MATH-164 - Chapter 1 - 4 Review - Exam 1
Match the linear correlation coefficient to the scatter diagram. The scales on the x- and y-axis are the same for each scatter diagram. (a) r=−1, (b) r=−0.992, (c) r=−0.049
(a) Scatter diagram II. (b) Scatter diagram I. (c) Scatter diagram III. (The linear correlation coefficient is a measure of the strength of linear relation between two quantitative variables. If r=+1 there is a perfect positive linear relation between the two variables. The closer r is to +1, the stronger is the evidence of a positive association between the two variables.)
A sample of 20 registered voters was surveyed in which the respondents were asked, "Do you think Chang, Johnson, Ohm, or Smith is most qualified to be a senator?" The results of the survey are shown in the table. Smith Ohm Chang Chang Johnson Ohm Ohm Ohm Chang Ohm Ohm Johnson Johnson Chang Chang Ohm Chang Ohm Smith Ohm (a) Determine the mode candidate. (b) Do you think it would be a good idea to rotate the candidate choices in the question? Why?
(a) ohm (Statcrunch/table/select data/frequency/compute then select the name with the highest frequency) (b) Yes, to avoid response bias
A television station asks its viewers to call in their opinion regarding the variety of sports
Convenience
In a relative frequency distribution, what should the relative frequencies add up to?
The relative frequencies add up to 1.
Determine whether the quantitative variable is discrete or continuous. Number of days of rainfall in a year Is the variable discrete or continuous?
The variable is discrete because it is countable.
Determine whether the quantitative variable is discrete or continuous. Number of pieces of lumber used to make a deck Is the variable discrete or continuous?
The variable is discrete because it is countable.
Determine whether the variable is qualitative or quantitative. Weight Is the variable qualitative or quantitative?
The variable is quantitative because it is a numerical measure.
The linear correlation between violent crime rate and percentage of the population that has a cell phone is −0.918 for years since 1995. Do you believe that increasing the percentage of the population that has a cell phone will decrease the violent crime rate? What might be a lurking variable between percentage of the population with a cell phone and violent crime rate?
Will increasing the percentage of the population that has a cell phone decrease the violent crime rate? Choose the best option below. no. What might be a lurking variable between percentage of the population with a cell phone and violent crime rate? the economy
The data to the right represent the number of chocolate chips per cookie in a random sample of a name brand and a store brand. Complete parts (a) to (c) below. Name Brand Store Brand 25 24 25 23 29 15 33 28 26 19 27 17 22 22 21 26 20 28 22 24 20 21 23 33 30 27
(a) Draw side-by-side boxplots for each brand of cookie. Label the boxplots "N" for the name brand and "S" for the store brand. Choose the correct answer below. Graph B. (statcrunch/graph/boxplot/select Name brand & Store brand/ click Draw boxes horizontally/ at the bottom click Use same x-axes,y-axis/Compute) (b) Does there appear to be a difference in the number of chips per cookie? Yes. The name brand appears to have more chips per cookie. (c) Does one brand have a more consistent number of chips per cookie? Yes. The name brand has a more consistent number of chips per cookie.
A club wants to sponsor a panel discussion on an upcoming election. The club wants to have four of its members lead the panel discussion. To be fair, however, the panel should consist of two members of each party. Below is a list of members in each party. Obtain a stratified sample of two people from party 1 and two from party 2. Which of the following is a possible list of club members to lead the panel discussion?
Pawlak, Wright, Ochs, Keating
To determine customer opinion of their pricing, Amtrak randomly selects 100 trains during a certain week and surveys all passengers on the trains. What type of sampling is used?
Cluster
The following graphic is a newspaper-type graph displaying women's preference for shoes. (a) Which type of shoe is preferred the most? The least? (b) How is the graph misleading?
a. Flats are preferred the most. Extra dash high heel shoes are preferred the least. b. The heights of the shoe used are not representative of the corresponding percentage used.
Classify the variable as qualitative or quantitative. If the variable is quantitative, state whether it is discrete or continuous. Number of new automobiles sold at a dealership on a given day
Quantitative; discrete
The following data represent the amount of time (in minutes) a random sample of eight students took to complete the online portion of an exam in a particular statistics course. Compute the mean, median, and mode time. 63.7, 74.7, 82.4, 107.5, 128.4, 100.8, 94.7, 123.3
The mean exam time is 96.94. The median exam time is 97.75 The mode does not exist. (statcrunch/summary stats/columns/ select the data/statistics select Mean, Median, Mode)
Karl and Leonard want to make perfume. In order to get the right balance of ingredients for their tastes, they bought 3 ounces of rose oil at $2.05 per ounce, 3 ounces of ginger essence for $3.06 per ounce, and 3 ounces of black currant essence for $3.87 per ounce. Determine the cost per ounce of the perfume.
The cost per ounce of the perfume is $2.99 (2.05+3.06+3.87=8.98/3=2.99)
The median for the given set of six ordered data values is 33.5. 9 12 27 _ 41 49 What is the missing value?
