Math 140 final
A statistics teacher taught a large introductory statistics class, with 500 students having enrolled over many years. The mean score over all those students on the first midterm was 𝜇=68 with standard deviation 𝜎=20 . One year, the teacher taught a much smaller class of only 25 students. The teacher wanted to know if teaching a smaller class affected scores in any way. We can consider the small class as an SRS of the students who took the large class over the years. The average midterm score was 𝑥¯=78 . The hypothesis the teacher tested was 𝐻0:𝜇=68 vs. 𝐻𝛼:𝜇≠68 The 𝑃P‑value for this hypothesis was found to be: 0.0233. 0.0062. 0.0124. 0.0248.
0.0124
An economist conducted a study of the possible association between weekly income and weekly grocery expenditures. The particular interest was whether higher income would result in shoppers spending more on groceries. A random sample of shoppers at a local supermarket was obtained, and a questionnaire was administered asking about the weekly income of the shopper's family and the grocery bill for that week. The gender of the shopper was also obtained. The correlation was found to be 𝑟=0.649 . The standard deviation for the grocery bills was 37.87, and for income it was 309.04 . Therefore, the slope of the least-squares line is: 0.0795 .0.0021 5.296. 0.649
0.0795
The average time taken for your Internet service provider to remotely resolve a trouble ticket has a Normal distribution, with a mean of 4.3 hours and a standard deviation of 3.1 hours. What percentage of the tickets are resolved in less than half an hour? 11.01 % 14.5% 85.5% 89.1%
11.01 %
For each of the states and Puerto Rico, the histogram below shows the average property damage (in millions of dollars) caused by tornadoes over a 50-year period. From the histogram, the median must be approximately: 25 . 30. 40. 15 .
15
You measure the lifetime of a random sample of 64 tires of a certain brand. The sample mean is 𝑥¯=50 months. Suppose that the lifetimes for tires of this brand follow a Normal distribution, with unknown mean 𝜇μ and standard deviation 𝜎=5 months, then a 99% confidence interval for μ is: 48.39 to 51.61. 49.8 to 50.2. 48.78 to 51.22. 40.2 to 59.8.
48.39 to 51.61.
Running times for 400meters are Normally distributed for young men between 18 and 30years of age, with a mean of 93 seconds and a standard deviation of 16 seconds. What would a man's running time have to be to put him in the top 11 % of runners? 130.2seconds 55.8seconds 51.8seconds 134.2 seconds
55.8seconds
The following is a histogram showing the distribution per year of the cumulative property damage caused by tornadoes, over the period 1950 to 1999, in each of the 50 states and Puerto Rico. The data are in millions of dollars, and the class intervals are 00 to <10<10 , 1010 to <20<20 , and so forth. The histogram:shows one high outlier. All of the answer options are correct. is skewed to the right. has a center of about $1010 million dollars.
All of the answer options are correct.
I collect a random sample of size n from a population and compute a 95% confidence interval for the proportion I observe from the population. What could I do to produce a new confidence interval with a smaller width, smaller margin of error, based on these same data? I could use a smaller confidence level. I could use a larger confidence level I could use the same confidence level but compute the interval n times; approximately 5% of these intervals will be larger. Nothing can guarantee absolutely that I will get a smaller interval; I can only say the chance of obtaining a smaller interval is 0.05.
I could use a smaller confidence level.
DDT is a pesticide banned in the United States for its danger to humans and animals. In an experiment on the impact of DDT, six rats were exposed to DDT poisoning and six rats were not exposed. For each rat in the experiment, a measurement of nerve sensitivity was recorded. The researchers suspected that the mean nerve sensitivity for rats exposed to DDT is greater than that for rats not poisoned. The data is displayed. Poisoned rats12.20716.86925.05022.4298.45620.589Unpoisoned rats11.0749.68612.0649.3518.1826.642 Let 𝜇1μ1 be the mean nerve sensitivity for rats poisoned with DDT. Let 𝜇2μ2 be the mean nerve sensitivity for rats not poisoned with DDT. The 𝑃P‑value for this test was between 0.01 and 0.05. Which statement is a reasonable conclusion? There is fairly strong evidence to support a conclusion that the mean nerve sensitivity is greater in rats exposed to DDT than in rats not exposed to DDT. This test is unreliable, because the populations we are sampling from are heavily skewed. There isn't much evidence to support a conclusion that the mean nerve sensitivity is greater in rats exposed to DDT than in rats not exposed to DDT. There are outliers in these data, so we can't rely on the two‑sample 𝑡t test.
There is fairly strong evidence to support a conclusion that the mean nerve sensitivity is greater in rats exposed to DDT than in rats not exposed to DDT.
