually exclusive events?
Student chose "recreation" and student chose "other" as their most likely activity on Saturday mornings.
Use the side-by-side boxplots below to answer the question. The boxplots summarize the number of sentenced prisoners by state in the Midwest and West. Pick the statement that best describes the shape of the distribution for the states in the West.
The data appears to be right-skewed with a possible outlier.
Below is the standard deviation for extreme 10k finish times for a randomly selected group of women and men. Chose the statement that best summarizes the meaning of the standard deviation. Women: s = 0.16 Men: s = 0.25
The distribution of women's finish times is less varied than the distribution of men's finish times.
Choose the scatterplot that matches the given correlation coefficient. r = 0.8787
negative scatterplot graph. scatterplots start with the left and end to the right.
Use the following information to answer the question. A random sample of 30 couples who were also new home owners were asked to report the cost of their first house and their combined age when they married. The output of a regression analysis for predicting home cost from combined age is shown. Assume that the conditions of the linear regression model are satisfied. If the slope were 1, what would that say about the association?
If the slope were 1, it would mean that on average, for every additional year in combined age, the home cost would be 1 dollar more.
In Los Angeles, juice cleansing is very popular. Some people have claimed that the cleanses are beneficial for weight loss, body detoxification, and treatment and prevention of illnesses. Can we conclude that juice cleansing causes these health benefits?
No, the claims are anecdotes and do not give us a true comparison group to find health differences.
Researchers conducted a study and determined that students who carpool have less friends than students who ride the bus to school. Can we conclude that carpooling causes students to have less friends?
No, this is an observational study and we cannot conclude causation.
A group of 500 patients who suffer from skin cancer were asked to participate in a study to determine the effectiveness of a new medication. The patients were randomly divided into two groups, one that was given the actual medication, and one that received a placebo pill. A good outcome was defined as the cancer being in remission after 6 months of treatment. The results of the study are below. Can we conclude that the cancer remissions were caused by the new medication?
Yes, this is a controlled experiment. Since a higher percent of patients who took the medication had cancer remissions, we can conclude causation
A dot plot of the speeds of a sample of 50 cars passing a policeman with a radar gun is shown below. What proportion of the motorists were driving above the posted speed limit of 65 miles per hour?
0.08
Use the side-by-side boxplots below to answer the question. The boxplots summarize the number of sentenced prisoners by state in the Midwest and West. Based on the boxplot for the Midwest, which of the following is true?
25% of the states sentenced more than 29,928 prisoners.
The distribution of the number of hours people spend at work per day is unimodal and symmetric with a mean of 8 hours and a standard deviation of 0.5 hours. If Anthony's z-score for his work hours was -1.3, how many hours did he work?
7.35 hours
The following side-by-side bar graph shows the level of post-secondary education achieved ten years after high school for graduates from the years 1999 and 2001. Use the bar graph to answer the question. In which category was there more variability?
No College
Use the following information to answer the question. Here is a table recording the number of deaths for the top thirteen worst U.S. tornados since 1925. A histogram showing the distribution is also included.
Median: 181.0
What feature of a distribution can NOT be determined from a boxplot?
Modality
The following boxplot contains information about the length of time (in minutes) it took men participants to finish the marathon race at the 2012 London Olympics. The slowest 25% of men participants ran the marathon how quickly?
More than 143 minutes.
At one college, GPA's have a distribution that is unimodal and symmetric with a mean of 2.7 and a standard deviation of 0.5. Is a GPA of 3.8 more than one standard deviation above the mean?
Yes
Suppose that a recent poll of American households about pet ownership found that for households with pets, 45% owned a dog, 34% owned a cat, and 10% owned a bird. Suppose that three households are selected randomly and with replacement and the ownership is mutually exclusive. What is the probability that at least one of the three randomly selected households own a bird? (Round to the nearest hundredth)
0.27
Suppose that a recent poll of American households about pet ownership found that for households with pets, 45% owned a dog, 34% owned a cat, and 10% owned a bird. Suppose that three households are selected randomly and with replacement and the ownership is mutually exclusive. What is the probability that none of the three randomly selected households own a cat? (Round to the nearest hundredth)
0.29
Given the following scatterplot, if a point was added in the upper left corner with an x-value of 10 and a y-value of 20, what would happen to the value of the correlation coefficient, r?
r will get closer to 0.