The missing value is 40. Since the number of observations is even, the median is the mean of the two middle observations in the data set. Determine the positions of the two middle values. The two middle observations lie in the third and fourth positions. Thus, the median is the mean of the third and fourth observations in the data set as shown below, where x3 and x4 are the third and fourth observations in the data set, respectively. 27+x4/2=33.5 27+x4=2*33.5 x4=2*33.5-27 x4=40
For a poll of voters regarding a referendum calling for a national food and drug administration, design a sampling method to obtain the inviduals in the sample. Be sure to support your choice. Which sampling method would most likely be used in a poll of voters regarding a referendum calling for a national food and drug administration?
Use stratified random sampling. Since this is a national issue, different geographical locations are likely to have similar views.
The _________________ is the difference between consecutive lower class limits.
class width
Select the correct choice that completes the sentence below. For a distribution that is symmetric, the left whisker is ____________ the right whisker.
the same length as
Determine whether the following statement is true or false. Explain. When obtaining a stratified sample, the number of individuals included within each stratum must be equal.
False. Within stratified samples, the number of individuals sampled from each stratum should be proportional to the size of the strata in the population.
Determine whether the study depicts an observational study or an experiment. Office workers are randomly divided into two groups. One group takes meditation breaks throughout the day; the other takes 10-minute walks every 2 hours. After 1 month, each group is given a stress test to compare stress levels.
The study is an experiment because the researchers control one variable to determine the effect on the response variable.
____________________are the categories by which data are grouped.
Classes
The following graph is an ogive of a standardized test's scores. The vertical axis in an ogive is the cumulative relative frequency and can also be interpreted as a percentile. Complete parts a through c.
(a) Find and interpret the percentile rank of a test score with a value of 150. A test score of 150 corresponds to the 50th percentile rank since this percentage of test scores are less than or equal to a test score with a value of 150. (b) Find and interpret the percentile rank of a test score with a value of 160. A test score of 160 corresponds to the 80th percentile rank since this percentage of test scores are less than or equal to a test score with a value of 160. (c) What score corresponds to the 20th percentile? The 20th percentile corresponds to a test score of 140. (the information should be easily viewed from the graph.)
The accompanying data contains the depth (in kilometers) and magnitude, measured using the Richter Scale, of all earthquakes in a particular region over the course of a week. Depth is the distance below the surface at which the earthquake originates. A one unit increase in magnitude represents ground shaking ten times as strong (an earthquake with magnitude 4 is ten times as strong as an earthquake with magnitude 3). Complete parts (a) through (d) below.
(a) Find the mean, median, range, standard deviation, and quartiles for both the depth and magnitude of the earthquakes. Based on the values of the mean, median, and quartiles conjecture the shape of the distribution for depth and magnitude. Depth: μ=26..km; M=7.16km;Range=1514.01 km; σ=67.84km; Q1=2.54km; Q3=16.2km Magnitude: μ=1.625;M=1.29;Range=6.58; σ=1.25;Q1=0.88;Q3=1.845 (stat crunch/summary stats/columns/deph/click, Mean, Median, Range, Unadj. std. dev., Q1 &Q3/compute) Then do the same for magnitude Conjecture the shape of the distribution for depth. Choose the correct answer below. The mean is much larger than the median and is greater than Q3, so the distribution of depth is likely skewed right. Conjecture the shape of the distribution for magnitude. Choose the correct answer below. The mean is larger than the median, and the distance from Q1 to M is less than the distance from M to Q3, which suggests the distribution of magnitude is skewed right. The histograms for both depth and magnitude show skewed right distributions. The skewness is more defined for depth. (d) Determine the lower and upper fences for identifying outliers for both depth and magnitude. depth: lower fence=−17.95; upper fence=36.69 (Type integers or decimals rounded to two decimal places as needed.) magnitude: lower fence= −.57; upper fence=3.29
Arrange each of the steps in designing an experiment in the correct order. Drag each of the steps into the appropriate area below.
1. Identify the Problem to Be Solved. 2. Determine the Factors That Affect the Response Variable. 3. Determine the Number of Experimental Units. 4. Determine the Level of Each Factor. 5. Conduct the Experiment. 6. Test the Claim.
When the techniques used to select individuals to be in the sample favor one part of the population over another. When the individuals selected to be in the sample that do not respond to the survey have different opinions from those that do respond. When the answers on a survey do not reflect the true feelings of the respondent.
1. Sampling Bias 2. Nonreseponse Bias 3. Response Bias
Every possible sample of size n has an equally likely chance of occurring Separate the population into nonoverlapping groups and then obtain a simple random sample from each group. Select every kth individual from the population Select all the individuals within a randomly selected group of individuals. The individuals are easily obtained and not based on randomness. Studies based on this type of sampling method have results that are suspect.
1. Simple random sample 2. Stratified Sample 3. Systematic sample 4. Cluster Sample 5. Convenience Sample
What is a bar graph? What is a Pareto chart? What is a bar graph? What is a Pareto chart?
A bar graph is a horizontal or vertical representation of the frequency or relative frequency of the categories. The height of each rectangle represents the category's frequency or relative frequency. A Pareto chart is a bar graph whose bars are drawn in decreasing order of frequency or relative frequency.
A pharmaceutical company wants to conduct a survey of 25 individuals who have high cholesterol. The company has obtained a list from primary care physicians throughout the country of 4000 individuals who are known to have high cholesterol. Design a sampling method to obtain the individuals in the sample. Be sure to support the choice.