The owner of a chain of supermarkets notices that there was a positive correlation between the sales of beer and the sales of ice cream over the course of the previous year. During seasons when sales of beer were above average, sales of ice cream also tended to be above average. Likewise, during seasons when sales of beer were below average, sales of ice cream also tended to be below average. The owner is curious whether the observed association is due to a cause-and-effect relationship between eating ice cream and desiring beer. To investigate this, the owner should use: a well-designed experiment. the least-squares regression line. the correlation coefficient. the square of the correlation coefficient.
a well-designed experiment.
For this density curve, the mean is: less than the median. not possible to determine from the information given. equal to the median.
equal to the median.
A statistician wishing to test a hypothesis that students score at most 75% on the final exam in an introductory statistics course decides to randomly select 20 students in the class and have them take the exam early. The average score of the 20 students on the exam is 72% and the standard deviation in the population is known to be 𝜎=15%σ=15% . The statistician calculates the test statistic to be −0.8944−0.8944 . If the statistician chose to do a two‑sided alternative, the P‑value would be calculated by: finding the area to the right of the absolute value of −0.8944 and dividing it by two. finding the area to the left of −0.8944. finding the area to the right of −0.8944 and doubling it. finding the area to the left of −0.8944 and doubling it.
finding the area to the left of −0.8944 and doubling it.
Enteroliths are calcifications that form in the gut of a horse. The stones can cause considerable morbidity and mortality. A study was conducted to investigate the factors (such as diet and environment) that may be related to the formation of enteroliths. The study contained 62 horses with enteroliths (cases) and 75 horses without (controls). The graph below contains side-by-side boxplots of the ages for cases and controls. Based on the boxplots, the mean age for the cases: is higher than the mean age for the controls. cannot be determined from boxplots. is approximately the same as the mean age for the controls. is lower than the mean age for the controls.
is lower than the mean age for the controls.
Enteroliths are calcifications that form in the gut of horses. The stones can cause considerable morbidity and mortality. A study was conducted to investigate factors (such as age, diet, and environment) that may be related to the formation of enteroliths. The researchers decided to draw two histograms: one for horses with enteroliths (cases) and one for horses without (controls). The number of horses 20 years and older: is larger among the cases. cannot be determined from the histogram. is about the same for both. is smaller among the cases.
is smaller among the cases.
The graph below shows a distribution that is called a chi-squared distribution. For this distribution, the median: is larger than the mean 𝜇 . is smaller than the mean 𝜇. is equal to the mean 𝜇 . cannot be determined from the graph.
is smaller than the mean 𝜇.
The average age of residents in a large residential retirement community is 69 years with standard deviation 5.8 years. A simple random sample of 100 residents is to be selected, and the sample mean age 𝑥¯ of these residents is to be computed. We know the random variable 𝑥¯ has approximately a Normal distribution because: of the central limit theorem. of the law of large numbers. of the 68‑95‑99.7 rule. the population from which we're sampling has a Normal distribution.
of the central limit theorem.
When water flows across farmland, some soil is washed away, resulting in erosion. An experiment was conducted to investigate the effect of the rate of water flow (liters per second) on the amount of soil (kilograms) washed away. The data are given in the following table: Flow rate0.310.851.262.473.75Eroded soil0.821.952.183.016.07 The association between flow rate and the amount of eroded soil is: neither positive nor negative. positive. impossible to determine, because both variables are categorical. negative.
positive
A researcher wants to determine whether the rate of water flow (in liters per second) over an experimental soil bed can be used to predict the amount of soil washed away (in kilograms). The researcher measures the amount of soil washed away for various flow rates, and from these data calculates the least-squares regression line to be: amount of eroded soil =0.4+1.3(where 𝑥x is flow rate). The correlation between amount of eroded soil and flow rate would be: positive, but we cannot say what the exact value is. 1/1.3. either positive or negative, but it is impossible to say anything about the correlation from the information given.
positive, but we cannot say what the exact value is.
In a class of 100100 students, the grades on an accounting test are summarized in the following frequency table: Grade91-100 81-90 71-80 61-70 Frequency 11 31 42 16 The distribution of grades is: not able to be determined from the information given. skewed right. skewed left. symmetric.
skewed right.
John's parents recorded his height at various ages up to 6666 months. Below is a record of the results. Age (months)3648546066Height (inches)3538414345 John's parents decide to use the least-squares regression line of John's height on age to predict his height at age 2121 years (252252months). We conclude that: John's height (in inches) should be about half his age (in months). All of the answer options are correct. John's parents will get a fairly accurate estimate of his height at age 2121 years, because the data are clearly correlated. such a prediction could be misleading, because it involves extrapolation.
such a prediction could be misleading, because it involves extrapolation.