The data in the table represent the amount of raw material (in tons) put into an injection molding machine each day (x), and the amount of scrap plastic (in tons) that is collected from the machine every four Also shown below are the outputs from two different statistical technologies (TI-83/84 Calculator and Excel). A scatterplot of the data confirms that there is a linear association. Report the equation for predicting scrap from raw material using words such as scrap, not x and y. State the slope and intercept of the prediction equation. Round all calculations to the nearest hundredth.
scrap = -2.38 + 2.19(raw material); slope = 2.19 and the intercept is -2.38.
A store manager counts the number of customers who make a purchase in his store each day. The data are as follows. 10 11 8 14 7 10 10 11 8 7
. . . . . . . . . .
A die is rolled. The set of equally likely outcomes is {1, 2, 3, 4, 5, 6}. Find the probability of getting a 10.
0
In a study of 1350 elementary school children, 118 out of the 615 girls in the study said they want to be a teacher when they grow up. What percent of girls want to be a teacher when they grow up?
19.2%
Calculate the five-number summary for the following dataset. 41.19, 83.51, 19.98, 114.60, 63.08, 83.88
19.98, 41.19, 73.295, 83.88, 114.6
Suppose the ages and heights of 100 randomly selected people were recorded. Which variable is the explanatory variable and which one is the response?
Age is the explanatory variable and height is the response because a person's age could explain his/her height.
Use the following information to answer the question. The distribution of the number of hours people spend at work per day is unimodal and symmetric with a mean of 8 hours and a standard deviation of 0.5 hours.
No, 8.7 hours is less than 2 standard deviations above the mean.
Use the following information to answer the question. The following linear regression model can be used to predict ticket sales at a popular water park. Ticket sales per hour = -631.25 + 11.25(current temperature in °F) In this context, does the intercept have a reasonable interpretation?
No, at a temperature of 0°F, ticket sales would be -631.25 and it is not reasonable (or possible) to have negative ticket sales.
Which of the following statements is true about the Law of Large Numbers (LLN)?
The LLN states that if an experiment with a random outcome is repeated a large number of times, the empirical probability that is observed is likely to be close to the theoretical probability.
Choose the best statement to summarize the association shown between hat size and IQ in the scatterplot below.
The scatterplot does not show a trend that would indicate an association between hat size and IQ scores.
According to the following two-way table, why are percentages more useful than counts to compare pet preferences between males and females?
There are more males than females in the sample.
The graph shows a strong decreasing trend. Average number of years of education of married women of child bearing age
True
If a new report came out saying that the economic impact of great lakes sport fishing on the economy of Illinois was $93,588,546, would you say this was unusual? Note that this dollar amount must be converted before calculating a standard score.
Yes, it is unusually low.
A bag contains 7 red marbles, 8 blue marbles, and 9 green marbles. Jeffery claims that if a marble is selected at random from the bag, the probability of choosing a blue marble is 1/3. Is this an example of empirical probability or theoretical probability?
theoretical
A six-sided die is rolled and a coin is tossed. The probability of getting a tail on the coin and a 2 on the die is 8.3%. Is this an example of a theoretical or empirical probability?
theoretical
At one college, GPA's have a distribution that is unimodal and symmetric with a mean of 2.9 and a standard deviation of 0.4. Is a GPA of 3.8 more than one standard deviation above the mean?
yes
Use the following information to answer the question. The mean age of lead actors from the top ten grossing movies of 2007 was 36.4 years with a standard deviation of 9.87 years. Assume the distribution of the actors ages is approximately unimodal and symmetric.In 2007, popular actor and singer Justin Timberlake was 26-years-old. What is Justin Timberlake's age in 2007 if it is standardized? Would it be unusual for a 26-year-old actor to be in a top-grossing film of 2007? Assume the Empirical Rule applies and round to the nearest hundredth.
z = -1.05; It would not be unusual.
Which boxplot represents the same data as the histogram shown below?
|-[| ]-|
Which of the following sets of numbers would result in a positive correlation of 1?
x: 2 3 4 5 y: 2 3 4 5
The economic impact of fishing for nearly all great lakes states should fall within what range (in millions of dollars)?
$67.5 to $568.5
Find the probability that a female college student from the group chose "housework" as their most likely activity on Saturday mornings? (Round to the nearest thousandth)
0.163 [17/104=0.163]
If one student is randomly chosen from the group, what is the probability that the student chose "recreation" as their most likely activity on a Saturday morning?