A. Group the individuals by common primary care physician. For each group, assign all the individuals different numbers, and use a random number table to select an appropriate number of individuals. C. Group the individuals by common primary care physician. Assign each physician a different number and use a random number table to select physicians until the total number of patients of all the selected physicians is at least 25. D. Alphabetize the list of 4000 individuals by last name and select one of the first 160 individuals at random. Starting from the selected individual, read down the list and select every 160th individual.
Determine whether the following study depicts an observational study or a designed experiment. A sample of 504 patients in the early stages of a disease is divided into two groups. One group receives an experimental drug; the other receives a placebo. The advance of the disease in the patients from the two groups is tracked at 1-month intervals over the next year.
Experiment
True or False: A data set will always have exactly one mode.
False
Determine whether the following statement is true or false. The shape of the distribution shown is best classified as uniform.
False (The graph is symetrical.)
Determine whether the following statement is true or false. The shape of the distribution shown is best classified as skewed left.
False, (The graph is skewed right.)
Each of the following three data sets represents the IQ scores of a random sample of adults. IQ scores are known to have a mean and median of 100. Sample of Size 5 Sample of Size 12 Sample of Size 30 107 107 107 98 98 98 116 116 116 94 94 94 106 106 106 93 93 99 99 96 96 115 115 117 117 105 105 119 119 113 98 106 114 109 112 103 100 114 110 117 109 95 118 108 91 94 104
For each data set, compute the mean and median. What is the mean of the sample of size 5? 104.2 (Statcrunch/summary stats/columns/select data, Sample size 5, sample size 12, sample size 30/mean/compute then use this information to fill in the rest of the answers) What is the mean of the sample of size 12? 105.4 (Type an integer or decimal rounded to one decimal place as needed.) What is the mean of the sample of size 30? 106 (Type an integer or decimal rounded to one decimal place as needed.) What is the median of the sample of size 5? 106 (Type an integer or decimal rounded to one decimal place as needed.) What is the median of the sample of size 12? 105.5 (Type an integer or decimal rounded to one decimal place as needed.) What is the median of the sample of size 30? 106.5 (Type an integer or decimal rounded to one decimal place as needed.) For each data set recalculate the mean and median, assuming that the individual whose IQ is 107 is accidentally recorded as 170. What is the mean of the new sample of size 5? 116.8 (Statcrunch / change the 107 to 170 for each data set/summary stats/columns/select data, Sample size 5, sample size 12, sample size 30/mean/compute then use this information to fill in the rest of the answers) What is the mean of the new sample of size 12? 110.7 (Type an integer or decimal rounded to one decimal place as needed.) What is the mean of the new sample of size 30? 108.1 (Type an integer or decimal rounded to one decimal place as needed.) What is the median of the new sample of size 5? 106 (Type an integer or decimal rounded to one decimal place as needed.) What is the median of the new sample of size 12? 105.5 (Type an integer or decimal rounded to one decimal place as needed.) What is the median of the new sample of size 30? 107 (Type an integer or decimal rounded to one decimal place as needed.) For each sample size, state what happens to the mean and median. For each sample size, the mean increases, and the median remains mostly constant. Comment on the role that the number of observations plays in resistance. As the sample size increases, the impact of the mis-recorded data on the mean decreases.
Determine whether the underlined numerical value is a parameter or a statistic. Explain your reasoning. A certain zoo found that 8% of its 843 were nocturnal
Parameter, because the data set of all 843 animals in a zoo is a population.
Maytag wants to administer a satisfaction survey to its current customers. Using their customerdatabase, the company randomly selects 30 customers and asks them about their level of satisfaction with the company.
Simple random
To determine her blood sugar level, Jean divides up her day into three parts: morning, afternoon, and evening. She then measures her blood sugar level at 3 randomly selected times during each part of the day. What type of sampling is used?
Stratified
Determine the type of sampling used. Thirty-five sophomores, 22 juniors, and 35 seniors are randomly selected to participate in a study from 574 sophomores, 462 juniors, and 532 seniors at a certain high school.
Stratified sample
To estimate the percentage of defects in a recent manufacturing batch, a quality control manager at Toyota selects every 11th car that comes off the assembly line starting with the second until she obtains a sample of 120cars.
Systematic
Mr. Zuro finds the mean height of all 16 students in his statistics class to be 67.0 inches. Just as Mr. Zuro finishes explaining how to get the mean, Danielle walks in late. Danielle is 68.7 inches tall. What is the mean height of the 17 students in the class?
The mean height of the 17 students in the class is 67.1 inches. 67.0=x1+x2+x16/16 67.0*16=x1+x2+x16 1,072=x1+x2+x16 1,072+68.7=1,140.7 xT=1,140.7/17 xT=67.1
In a statistics class, the standard deviation of the heights of all students was 4.1 inches. The standard deviation of the heights of males was 3.3 inches and the standard deviation of females was 3.1 inches. Why is the standard deviation of the entire class more than the standard deviation of the males and females considered separately?
The standard deviation of the entire class is more than the standard deviation of the males and females considered separately because the distribution of the entire class has more dispersion.
Is the statement below true or false? There is not one particular frequency distribution that is correct, but there are frequency distributions that are less desirable than others.
The statement is true. Any correctly constructed frequency distribution is valid. However, some choices for the categories or classes give more information about the shape of the distribution.