An educator wishes to study the effects of sleep deprivation on the ability to concentrate. He decides to study the students in a calculus class. Before the start of the class, each student is asked about the number of hours slept the previous night. Each student's eye movement is then tracked throughout the lecture. The amount of time is recorded whenever the student is not focused on either the instructor or taking notes. The class is held at 11 a.m. and the instructor also asks questions about prior classes that day. The response variable is: the amount of time not focused. the number of hours slept the night before. the number of prior classes that day. the time of day the class is given.
the amount of time not focused.
Which choice does not determine the sampling distribution?t he population variance the population meant he sample sizet he population size
the population size
Which of the quantities must be known before calculating the margin of error? the population size All of the answer options are correct. the population mean the population variance
the population variance
The significance level is defined as: None of the answer options are correct. the probability of a Type I error. the probability that the power of the test is at least 0.9. the probability of a Type II error.
the probability of a Type I error.
The scores on the Wechsler Adult Intelligence Scale are approximately Normal, with 𝜇=100 and 𝜎=15σ. The proportion of adults with scores above 110 is closest to: 0.35 .0.08 0.25 .0.10
0.25
A researcher plans to conduct a test of hypotheses at the 𝛼=0.10 significance level. She designs her study to have a power of 0.7 at a particular alternative value of the parameter of interest. The probability that the researcher will commit a Type II error for the particular alternative value of the parameter at which she computed the power is: 0.7 0.3. 0.1 equal to 1−𝑃‑value and cannot be determined until the data have been collected.
0.3
An economist conducted a study of the possible association between weekly income and weekly grocery expenditures. The particular interest was whether higher income would cause shoppers to spend more on groceries. A random sample of shoppers at a local supermarket was obtained. A questionnaire was administered asking about the weekly income of each shopper's family and their grocery bill for that week. The gender of each shopper was also obtained. The data below are expenditures and income for 1010 selected survey participants. Income 98 201 298 398 481 Grocery 52 78 108 121 The correlation for -0.4212 . -0.649 0.649 0.4212
0.649
For each menu item at a fast food restaurant, the fat content (in grams) and the number of calories were recorded. A scatterplot of these data is given: The restaurant decides to add six new high-calorie, low-fat pasta dishes to its menu. What is a plausible value for the new correlation coefficient describing the relationship between fat and calories? -0.7. +0.7 . +0.2. -0.2.
0.7
For this density curve, the third quartile is: 0.5 0.75 1.75 1.5
1.5
A survey of 1010 students was conducted to investigate the amount of time they spend on social media each day. Students were given a timer and asked to record the number of minutes spent every time they accessed social media. The students' total times for one day are given below (in minutes). 45 57 63 79 84 92 99 105 117 145 The first quartile for these data is: 105 92. 63. 88.
63
The 18 faculty members in a college math department range in age from 32 to 68 . A stemplot follows: 34562033434885796899993248994035695347899638 The 1.51.5 × 𝐼𝑄𝑅IQR rule would identify an age as a high outlier if it exceeded: 77 years. 28.5 years. 191years. 86.5years.
77
A 99% confidence interval for the mean 𝜇μ of a population is computed from a random sample and found to be 6±3 . We may conclude that: if we took many additional random samples and computed a 99% confidence interval for μ from each, approximately 99% of these intervals would contain μ . all of the answer options are correct. there is a 99% probability that the true mean is 6, and there is a 99% chance that the true margin of error is 3. there is a 99% probability that 𝜇μ is between 3 and 9.
if we took many additional random samples and computed a 99% confidence interval for μ from each, approximately 99% of these intervals would contain μ .
If the confidence level is increased from 90% to 99% for an SRS of size 𝑛n , the width of the confidence interval for the mean 𝜇 will: decrease. stay the same. increase. The answer cannot be determined from the information given.
increase.
When designing a test of inference, which of the given will increase the power of the test? increasing the effect size increasing the significance level increasing the sample size None of the answer options are correct.
increasing the sample size
Birth weights at a local hospital have a Normal distribution, with a mean of 110 oz and a standard deviation of 15 oz. The proportion of infants with birth weights between : .477 .136 .636 .819
.136
Researchers doing a study comparing time spent on social media and time spent on studying randomly sampled 200 students at a major university. They found that students in the sample spent an average of 2.3 hours per day on social media and an average of 1.8 hours per day on studying. If all the students at the university in fact spent 2.2 hours per day on studying, with a standard deviation of 2 hours, the probability of getting a sample average of 1.8 or less is: 0.9977. 0.0023. 0.5893. 0.4207.
0.0023.
In a large population of college‑educated adults, the mean IQ is 112 with standard deviation 25. Suppose 300 adults from this population are randomly selected for a market research campaign. The probability that the sample mean IQ is greater than 115 is: 0.528 0.019 .0.452. 0.981.
0.019
The typical college freshman spends an average of 𝜇=150 minutes per day, with a standard deviation of 𝜎=50 minutes, on social media. The distribution of time on social media is known to be Normal. The third quartile is: 0.75minutes. 183.72 minutes. 0.25minutes. 116.27 minutes.