0.310 [62/200 = 0.310]
Swinging Sammy Skor's batting prowess was simulated to get an estimate of the probability that Sammy will get a hit. Let 1=HIT and 0=OUT The output from a simulation was as follows. 1 0 0 0 0 0 0 1 0 0 1 0 1 0 0 0 0 1 0 1 1 0 0 0 0 1 0 0 0 1 1 0 1 0 0 0 0 0 1 0 0 1
0.310 [with 13 #1's]
If one car buyer is randomly chosen from the group, what is the probability amongst female buyers that they chose "price" as their most important factor for the purchase?
0.375
Swinging Sammy Skor's batting prowess was simulated to get an estimate of the probability that Sammy will get a hit. Let 1=HIT and 0=OUT The output from a simulation was as follows. 1 0 0 0 1 0 0 1 0 0 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 0 0 1 1 1 1 Estimate the probability that he gets a hit.
0.476 [with 20 #1's]
If one student is randomly chosen from the group, what is the probability that the student is female or chose "homework" as their most likely activity on a Saturday morning?
0.665
The data below are the ages and annual pharmacy b ills (in dollars) of 9 randomly selected employees. Calculate the linear correlation coefficient.
0.960
In an area of the Great Plains, records were kept on the relationship between the rainfall (in inches) and the yield of wheat (bushels per acre). Calculate the linear correlation coefficient. Rainfall , x: 13.4 11.7 16.3 15.4 21.7 132. 9.9 18.5 18.9 Yield, y: 55.5 51.2 638 64 87.4 54.2 36.9 81 83.8
0.981
The table shows the number of minutes ridden on a stationary bike and the approximate number of calories burned. Plot the points on the TI calculator then choose the most likely correlation coefficient from the answer choices below.
0.99
Use the following information to answer the question. The mean age of lead actresses from the top ten grossing movies of 2010 was 29.6 years with a standard deviation of 6.35 years. Assume the distribution of the actresses' ages is approximately unimodal and symmetric. Between what two values would you expect to find about 95% of the lead actresses ages?
16.9 and 42.3 years
The salaries of ten randomly selected doctors are shown below. 109000 10900 173000 219000 241000 100000 140000 808000 235000 156000
164500
At one college, GPA's have a distribution that is unimodal and symmetric with a mean of 3.1 and a standard deviation of 0.6. What is the range of GPA's from one standard deviation below the mean to one standard deviation above the mean?
2.5 to 3.7
Ten households were asked how many pets they currently own. The results are shown below. 1 0 2 4 3 2 1 1 6 4 What is the IQR for this set of data?
3
Use the following information to answer the question. The distribution of the number of hours of sleep people get per night is unimodal and symmetric with a mean of 6 hours and a standard deviation of 1.5 hours. Approximately what percent of people sleep between 6 and 7.5 hours per night?
34%
There were fifteen people who participated in the class between the ages of 25 and 45. Use the histogram to answer the question. What is the approximate percentage of participants that had a heart rate less than 130 bpm?
47%
In a sample of 775 senior citizens, approximately 67% said that they had seen a television commercial for life insurance. About how many senior citizens is this?
519
In a study of 1200 adults, 480 out of the 630 women in the study said they attended a state college or university. What percent of women attended a state college or university?
52.5%
Determine the interquartile range. 2, 3, 5, 8, 9, 12, 2, 3, 5, 8, 9, 12
6
A group of 500 patients who suffer from hypothyroidism, a condition in which your thyroid does not produce enough of certain hormones, were asked to participate in a study to determine the effectiveness of a new medication. The patients were randomly divided into two groups, one that was given the actual medication, and one that received a placebo pill. The results of the study are below. What percent of patients who took the medication had improved symptoms?
75.9%
Which of the following statements about bar graphs is true?
All of these are true for bar graphs.
Which of the following statements is not true about probability?
All of these are true statements
What is the difference between a bar chart and a histogram?
A bar chart represents categorical data and a histogram represents numerical data.
Which of the following are mutually exclusive events?
A car buyer chose "fuel efficiency" and "other" as their most important factor for their purchase.
Which of the following statements regarding the correlation coefficient is true?
A correlation coefficient of -1 means that as one variable increases, the other decreases.
The following calculator screenshots show the scatterplot and the correlation coefficient between the number of days absent and the final grade for a sample of college students in a general education statistics course at a large community college. The relationship between "days absent" and "final grade" can be described as
A strong negative linear relationship
The mean can be thought of as the balancing point of a distribution. According to this description, at what value is the following distribution balanced?