According to the National Center for Health Statistics, a 19-year-old female whose height is 67.1 inches has a height that is at the 85th percentile. Explain what this means.
This means that 85% of 19-year-old females have a height that is 67.1 inches or less, and 15% of 19-year-old females have a height that is more than 67.1 inches.
Determine whether the following statement is true or false. Explain. When conducting a cluster sample, it is better to have fewer clusters with more individuals when the clusters are heterogeneous.
True, because when the clusters are heterogeneous, they are scaled down versions of the population.
The data on the right relate to characteristics of high-definition televisions A through E. Identify the individuals, variables, and data corresponding to the variables. Determine whether each variable is qualitative, continuous, or discrete.
What are the individuals being studied? The high-definition television setups A through E. What are the variables and their corresponding data being studied? Size (48,46,43,43,50),screen type (Projection,Plasma, Plasma,Plasma, Plasma),and number of channels available(300,117,423,269,289) Determine whether each variable is qualitative, continuous, or discrete. Size is a continuous variable.
What does it mean to say that two variables are positively associated? Negatively associated?
What does it mean to say that two variables are positively associated? There is a linear relationship between the variables, and whenever the value of one variable increases, the value of the other variable increases. What does it mean to say that two variables are negatively associated? There is a linear relationship between the variables, and whenever the value of one variable increases, the value of the other variable decreases.
A sample of 100 randomly selected registered voters in a city was asked their political affiliation: Democrat (D), Republican (R), or Independent (I). The results of the survey are available below. Complete parts (a) through (e) below. (a) Construct a frequency distribution of the data. (e) What appears to be the most common political affiliation in the city?
a. Affiliation Frequency Democrat 46 Independent 16 Republican 38 b. Affiliation Frequency Democrat 0.46 Independent 0.16 Republican 0.38 c. statcrunch /bar plot/with data/select data/frequency d. statcrunch /pie chart/with data/select data e. The most common political affiliation is Democrat.
Explain the meaning of the accompanying percentiles. (a) The 10th percentile of the head circumference of males 3 to 5 months of age in a certain city is 41.0 cm. (b) The 80th percentile of the waist circumference of females 2 years of age in a certain city is 49.8 cm. (c) Anthropometry involves the measurement of the human body. One goal of these measurements is to assess how body measurements may be changing over time. The following table represents the standing height of males aged 20 years or older for various age groups in a certain city in 2015. Based on the percentile measurements of the different age groups, what might you conclude? Age 10th Percentile 25th Percentile 50th Percentile 75th Percentile 90th Percentile 20-29 166.8 171.5 176.7 181.4 186.8 30-39 166.9 171.3 176.0 181.9 186.2 40-49 167.9 172.1 176.9 182.1 186.0 50-59 166.0 170.8 176.0 181.2 185.4 60-69 165.3 170.1 175.1 179.5 183.7 70-79 163.2 167.5 172.9 178.1 181.7 80 or older 161.7 166.1 170.5 175.3 179.4
a. 10% of3- to5-month-old males have a head circumference that is 41.0 cm or less. b. 80% of 2-year-old females have a waist circumference that is cm or less c.At each percentile, the heights generally decrease as the age increases. Assuming that an adult male does not grow after age 20, the percentiles imply that adults born in 1990 are generally taller than adults who were born in 1950.
The following frequency histogram represents the IQ scores of a random sample of seventh-grade students. IQs are measured to the nearest whole number. The frequency of each class is labeled above each rectangle. Use the histogram to answers parts (a) through (g). (a) How many students were sampled? (b) Determine the class width. (c) Identify the classes and their frequencies. Choose the correct answer below. (d) Which class has the highest frequency? (e) Which class has the lowest frequency? (f) What percent of students had an IQ of at least 130? (g) Did any students have an IQ of 164?
a. 200 students (sum all the frequencies or numbers on top of the histogram) b. The class width is 10. c. 60-69, 2;70-79,3;80-89,13;90-99,48;100-109,52;110-119,40;120-129,30;130-139,9;140-149, 2;150-159, 1 d. 100-109 e. 150-159 f. 6% (To find the percent, first find the number of students that have IQ scores of at least 130. 9+2+1=12 then 12/200 x100=6) g. No, because there are no bars, or frequencies, greater than an IQ of 160.
The following graph represents the results of a survey, in which a random sample of adults in a certain country was asked if a certain action was morally wrong in general. Complete parts (a) through (c) below. (a) What percent of the respondents believe the action is morally acceptable? (b) If there are 275 million adults in the country, how many believe that the action is morally wrong? (c) If a polling organization claimed that the results of the survey indicate that 10% of adults in the country believe that the action is acceptable in certain situations, would you say this statement is descriptive or inferential? Why
a. About 70% of the respondents b. About 52 million adults (First determine the percent of adults who believe the action is morally wrong. From the chart, about 19% of adults believe the action is morally wrong. 275x19%=52) c. The statement is inferential because it makes a prediction. (Descriptive statements give information that is known. Inferential statements use known information to make predictions about unknown things that are related.)