183.72 minutes.
Some of the variables from a survey conducted by the U.S. Census Bureau are the number of people living in a household, the total household gross income, and the ages of household residents. Which of the variables is quantitative? the ages of household residentsthe number of people living in a household All of the answer options are correct .the total household gross income
All of the answer options are correct
A sociologist studying freshmen at a major university carried out a survey, asking, among other questions, how often students went out per week, how many hours they studied per day, and how many hours they slept at night. The sociologist used an introductory sociology class to carry out the survey and asked only the freshmen to answer the questions. The sample is called: a targeted sample. a volunteer sample. a random sample. a convenience sample.
a convenience sample.
Using the standard Normal distribution tables, the area under the standard Normal curve corresponding to -0.5<𝑍<1.2is: 0.8849 0.5764 0.3085 0.2815
0.5764
If the probability that you fail to reject the null hypothesis is 20% when you should have rejected it because there is a real effect that you were unable to detect, given your data, the power of the test is: 0.8. 0.9. It is not possible to determine the power without knowing the sample size. 𝛽
0.8
A 95% confidence interval for the mean hours freshmen spent on social media per day was calculated to be (2.5 hours, 3.1 hours). The confidence interval was based on an SRS of size 𝑛=50 . The standard deviation is given by: 0.3. 1.0823 0.2772. 1.96.
1.0823
Enteroliths are calcifications that form in the gut of a horse. The stones can cause considerable morbidity and mortality. A study was conducted to investigate the factors (such as diet and environment) that may be related to the formation of enteroliths. The study contained seven stallions; their ages (in years) are as follows: 1020413211616 The 𝐼𝑄𝑅IQR of age for the stallions is: 17 . 10 . 16 . 21 .
10
A sample of 𝑛=25 diners at a local restaurant had a mean lunch bill of $16 with a standard deviation of 𝜎=$5 . The margin of error for a 98% confidence interval is given by: 1.96. 2.33. 1.65. 2.575.
2.33.
An appropriate graphical way to display housing (stall, small paddock, large paddock, pasture, or other housing) for horses is given by: a stemplot. a pie chart. All of the answer options are correct.a histogram.
a pie chart.
A poll was conducted of more than 5050 ,000000 buyers of new cars, 9090 days after the cars were purchased. The data on problems per 100100 vehicles for cars made by Toyota and General Motors (GM) are given in the time plot below for the years 1998-2004.1998-2004. The solid line is for GM and the dashed line is for Toyota. In 2002 , the number of problems per 100 vehicles was: about 20 % higher for GM than for Toyota. about twice as high for GM as for Toyota. about twice as high for Toyota than for GM. about 20 % higher for Toyota than for GM.
about 20 % higher for GM than for Toyota.
A modified boxplot for a right-skewed data set uses a special character to point to :the maximum. an outlier. the median. the third quartile.
an outlier.
The volume of oxygen consumed (in liters per minute) while a person is at rest and while a person is exercising (running on a treadmill) were both measured for 50 subjects. The goal is to determine if the volume of oxygen consumed during aerobic exercise can be estimated from the amount consumed at rest. The results are plotted below. The scatterplot suggests that there is: both a positive association between volume of oxygen consumed at rest and while running, and an outlier in the plot. neither a positive association between volume of oxygen consumed at rest and while running, nor an outlier in the plot. an outlier in the plot. a positive association between the volume of oxygen consumed at rest and while running.
both a positive association between volume of oxygen consumed at rest and while running, and an outlier in the plot.
A certain make of automobile has an average highway gas mileage of 30 miles per gallon (mpg). An engineer designs an improved engine, which has an average highway gas mileage of 30.2 mpg, based on a sample of 3600 cars with the new engine. Although the difference is quite small, the effect is statistically significant because: the mean of 30.2 is large compared to the gas mileage of most cars. the sample size is very large. new designs typically have less variability than standard designs, so small differences can appear to be statistically significant. All of the answer options are correct.
the sample size is very large.
The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures the motivation, attitudes, and study habits of college students. Scores range from 0 to 200 and follow, approximately, a Normal distribution, with mean of 110 and standard deviation 𝜎=20. You suspect that incoming freshman have a mean 𝜇 that is different from 110, because they are often excited yet anxious about entering college. To verify your suspicion, you test the hypotheses 𝐻0:𝜇=110, 𝐻𝛼:𝜇≠110 . You give the SSHA to 50 students who are incoming freshman and find their mean score. Suppose you observed the same sample mean 𝑥=115.35 but it was based on a sample of 100 students. What would the corresponding 𝑃P‑value be? 0.9926 0.0074 None of the answer options are correct. 0.0037
0.0074
A company produces precision 1000‑millimeter rulers. The actual distribution of the lengths of the rulers produced by this company is Normal, with mean μ and standard deviation 𝜎=0.02millimeters. Suppose I select a simple random sample of four of the rulers produced by the company and I measure their lengths in millimeters. The sample yields 𝑥=1000. A 90% confidence interval for 𝜇is: 1000±0.0196 .1000±0.0165 .1000±0.0115 1000±0.0082 .