About 105
Use the following information to answer the question. The following linear regression model can be used to predict ticket sales at a popular water park. Ticket sales per hour = -631.25 + 11.25(current temperature in °F) What is the predicted number of tickets sold per hour if the temperature is 79°F? Round to the nearest whole ticket.
About 258 tickets
Determine which of the following five variables are numerical and which are categorical. age, gender, weight, ethnicity, favorite math class
Age and weight are numerical variables. Gender, ethnicity, and favorite math class are categorical variables.
What key things should you look for when examining the potential linear association between two variables?
All of Theses
If 20 babies are born, how often are there 8 or less male babies? Assume that the gender of a baby is a random event. Which of the following experiments would not simulate this situation?
All of these will simulate the gender of twenty babies.
What effects might an outlier have on a regression equation?
An outlier may affect both the slope and the correlation coefficient of a regression equation.
A group of junior high athletes was asked what team sport was their favorite. The data are summarized in the table below. On the pie chart, which area would correspond to the category "Soccer"?
Area A
A group of cancer patients is divided into two groups. One group is given a new drug to fight the side effects of chemotherapy and the other group is given a placebo. After three months they are asked to respond to a questionnaire about the frequency and severity of their side effects to see whether the new drug improved the overall negative side effects of chemotherapy.
Controlled experiment
Is the following an example of theoretical probability or empirical probability? A survey was conducted to determine a group of elderly adults' favorite breeds of dogs. He concludes that the probability that the elderly adults prefer a poodle is about 30%.
empirical
Marital status of each member of a randomly selected group of adults is an example of what type of variable?
Categorical variable
A class of 30 introductory statistics students took a quiz worth 100 points. The standard deviation of the scores was 0. What must be true about the students' scores?
Every student received the same score.
Here are the ages of the male and female employees at First River Bank. Compare the interquartile ranges of the ages of male and female employees.
Male: 7.5 Female: 10
The scatterplot below shows the hat size and IQ of some adults. Is the trend positive, negative, or near zero?
Near Zero
A study in the Los Angeles Times reported that the number of liquor stores in a neighborhood has a strong positive linear association with the amount of crime in that neighborhood. What can you determine about the relationship between the number of liquor stores and the amount of crime?
Neighborhoods with a higher number of liquor stores tend to have a higher amount of crimes.
The number of hours needed by sixth grade students to complete a research project was recorded. A student is selected at random. The events A and B are defined as follows. A = event the student took at most 8 hours B = event the student took at least 7 hours Are the events A and B mutually exclusive?
No
One question, summarized in the table below reflecting probabilities, asked each respondent to choose whether or not they use a cell phone app to shop. The major age groupings were under 40 or 40 years or older.
None of these
Classify the events as independent or not independent: Events A and B where the probability of event A occurring is 0.2, the probability of event B occurring is 0.3, and the probability of both event occurring is 0.05.
Not independent
Classify the events as independent or not independent: Events A and B where the probability of event A occurring is 0.5, the probability of event B occurring is 0.7, and the probability of both event occurring is 0.34.
Not independent
The five-number summary of the ages of a group of 100 adults is listed below. Consider the following two statements regarding outliers for this data and determine which, if any, are correct. (i) There is at least one adult whose age is a low outlier. (ii) There is at least one adult whose age is a high outlier.
Only statement (ii) is correct
A school board member says, "The typical bus ride to school for a student living in the city limits is more than the bus ride to school for a student living in the suburbs." What does this statement mean?
The center of the distribution of bus ride times for a city-dweller is more than the center of the distribution for those living in the suburbs
A city planner says, "The typical commute to work for someone living in the city limits is less than the commute to work for someone living in the suburbs." What does this statement mean?
The center of the distribution of commute times for a city-dweller is less than the center of the distribution for those living in the suburbs.
The bar charts below depict the marital statuses of Americans, separated by gender. Which bar chart shows more variability in marital status? Why?
The female bar chart shows more variability because there are more observations in the different categories than there are for males.
Use the following regression equation regarding car mileage to answer the question. Highway = 0.892 + 1.337 ∙ (City) Note that City is the estimated miles per gallon (mpg) a car gets while driving on city streets, and Highway is the estimated miles per gallon (mpg) a car gets while driving on highways. Interpret the intercept in the context of the data. State whether the value is meaningful.
The intercept is 0.892. If a car gets 0 mpg in the city, it will get 0.892 mpg on the highway. The value is not meaningful because if a car is not moving, it cannot have a mpg value.