Is there a relation between the age difference between husband/wives and the percent of a country that is literate? Researchers found the least-squares regression between age difference (husband age minus wife age), y, and literacy rate (percent of the population that is literate), x, is y=−0.0424x+8.2. The model applied for 17≤x≤100. Complete parts (a) through (e) below. (a) Interpret the slope. Select the correct choice below and fill in the answer box to complete your choice. (b) Does it make sense to interpret the y-intercept? Explain. Choose the correct answer below. (c) Predict the age difference between husband/wife in a country where the literacy rate is 43 percent. (d) Would it make sense to use this model to predict the age difference between husband/wife in a country where the literacy rate is 11%? (e) The literacy rate in a country is 98% and the age difference between husbands and wives is 2 years. Is this age difference above or below the average age difference among all countries whose literacy rate is 98%? Select the correct choice below and fill in the answer box to complete your choice.
a. For every unit increase in literacy rate, the age difference falls by 0.0424 units, on average. b. No—it does not make sense to interpret they-intercept because anx-value of 0 is outside the scope of the model. c. 6.4 years (y=−0.0424(43)+8.2.) d. No—it does not make sense because anx-value of 11 is outside the scope of the model. e. Below—the average age difference among all countries whose literacy rate is 98% is 4.0 years. (y=−0.0424(98)+8.2.)=4.0
A data set is given below. x y 1 5.3 2 5.9 4 4.9 5 3.1 6 2.3 6 2.7 (a) Draw a scatter diagram. Comment on the type of relation that appears to exist between x and y. (b) Given that x=4.0000, sx=2.0976, y=4.0333, sy=1.5161, and r=−0.9182, determine the least-squares regression line. (c) Graph the least-squares regression line on the scatter diagram drawn in part (a).
a. Graph A (statcrunch/graph/scatterplot/x variable, X/y variable, y/compute) There appears to be a linear, negative relationship. b. y= −0.664x+6.688 (statcrunch/stat/regression/simple linear/x variable, X/y variable, y/compute) C. Graph A (see the graph from the previous statcrunch)
Violent crimes include rape, robbery, assault, and homicide. The following is a summary of the violent-crime rate (violent crimes per 100,000 population) for all states of a country in a certain year. Complete parts (a) through (d). Q1=273.8, Q2=387.4, Q3=529.7 (a) Provide an interpretation of these results. Choose the correct answer below (b) Determine and interpret the interquartile range. Interpret the interquartile range. Choose the correct answer below. (c) The violent-crime rate in a certain state of the country in that year was 1,679. Would this be an outlier? (d) Do you believe that the distribution of violent-crime rates is skewed or symmetric? The violent-crime rate in a certain state of the country in that year was 1,679. Would this be an outlier?
a. 25% of the states have a violent-crime rate that is 273.8 crimes per 100,000 population or less. 50% of the states have a violent-crime rate that is 387.4 crimes per 100,000 population or less. 75% of the states have a violent-crime rate that is 529.7 crimes per 100,000 population or less. b. The interquartile range is 255.9 crimes per 100,000 population. (IQR=Q3-Q1 then 529.7-273.8=255.9) The middle 50% of all observations have a range of 255.9 crimes per 100,000 population. c. The lower fence is −110.05 crimes per 100,000 population. The upper fence is 913.55 crimes per 100,000 population. (Lower fence=Q1-1.5(IQR) / Upper fence-Q3+1.5(IQR) Lower fence 273.8-1.5(255.9)=-110.05 Upper fence 529.7+1.5(255.9)=913.55) Yes, because it is greater than the upper fence. d. The distribution of violent-crime rates is skewed right. (When data are either skewed left or skewed right, there are extreme values in the tail, which tend to pull the mean in the direction of the tail. For example, in skewed-right distributions, there are large observations in the right tail. Another way to determine whether the distribution is skewed or symmetric is to compare the difference Q2−Q1 to the difference Q3−Q2. If the differences are about equal, the distribution is symmetric. If the differences are not approximately equal, the distribution is skewed.)
Lyme disease is an inflammatory disease that results in a skin rash and flulike symptoms. It is transmitted through the bite of an infected deer tick. The following data represent the number of reported cases of Lyme disease and the number of drowning deaths for a rural county. Cases_of_Lyme_Disease Drowning_Deaths Month 3 0 J 1 1 F 3 2 M 4 1 A 5 2 M 15 10 J 22 16 J 13 5 A 6 3 S 5 3 O 4 1 N 1 0 D Critical Values for Correlation Coefficient n 3 0.997 4 0.950 5 0.878 6 0.811 7 0.754 8 0.707 9 0.666 10 0.632 11 0.602 12 0.576 13 0.553 14 0.532 15 0.514 16 0.497 17 0.482 18 0.468 19 0.456 20 0.444 21 0.433 22 0.423 23 0.413 24 0.404 25 0.396 26 0.388 27 0.381 28 0.374 29 0.367 30 0.361 Complete parts (a) through (c) below. (a) Draw a scatter diagram of the data. Choose the correct graph below. (b) Determine the linear correlation coefficient between Lyme disease and drowning deaths. (c) Does a linear relation exist between the number of reported cases of Lyme disease and the number of drowning deaths?
a. Graph D. (statcrunch/graph/scatterplot/x variable, cases of lyme disease/y variable, drowning deaths/compute) b. The linear correlation coefficient between Lyme disease and drowning deaths is r=0.964. (Open StatCrunch/Stat / Summary Stats / Correlation / Select column(s): Select both cases of lyme disease and drowning deaths / Compute) c. The variables Lyme disease and drowning deaths are positively associated because r is positive and the absolute value of the correlation coefficient, 0.964, is greater than the critical value, 0.576. Do you believe that an increase of Lyme disease causes an increase in drowning deaths? What is a likely lurking variable between cases of Lyme disease and drowning deaths? An increase in Lyme disease does not cause an increase in drowning deaths. The temperature and time of year are likely lurking variables.