1000±0.0165
The scores of a certain population on the Wechsler Intelligence Scale for Children (WISC) are thought to be Normally distributed, with mean 𝜇μ and standard deviation 𝜎=10 . A simple random sample of 25 children from this population is taken and each is given the WISC. The mean of the 25 scores is x¯=104.32 . Based on these data, a 95% confidence interval for μ is: 104.32±3.92 104.32±19.6 104.32±3.29 104.32±.78
104.32±3.92
A group of veterinary researchers plans a study to estimate the average number of enteroliths in horses suffering from them. Previous research has shown the variability in the number to be 𝜎=2 . The researchers wish the margin of error to be no larger than 0.5 for a 99% confidence interval. To obtain such a margin of error, the researchers need at least: 54 observations. 106 observations. 107 observations. 53 observations.
107 observations.
If we want to estimate 𝑝p , the population proportion of likely voters that believe the economy's state is the most urgent national concern, with 99% confidence and a margin of error no greater than 3%, how many likely voters need to be surveyed? Assume that you have no idea of the value of p . 716 56 1844 22
1844
Suppose a 95% confidence interval is given by (15,20) . The margin of error is: 1.65 1.96 5. 2.5.
2.5
A group of four friends has a median age of 22 . Three of the friends are ages 20 , 18 , and 24 . The age of the fourth friend must be: 24 or older. 22 . None of these choices are correct; we can't tell from the information provided. 18 or younger.
24 or older.
A survey of 1010 students was conducted to investigate the amount of time they spend on social media each day. Students were given a timer and asked to record the number of minutes spent every time they accessed social media. The students' total times for one day are given below (in minutes). 45 57 63 79 84 92 99 105 117 145 The standard deviation for these data is: 893.41 28.4 29.9 804.29
29.9
An economist conducted a study of the possible association between weekly income and weekly grocery expenditures. The particular interest was whether higher income would result in shoppers spending more on groceries. A random sample of shoppers at a local supermarket was obtained, and a questionnaire was administered asking about the weekly income of the shopper's family and the grocery bill for that week. The gender of the shopper was also obtained. The correlation was found to be 𝑟=0.649. The amount of variation in the response explained by the regression line is: 64.9% 42.1 % 0.649 %. 0.421 %.
42.1 %
A marketing consultant is hired by a major restaurant chain wishing to investigate the preferences and spending patterns of lunch customers. The CEO of the chain hypothesized that the average customer spends at least $13.50 on lunch. A survey of 25 customers sampled at one of the restaurants found the average lunch bill per customer to be 𝑥¯=$14.50 . Based on previous surveys, the restaurant informs the marketing manager that the standard deviation is 𝜎=$3.50 . To address the CEO's conjecture, the marketing manager carried out a hypothesis test of 𝐻0:𝜇=13.50 vs. 𝐻𝛼:𝜇>13.50 and obtained a 𝑃P‑value == 0.077. To illustrate his results, the director also wanted to calculate a 95% confidence interval with a margin of error 𝑚=$1.00. The required sample size equals: 100. 48. 25. 30.
48
Suppose we want a 90% confidence interval for the average amount of time (in minutes) spent per week on homework by the students in a large introductory statistics course at a major university. The interval is to have a margin of error of 3 minutes. The amount of time spent has a Normal distribution, with a standard deviation 𝜎=40minutes. The number of observations required is closest to: 683 .1180. 482 .22.
482
An economist conducted a study of the possible association between weekly income and weekly grocery expenditures. The particular interest was whether higher income would result in shoppers spending more on groceries. A random sample of shoppers at a local supermarket was obtained, and a questionnaire was administered asking about the weekly income of the shopper's family and the grocery bill for that week. The gender of the shopper was also obtained. The data below are expenditures and income for 1010 selected survey participants. Income 98 201 298 398 481 Grocery 52 78 108 121 The intercept of the regression line for these data is given by: 105.9 43.82 61.91 0.079
61.91
The stemplot below displays midterm exam scores for 34 students taking a calculus course. The highest possible test score was 100100 . The teacher declared that an exam grade of 6565 or higher was good enough for a grade of C or better. 3456789613201084330138431394525536576688936841485334462335567700123566889811359039 The percent of students earning a grade of C or higher (as declared by the teacher) is closest to: 50%. 80 %. 35%. 65 %.