Salary = 95000 + 1280 ∙ (Years) Note that Years is the number of years a professor has worked at a college, and Salary is the annual salary (in dollars) the professor earns. Interpret the intercept in the context of the data. State whether the value is meaningful.
The intercept is 95000. If a professor has completed 0 years of work at a college, his/her salary is expected to be $95,000. The value is meaningful because it represents the starting salary of a professor.
The distribution of the number of "friends" all users of a popular social media site have is strongly skewed to the right. Which of the following is true?
The median number of friends is smaller than the mean.
Suppose we have a distribution of the number of "friends" all users of a popular social media site have. What measure of spread would be best to describe this data?
The spread should be described with the IQR because the distribution will be skewed to the right.
The following histogram represents audience movie ratings (on a scale of 1-100) of 489 movies. What is the typical movie rating given by audiences according to this distribution?
The typical value is about 60.
Use the side-by-side boxplots below to answer the question. The boxplots summarize the number of sentenced prisoners by state in the Midwest and West. Using the boxplot for the West, determine which of the following statements about the distribution cannot be justified.
There are fewer states with 3887.5 to 6887 prisoners than states with 6887 to 15,706 prisoners.
A college instructor uses the model to predict the attention span of the students in her class who have an average age of 29. Choose the best statement to summarize why this is not an appropriate use for the model. attention span = 4.68 + 3.40(age)
This is an inappropriate use of the model because the model was used to make predictions beyond the scope of the data. The college instructor is extrapolating.
The age distribution of students at a community college is recorded. A student from the community college is selected at random. The events A and B are defined as follows. A = event the student is at most 24 B = event the student is at least 40 Are the events A and B mutually exclusive?
Yes
A group of 500 patients who suffer from hypothyroidism, a condition in which your thyroid does not produce enough of certain hormones, were asked to participate in a study to determine the effectiveness of a new medication. The patients were randomly divided into two groups, one that was given the actual medication, and one that received a placebo pill. The results of the study are below. Was the new medication effective in treating hypothyroidism?
Yes, a higher percent of patients who took the medication had improved symptoms than the patients who took the placebo.
Answer the question about the Law of Large Numbers. A fair coin is tossed 5000 times. What can you say about getting the outcome of exactly 2500 tails? a. Since the probability of a tail is 0.5 for each toss, you should expect exactly 2500 tails in 5000 tosses. b. You should not expect exactly 2500 tails in 5000 tosses, but the proportion of tails should approach 0.5 as the number of tosses increases. c. You should expect between 2400 and 2600 tails in 5000 tosses. d. Getting 2500 tails is no more likely than getting any other number of tails in 5000 tosses.
You should not expect exactly 2500 tails in 5000 tosses, but the proportion of tails should approach 0.5 as the number of tosses increases.
The table gives the GPA of some students in two math classes. One class meets in the morning and one in the afternoon. Is the format of the data set stacked or unstacked?
unstacked
The following nine values represent race finish times in hours for a randomly selected group of participants in an extreme 10k race (a 10k race with obstacles). Which of the following is closest to the mean of the following data set? 1.0, 1.2, 1.2, 1.3, 1.4, 1.5, 1.5, 1.7, 2.1
x is about 1.4 hours
A manager wishes to determine the relationship between the number of years the manager's sales representatives have been with the company and their average monthly sales (in thousands of dollars). Calculate the linear correlation coefficient.
0.632
Find the standard deviation for the given sample data. Round your answer to one more decimal place than is present in the original data. Christine is currently taking college astronomy. The instructor often gives quizzes. On the past seven quizzes, Christine got the following scores: 44 20 37 28 19 52 55
14.7
Use the following information to answer the question. The mean age of lead actors from the top ten grossing movies of 2007 was 36.4 years with a standard deviation of 9.87 years. Assume the distribution of the actors ages is approximately unimodal and symmetric. Between what two values would you expect to find about 68% of the lead actors ages?
26.53 and 46.27 years
Calculate the five-number summary for the following dataset. 51 53 62 34 36 39 43 63 73 79
34, 39, 52, 63, 79
The number of students enrolled in a college algebra class for the last seven semesters are listed below. Find the median. 60 61 55 57 64 58 58
58
The number of students enrolled in a college algebra class for the last seven semesters are listed below. Find the median. 71 68 68 76 72 73 68
71
A large state university conducted a survey among their students and received 400 responses. The survey asked the students to provide the following information: * Age * Year in School (Freshman, Sophomore, Junior, Senior) * Major What type of graph would you use to describe the variable Major?