A professor wanted to compare two types of teaching styles. One type is by tutorials and the other is giving a lecture. It is a common belief that tutorials result in better retention. This belief is tested by having 10 students learn a topic by each method and then having them take a test on their knowledge of the material that was covered. A coin flip was used to determine which type of teaching method a student would be given first. Results indicated that there was no difference in the two types of presentation. Complete parts (a) through (f) below. (a) What type of experimental design is this? (b) What is the response variable in this study? (c) What is the factor that is set to predetermined levels? What is the treatment? (d) Identify the experimental units. Choose the correct answer below. (e) Why is a coin used to decide the teaching method a student would be given first? (f) Draw a diagram to illustrate the design. Choose the correct diagram below.
a. Matched-pairs design b. The score on the test c. The factor is the type of presentation. The treatments are by tutorials and giving a lecture. d. The students e. To eliminate bias as to which presentation was used first. f. Figure 2 - Square blocks
The manager of a shopping mall wishes to expand the number of shops available in the food court. He has a market researcher survey the first 110 customers who come into the food court during weekday evenings to determine what types of food the shoppers would like to see added to the food court. Complete parts (a) and (b) below. (a) The survey has bias. Determine whether the flaw is due to the sampling method or the survey itself. For biased surveys, identify the cause of the error. What is the cause of the bias? (b) Suggest a remedy to the problem. Which of the following is the best way to remedy this problem?
a. Sampling bias b. Ask customers throughout the day on both weekdays and weekends.
Determine whether the scatter diagram indicates that a linear relation may exist between the two variables. If the relation is linear, determine whether it indicates a positive or negative association between the variables. Use this information to answer the following. a. Do the two variables have a linear relationship? b. If the relationship is linear do the variables have a positive or negative association?
a. The data points do not have a linear relationship because they do not lie mainly in a straight line. b. The relationship is not linear.
(a) Identify the shape of the distribution, and (b) determine the five-number summary. Assume that each number in the five-number summary is an integer. a. Choose the correct answer below for the shape of the distribution.
a. The distribution is skewed right. (the tail is longer on the right) b. The five-number summary is 0,1,4,7,19. (count the numbers on the graph for the numbers)
The data in the table to the right are based on the results of a survey comparing the commute time of adults to their score on a well-being test. Commute Time (in minutes) Well-Being Score 7 69.4 16 68.3 25 67.4 36 67.3 53 66.7 70 65.1 102 63.2 Complete parts (a) through (d) below. a. Which variable is likely the explanatory variable and which is the response variable? (b) Draw a scatter diagram of the data. Which of the following represents the data? (c) Determine the linear correlation coefficient between commute time and well-being score. (d) Does a linear relation exist between the commute time and well-being index score?
a. The explanatory variable is commute time and the response variable is the well-being score because commute time affects the well-being score. b. Graph B (statcrunch/graph/scatterplot/x variable, commute/y variable, well being score/compute) c. r=-0.986 (Open StatCrunch/Stat / Summary Stats / Correlation / Select column(s): Select both commute time and score / Compute) d. Yes, there appears to be a negative linear association because r is negative and is less than the opposite of the critical value. (To determine if a linear relation exists, compare the linear correlation coefficient to the critical value. If the linear correlation coefficient is greater than the critical value, there is a positive linear association. If the linear correlation coefficient is less than the negative of the critical value, there is a negative linear association. Otherwise, there is no linear association. The critical value with n=7, rounded to three decimal places, is 0.754. The absolute value of the linear correlation coefficient is 0.978. The absolute value of the linear correlation coefficient is greater than the critical value since |-0.986|>0.754.)
Will the following variables have positive correlation, negative correlation, or no correlation?
positive
The following data represent exam scores in a statistics class taught using traditional lecture and a class taught using a "flipped" classroom. Complete parts (a) through (c) below. (a) Which course has more dispersion in exam scores using the range as the measure of dispersion? (b) Which course has more dispersion in exam scores using the sample standard deviation as the measure of dispersion? (c) Suppose the score of 59.4 in the traditional course was incorrectly recorded as 594. How does this affect the range?
a. The traditional course has a range of 27.6, while the "flipped" course has a range of 28.4. The flipped course has more dispersion. (The range, R, of a variable is the difference between the largest data value and the smallest data value. Look at the data set, find the largest for the traditional and the smallest. Subtract to find the range for the traditional course. Do the same for the flip. The one with the largest number has more dispersion) b. The traditional course has a standard deviation of 8.790, while the "flipped" course has a standard deviation of 7.681. The traditional course has more dispersion. (Statcrunch/summary stats/columns/select data, Traditional, Flipped/std. dev/compute) c. The range is now 537.6. (Recalculate the range based on this change to the data set. The largest value is now 594, while the smallest value is now 56.4. Subtract to find the new range. 594-56.4=537.6) How does this affect the standard deviation? The standard deviation is now 144.852. (Recalculate the Standard deviation based on this change to the data set. Change the 59.4 for 594 and re-calculate the std. dev on the traditional data set) What property does this illustrate? Neither the range nor the standard deviation is resistant.