65%
A frequent flyer was interested in the relationship between dollars spent on flying and the distance flown. She sampled 2020frequent flyers of a certain airline. She collected the number of miles flown in the previous year and the total amount of money the flyer spent. A regression line of distance flown on money spent was fit to the data, and the intercept and slope were calculated to be 𝑎=24,000a=24,000 and 𝑏=10b=10 . One of the randomly sampled frequent flyer was found to have spent $2500$2500and flown 4100041000 miles. The residual for this observation is: 1200012000 miles. -16000-16000 miles. -8000-8000 miles. 40004000 miles.
8000 miles.
The table below gives exam scores for 30 students. Score4563687278848791949799100Freq122435333211 The mean for these data (rounded to the nearest integer) is: 82 . 85 . 87 . 84 .
82
Which of these statements is true? A parameter characterizes a population, whereas a statistic describes a sample. You can have statistics and parameters from both samples and populations. A statistic characterizes a population, whereas a parameter describes a sample. None of the answer options are correct.
A parameter characterizes a population, whereas a statistic describes a sample.
A survey of radio stations was conducted following the attacks on the World Trade Center in 2001 . One of the variables recorded was the region in which the station was located (east, center, or west). In addition to the variable "region," the following information was collected: the quartile of the media market (top, second, third, and fourth), state, rank (a number between 1 and 205 ), and share (a number between 0 and 7 ). The side-by-side boxplots of station rank, above, show: more variability in ranks of coast stations. similar minimum ranks between regions. different median ranks between the regions. All of the answer options are correct.
All of the answer options are correct.
Advice columnist Ann Landers once asked her readers with children to answer the following question: "If you had it to do over again, would you have children?" Readers were invited to send a response to this question by mail. Of the approximately 10,000 responses Landers received, approximately 70% said "no." The sample is: all readers .the approximately 70% of women who answered "no. "the respondents who regretted having children. the approximately 10,000 readers who wrote in.
the approximately 10,000 readers who wrote in.
The following is a histogram showing the distribution per year of the cumulative property damage caused by tornadoes, over the period 1950 to 1999, in each of the 50 states and Puerto Rico. The data are in millions of dollars, and the class intervals are 0 to <10<10 , to <20 , and so forth. Which of the following statements is true? Approximately 25% of the annual reports of property damage were less than $10 million. None of the answer options is correct. Approximately 50% of the annual reports of property damage were less than $10 million. Approximately 25% of the tornadoes caused less than $10 million in damage.
Approximately 50% of the annual reports of property damage were less than $10 million.
Which of the following statements is correct? Changing the units of measurement of 𝑥 or 𝑦y does not change the value of the correlation 𝑟 .The correlation always has the same units as the 𝑦 variable but not the 𝑥 variable. A negative value for the correlation r indicates the data are strongly unassociated. The correlation always has the same units as the 𝑥 variable but not the 𝑦 variable.
Changing the units of measurement of 𝑥 or 𝑦y does not change the value of the correlation 𝑟
A marketing consultant is hired by a major restaurant chain wishing to investigate the preferences and spending patterns of lunch customers. The CEO of the chain hypothesized that the average customer spends at least $13.50 on lunch. A survey of 25 customers sampled at one of the restaurants found the average lunch bill per customer to be 𝑥¯=$14.50. Based on previous surveys, the restaurant informs the marketing manager that the standard deviation is 𝜎=$3.50 To address the CEO's conjecture, the marketing manager carried out a hypothesis test of 𝐻0:𝜇=13.50 vs. Hα:μ>13.50 and obtained a 𝑃‑value == 0.077. The marketing chooses a significance level of 𝛼=0.10 If he uses this significance level throughout his work, how often will he reject a true null hypothesis? The frequency of his rejection is not known; it depends on getting good samples. He will reject 1% of all true null hypotheses. He will reject 5% of all true null hypotheses. He will reject 10% of all true null hypotheses.
He will reject 10% of all true null hypotheses.
Consumers' Union measured the gas mileage per gallon of thirty-eight 1998-991998-99 model automobiles on a special test track. The following pie chart provides information about the country of manufacture of the cars that Consumers' Union used. Based on this pie chart, we may conclude that: Swedish cars get gas mileages that are between those of Japanese cars and U.S. cars. Mercedes Benz, Audi, Porsche, and BMW represent approximately one-quarter of the cars tested .Japanese cars get significantly lower gas mileage than cars of other countries. We know this because their slice of the pie is at the bottom of the chart. More than half of the cars in the study were from the United States.
More than half of the cars in the study were from the United States.
An economist conducted a study of the possible association between weekly income and weekly grocery expenditures. Of particular interest was whether higher income would result in shoppers spending more on groceries. A random sample of shoppers at a local supermarket was obtained. A questionnaire was administered asking about the weekly income of each shopper's family and their grocery bill for that week. A graphical display of the relationship between grocery expenditure and income might be: None of the answer options is correct. a side-by-side boxplot.a side-by-side pie chart .a side-by-side histogram.