A bar chart because Major is a categorical variable.
The histogram below shows the distribution of pass rates on a swimming test taken by all children who completed a four week summer swim course at the local YMCA. What is the typical pass rate for the swim test?
About 75%
A doctor is interested in determining whether a certain medication increases the risk of high blood pressure. He randomly selects 100 people for his study - 50 who will take the medication, and 50 who will take a placebo. He checks the patients' blood pressures weekly for six months.
Controlled experiment
A group of students is divided into two groups. One group is a given a new chewable vitamin and the other group is given a placebo. After six months they are asked to fill out a questionnaire and given a health exam to see whether the new vitamin has health benefits that are better than a placebo.
Controlled experiment
The scatterplot below shows the relationship between the ages of women when they first married and the ages when they had their first child. The correlation coefficient between the values is 0.9315. The regression equation for the data is = 6.404 + 0.955 ∙ (Age-married) Would it be appropriate to say that the age at which a woman first marries causes her to have her first child after that age?
No, correlation never implies causation.
A doctor is interested in determining whether a certain medication reduces migraines. She reviews her patients' medical records and finds that a higher proportion of people who take the medication have fewer migraines than those who did not take the medication.
Observational study
Parking at a university has become a problem. University administrators are interested in determining the average time it takes a student to find a parking spot. An administrator inconspicuously followed 180 students and recorded how long it took each of them to find a parking spot. Which of the following types of graphs should NOT be used to display information concerning the students parking times?
Pie Chart
What is the typical value for the histogram shown below?
Since the data are bimodal, there are two typical values - one is about 50 and the other is about 90.
The following side-by-side bar graph shows the level of post-secondary education achieved ten years after high school for graduates from the years 1999 and 2001. Use the bar graph to answer the question. What is the mode response for 2001?
Some College
The following data give the distribution of the types of houses in a town containing 22,000 houses: House Type cape garrison split Frequency 5500 8800 7700 Percentage 25% 35% 40%
Splits: 40% Capes: 25% Garrison: 35%
Suppose we have a data set of the number of car accidents per day in Los Angeles during the year 2013. The data was input into a spreadsheet manually by an assistant at the Department of Transportation. For one day in July 2013, he input that there were 14 car accidents; but there were actually only 140 that day. How will this error affect the measures of center for this data?
The mean will be lower than it should be, but the median will not be affected.
Use the following information to answer the question. Here is a table recording the number of deaths for the top thirteen worst U.S. tornados since 1925. A histogram showing the distribution is also included. The worst tornado on record since 1925 is a tornado that went through Missouri, Illinois, and Indiana on March 18, 1925. It killed 689 people. Suppose that when this value was entered into a calculator or other software a mistake was made and it was entered as 1,689. Choose the statement that describes what affect this mistake will have on the mean and median.
The median will not be affected by the error, but the mean will be higher than it should be.
A word cloud was created using the first chapter of John Green's The Fault in Our Stars. (Note that filler words such as "the," "a/an," and "and" were excluded from the plot.) According to the word cloud, what is the most common word in the first chapter of The Fault in Our Stars? Why?
The most common word is "augustus" because it is the largest in size.
Before opening a new dealership, an auto manufacturer wants to gather information about car ownership and driving habits of the local residents. The marketing manager of the company randomly selects 1000 households from all households in the area and mails a questionnaire to them. Of the 1000 surveys mailed, she receives 85 back. What is the problem with how the information is gathered?
The only responses were from people who chose to send the survey back.
Salary = 95000 + 1280 ∙ (Years) Note that Years is the number of years a professor has worked at a college, and Salary is the annual salary (in dollars) the professor earns. Interpret the slope in the context of the data.
The slope is 1280. For every additional year a professor works at a college, his/her salary is predicted to increase by $1,280.
Use your intuition to decide whether the following two events are likely to be independent or associated. Event A: Drawing a club from a deck of cards. Event B: Drawing a card with a black symbol from a deck of cards.
associated
A homeowner notices that 8 out of 14 days the mail arrives before 3pm. She concludes that the probability that the mail will arrive before 3pm tomorrow is about 57%. Is this an example of a theoretical or empirical probability?
empirical
Is the following an example of theoretical probability or empirical probability? A homeowner notes that five out of seven days the newspaper arrives before 5 pm. He concludes that the probability that the newspaper will arrive before 5 pm tomorrow is about 71%.
empirical
The annual profits of five large corporations in a certain area are given below. Which measure of central tendency should be used?
median