The data represent the age of world leaders on their day of inauguration. Find the five-number summary, and construct a boxplot for the data. Comment on the shape of the distribution. 43 44 67 63 50 48 55 46 51 52 46 61 56 51 44
a. The five-number summary is 43,46,51,56,67. (statcrunch/summary stats/columns/ Min,Q1,Median,Q3,Max/Compute) Graph B (statcrunch/graph/boxplot/ click Draw boxes horizontally/Compute) The distribution is skewed to the right.
The table shows the weekly income of 20 randomly selected full-time students. If the student did not work, a zero was entered. (a) Check the data set for outliers. (b) Draw a histogram of the data. (c) Provide an explanation for any outliers. 476 478 0 365 0 77 0 438 0 469 98 443 3096 518 228 505 343 374 180 523
a. The outlier(s) is/are 3096. (stat crunch/summary stats/columns/select data/click, Q1 &Q3/compute - then compute Lower fence and upper fence Lower fence=Q1-1.5(IQR) / Upper fence-Q3+1.5(IQR) A data point is considered an outlier using this method if it is less than the lower fence, , or greater than the upper fence.) or just look at the data and pick the large number. b. Graph B. (Do a histogram, select data, bins: start at 0, width at 100.) c. A student with unusually high income A student providing false information Data entry error
The data available below represent the average number of hours per week that a random sample of 40 college students spend online. The data are based on a study of undergraduate students and information technology. Construct a stem-and-leaf diagram of the data and comment on the shape of the distribution. 18.9 22.9 18.6 15.2 13.6 14.0 22.2 18.0 16.4 20.1 24.4 13.4 21.1 14.5 15.3 17.4 18.8 15.6 17.1 19.2 13.7 15.1 16.6 25.7 23.4 16.5 21.9 20.6 17.4 14.5 14.8 21.1 17.3 18.8 18.6 20.8 14.7 17.9 17.1 23.8
a. statcrunch/graph/Stem and Leaf/Leaf unit/Select 0.1 The distribution is skewed right.
A pediatrician wants to determine the relation that exists between a child's height, x, and head circumference, y. She randomly selects 11 children from her practice, measures their heights and head circumferences, and obtains the accompanying data. Height (inches), x Head Circumference (inches), y 27.5 17.8 24.5 17.3 25.5 17.3 26 17.8 24.25 17.1 28 17.9 26.5 17.6 27.25 17.8 26 17.5 26 17.7 28 17.8 Complete parts (a) through (g) below (a) Find the least-squares regression line treating height as the explanatory variable and head circumference as the response variable. (b) Interpret the slope and y-intercept, if appropriate.First interpret the slope. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.Interpret the y-intercept, if appropriate. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (c) Use the regression equation to predict the head circumference of a child who is 24.25 inches tall. (d) Compute the residual based on the observed head circumference of the 24.25-inch-tall child in the table. Is the head circumference of this child above or below the value predicted by the regression model? (e) Draw the least-squares regression line on the scatter diagram of the data and label the residual from part (d). Choose the correct graph below. (f) Notice that two children are 26 inches tall. One has a head circumference of 17.5 inches; the other has a head circumference of 17.7 inches. How can this be? (g) Would it be reasonable to use the least-squares regression line to predict the head circumference of a child who was 32 inches tall? Why?
a. y=0.183x+12.8b. For every inch increase in height, the head circumference increases by 0.183 in., on average. It is not appropriate to interpret the y-intercept. (statcrunch/stat/regression/simple linear/x variable, X/y variable, y/compute) c. y=17.24 in. (y=0.183(24.25)+12.8) d. The residual for this observation is −.14, meaning that the head circumference of this child is below the value predicted by the regression model. (17.1-17.24=-.14) e. Graph A (statcrunch/stat/regression/simple linear/x variable, X/y variable, y/compute) see graph f. For children with a height of 26 inches, head circumferences vary. No—this height is outside the scope of the model.(look at the data all subjects were under 28-inch height)
The data to the right represent the weights (in grams) of a random sample of 50 candies. 0.85 0.85 0.86 0.81 0.85 0.87 0.98 0.83 0.85 0.86 0.83 0.88 0.77 0.83 0.97 0.83 0.71 0.83 0.71 0.82 0.91 0.76 0.76 0.92 0.85 0.91 0.86 0.86 0.81 0.76 0.98 0.82 0.76 0.75 0.82 0.77 0.83 0.85 0.87 0.76 0.76 0.96 0.75 0.72 0.85 0.85 0.88 0.95 0.95 0.83 Complete parts (a) through (f). (a) Determine the sample standard deviation weight. (b) On the basis of the histogram to the right, comment on the appropriateness of using the Empirical Rule to make any general statements about the weights of the candies. (c) Use the Empirical Rule to determine the percentage of candies with weights between 0.700 and 0.976 grams. Hint:x=0.838 (d) Determine the actual percentage of candies that weigh between 0.700 and 0.976 grams, inclusive. (e) Use the Empirical Rule to determine the percentage of candies with weights more than 0.907 gram. (f) Determine the actual percentage of candies that weigh more than 0.907 gram.