None of the answer options is correct.
Which of the following is correct? The correlation 𝑟r is the slope of the least-squares regression line. The square of the correlation is the proportion of the data lying on the least-squares regression line. The square of the correlation is the slope of the least-squares regression line. The mean of the residuals from least-squares regression is zero.
The mean of the residuals from least-squares regression is zero.
An SRS of 25 recent birth records at the local hospital was selected. In the sample, the average birth weight was 𝑥=119.6 ounces. Suppose the standard deviation is known to be 𝜎=6.5 ounces. Assume that in the population of all babies born in this hospital, the birth weights follow a Normal distribution, with mean 𝜇 . If the sample size of birth records increases, how does the sampling distribution change? The sampling distribution will remain Normal, regardless of the sample size, and will have the same average and standard deviation as the sampling distribution computed from the smaller sample. The shape of the distribution will change, but it is dependent upon the new data that is collected. The sampling distribution will remain Normal and the mean will remain the same, regardless of the sample size, but its standard deviation will be smaller than the sampling distribution based on the smaller sample. The shape of the distribution will change, but it is not possible to determine what the new distribution will be without knowing the new data.
The sampling distribution will remain Normal and the mean will remain the same, regardless of the sample size, but its standard deviation will be smaller than the sampling distribution based on the smaller sample.
A marketing consultant is hired by a major restaurant chain wishing to investigate the preferences and spending patterns of lunch customers. The CEO of the chain hypothesized that the average customer spends at least $13.50 on lunch. A survey of 25 customers sampled at one of the restaurants found the average lunch bill per customer to be 𝑥¯=$14.50. Based on previous surveys, the restaurant informs the marketing manager that the standard deviation is 𝜎=$3.50. To address the CEO's conjecture, the marketing manager carried out a hypothesis test of 𝐻0:𝜇=13.50 vs. 𝐻𝛼:𝜇>13.50 and obtained a 𝑃‑value == 0.077. At level of significance 𝛼=0.05, the null hypothesis is not rejected. However, the marketing director later finds that, in fact, the average lunch price is above $13.50. The failure of the sample of 25 lunch prices to detect this fact was: a Type II error. an error of the third kind .just bad data .a Type I error.
Type II error
You recently took a statistics exam in a large class. The instructor tells the class that the scores were Normally distributed, with a mean of 7272 (out of 100100) and a standard deviation of 1212 . Your score was 9090 . Your friend had a time conflict and took a course with another instructor. Your friend had a score of 7575 on a test, with a mean of 6060 and a standard deviation of 1010 . What can you conclude? Your friend actually ranked better. The tests cannot be compared. You and your friend ranked equally well. You clearly ranked better.
You and your friend ranked equally well.
An educator wishes to study the effects of sleep deprivation on the ability to concentrate. He decides to study the students in a calculus class. After consultation with a statistician, the educator decides to randomly allocate students to either a group that will sleep for 8 hours the night before class or 6 hours. The educator does not know which group a student belongs to when she or he comes to class. This study is: a placebo controlled study, because 8 hours is normal sleeping time. double‑blinded, because the students have been told not to inform the educator about the treatment group they belong to. double‑blinded, because the educator does not know who belongs to the 6‑ or 8‑hour group. a single‑blinded randomized study, because the educator does not know the treatment groups students belong to but the students know.
a single‑blinded randomized study, because the educator does not know the treatment groups students belong to but the students know.
A sociologist studying freshmen at a major university carried out a survey, asking, among other questions, how often students went out per week, how many hours they studied per day, and how many hours they slept at night. The sociologist used an introductory sociology class to carry out the survey. The sociologist has learned from previous studies that females and males often behave differently regarding study and sleep patterns. She decides that she needs to ensure adequate numbers of females and males. She should take: a stratified random sample. a multigroup sample. a multistage sample. two convenience samples, one of females and one of males.
a stratified random sample.
A public opinion poll in Ohio was set up to determine whether registered voters in the state approved of a measure to ban smoking in all public areas. The researchers selected a simple random sample of 50 registered voters from each county in the state and asked whether the voters approved or disapproved of the measure. This is an example of: a simple random sample. a systematic county sample. a multistage sample .a stratified sample.
a stratified sample.
The power of a statistical test of hypotheses is: the extent to which the test will reject both one‑sided and two‑sided hypotheses. the smallest significance level at which the data will allow you to reject the null hypothesis. equal to 1−−P‑value. defined for a particular alternative value of the parameter of interest and is the probability that a fixed level α significance test will reject the null hypothesis when the particular alternative value of the parameter is true.
defined for a particular alternative value of the parameter of interest and is the probability that a fixed level α significance test will reject the null hypothesis when the particular alternative value of the parameter is true.