a. 0.069gram(s) (Statcrunch/summary stats/columns/select data/Unadj. std. dev/compute) b. The histogram is approximately bell-shaped so the Empirical Rule can be used. (The Empirical Rule says that if a distribution is roughly bell shaped, the following is true. · Approximately 68% of the data will lie within 1 standard deviation of the mean. · Approximately 95% of the data will lie within 2 standard deviations of the mean. · Approximately 99.7% of the data will lie within 3 standard deviations of the mean.) c. 95% d. 95% e.16% f. 18%
The side-by-side bar graph available below shows the approximate average grade point average for the years 1991-1992, 1996-1997, 2001-2002, and 2006-2007 for colleges and universities. Complete parts (a) through (c) below. (a) Does the graph suggest that grade inflation is a problem in colleges? (b) In public schools, the average GPA was 2.86 in 1991-1992 and 3.02 in 2006-2007. In private schools, the average GPA was 3.09 in 1991-1992 and 3.30 in 2006-2007. Determine the percentage increase in GPAs for public schools from 1991 to 2006. Determine the percentage increase in GPAs for private schools from 1991 to 2006. Which type of institution appears to have the higher inflation? (c) Do you believe the graph is misleading?
a. Yes, because the GPAs increased over time for all schools. b. The increase is 66% for public schools and 77% for private schools. So, private schools appear to have the higher inflation. c. Yes, because the vertical axis does not start at 0.
On an international exam, students are asked to respond to a variety of background questions. For the 41 nations that participated in the exam, the correlation between the percentage of items answered in the background questionnaire (used as a proxy for student task persistence) and mean score on the exam was 0.718. Does this suggest there is a linear relation between student task persistence and achievement score? Write a sentence that explains what this result might mean. Critical Values for Correlation Coefficient n 3 0.997 4 0.950 5 0.878 6 0.811 7 0.754 8 0.707 9 0.666 10 0.632 11 0.602 12 0.576 13 0.553 14 0.532 15 0.514 16 0.497 17 0.482 18 0.468 19 0.456 20 0.444 21 0.433 22 0.423 23 0.413 24 0.404 25 0.396 26 0.388 27 0.381 28 0.374 29 0.367 30 0.361 a. Does this suggest there is a linear relation between student task persistence and achievement score? Choose the best response below. b. What does this result mean?
a. Yes, since 0.718 is greater than the critical value for 30. b. Countries in which students answered a greater percentage of items in the background questionnaire tended to have higher mean scores on the exam.
The data available below represent the diameter (in inches) of a random sample of 34 of a particular brand of chocolate chip cookie. Complete parts (a) through (d) below. (a) Construct a frequency distribution of the data.
a./b Class Frequency 2.2000-2.2199 - 22 2.2200-2.2399 - 33 2.2400-2.2599 - 55 2.2600-2.2799 - 66 2.2800-2.2999 - 44 2.3000-2.3199 - 77 2.3200-2.3399 - 55 2.3400-2.3599 - 11 2.3600-2.3799 - 1 (statcrunch /data/bin/select data/use fixed with with bins/start 2.200/binwidth 2.2000-2.2200=0.02 then do a frequency table using the bin data. stat/tables/frequency/select bin data/frequency and relative frequency) c. statcrunch/graph/histogram/frequency The distribution is symmetric. d. statcrunch/graph/histogram/relative frequency
Select the correct choice that completes the sentence below. For a distribution that is skewed right, the median is _______ of the box.
left of center
For a distribution that is skewed left, the left whisker is ________________ the right whisker.
longer than
The ______ class limit is the smallest value within the class and the ______ class limit is the largest value within the class.
lower upper
The accompanying frequency distribution represents the travel time to work (in minutes) for a random sample of 895 adults in a certain country. (a) Approximate the mean travel time to work for adults in this country. (b) Approximate the standard deviation travel time to work for adults in this country. Travel Time (minutes) Frequency 0-9 125 10-19 271 20-29 186 30-39 121 40-49 54 50-59 62 60-69 43 70-79 20 80-89 13
(a) The mean travel time is 27.2 minutes. (Statcrunch/summary stats/Group/Binned data/Binned in, Travel Time/Counts in, Frequency /click limits/Mean/compute) (b) The standard deviation travel time is 19.1 minutes. (Statcrunch/summary stats/Group/Binned data/Binned in, Travel Time/Counts in, Frequency /click Consecutive lower limits/Unadj. Std. dev/compute)
Clarissa has just completed her second semester in college. She earned a grade of D in her 3-hour topology course, a grade of B in her 2-hour economics course, a grade of D in her 4-hour engineering course, and a grade of C in her 4-hour philosophy course. Assuming that A equals 4points, B equals 3points, C equals 2points, D equals 1point, and F is worth nopoints, determine Clarissa's grade-point average for the semester.
Clarissa's grade point average is 1.62 total the number, of course, hours Σwi= total hrs For the weighted mean formula, multiply each numerical grade by the corresponding hrs. Σxiwi= Find the sum of the xiwi. Σxiwi= total Now use the formula given earlier to compute the weighted mean. xw=ΣxiwiΣwi=total/total hrs=GPA