A simple random sample of 1000 American adults found that the average number of hours spent watching television during a typical week was 13.8. A simple random sample of 500 Canadians yielded an average of 12.5 hours per week of television viewing. Assume that for the American and Canadian distributions for weekly television, viewing times have the same standard deviations. The sampling variability associated with these sample means is: smaller for the sample of Canadians, because their population is smaller. larger for the sample of Canadians, because Canadian citizens are more widely dispersed throughout their country than American citizens are in the United States. Hence, Canadians have more variable views. larger for the sample of Canadians, because the sample size is smaller. smaller for the sample of Canadians, because the population of Canada is less than half that of the United States.
larger for the sample of Canadians, because the sample size is smaller.
To select a sample of undergraduate students in the United States, I first select a simple random sample of four states. From each of these states, I select a simple random sample of two colleges or universities. Finally, from each of these eight colleges or universities, I select a simple random sample of 20 undergraduates. My final sample consists of 160 undergraduates. This is an example of: multistage sampling. convenience sampling. stratified random sampling. simple random sampling.
multistage sampling.
The data and the graph below show the scores students in an advanced statistics course received for homework (Hw) completed and for the subsequent midterm exam. Homework scores are based on assignments that preceded the exam. The maximum homework score a student could obtain was 500 and the maximum midterm score was 350. Hw score387275280459395314428366421234Exam score190200108323315256341236285125 The residual for the student whose homework score was 395 is: positive. zero. undetermined. negative.
positive.
A 95% confidence is given by (15,20) . The interval is based on a sample of size 𝑛=25 . If we want to reduce the margin of error by half, we need to: double the sample size. reduce the sample size by half. reduce the sample size to one-quarter of the current sample size. quadruple the sample size.
quadruple the sample size
You recently took a statistics exam in a large class with n = 500 students. The instructor tells the class that the scores were Normally distributed, with a mean of 72 (out of 100) and a standard deviation of 88 , but when you talk to other students in the class, you find out that more than 30 students have scores below 45 . That violates which rule for the Normal distribution? It does not violate any rule; anything can happen. the 30-60-900 rule the 68-95-99.7 rule the 1-2-3 rule
the 68-95-99.7 rule
Does exposure to classical music (through instrument lessons or concert attendance) improve a child's scholastic performance? In a study, researchers measured the amount of exposure to classical music for a group of children, along with their scores on the state's academic proficiency exam. The explanatory variable in this study is: whether a child passed the state's proficiency exam. the type of instrument a child plays. the amount of exposure a child has to classical music the child's score on the state's proficiency exam.
the amount of exposure a child has to classical music
Consider the following scatterplot of two variables 𝑥x and 𝑦y . We may conclude: the correlation between 𝑥x and 𝑦y could be any number between -1-1 and +1 ; we can say nothing more without knowing the actual values. the correlation between 𝑥x and 𝑦y must be close to -1, because there is a nearly perfect relation between them but it is not a straight line relation. the correlation between 𝑥x and 𝑦y is close to 0 because, although there is a strong relationship between these variables, it isn't a linear relationship. the correlation between 𝑥x and 𝑦y must be close to 1 , because there is a nearly perfect relation between them.
the correlation between 𝑥x and 𝑦y is close to 0 because, although there is a strong relationship between these variables, it isn't a linear relationship.
A sociologist studying freshmen at a major university carried out a survey, asking, among other questions, how often students went out per week, how many hours they studied per day, and how many hours they slept at night. The sociologist used an introductory sociology class to carry out the survey. The population of interest is: the freshmen at the university .the students in the sociology class. the freshmen in the sociology class. the students at the university.
the freshmen at the university
Four golfers are asked to play a round of golf each on two consecutive Saturday afternoons. During the first round, one of two club types is to be used. During the second round, another club type is to be used. The order in which a golfer uses each brand is determined randomly. Scores are recorded, and the results are displayed. GolferBrand 1Brand 21939528886311211147977 To determine if the mean scores differ by brand of club, we would use: the one‑sample 𝑡t test. any of the answer options—it is at the experimenter's discretion. the two‑sample 𝑡t test. the matched pairs t test.
the matched pairs t test.
There are three children in a room, ages 3 , 4, and 5 . If another 4 -year-old enters the room: the mean age and variance will stay the same. the mean age will stay the same, but the variance will decrease. the mean age and variance will increase. the mean age will stay the same, but the variance will increase.
the mean age will stay the same, but the variance will decrease.
A statistic is said to be unbiased if: it is used for only honest purposes. the person who calculated the statistic and the subjects whose responses make up the statistic were truthful. the person computing it does not favor any particular outcome. the mean of its sampling distribution is equal to the true value of the parameter being estimated.
the mean of its sampling distribution is equal to the true value of the parameter being estimated.
A veterinarian was studying suspected causes of enteroliths, concrete‑like balls in the colons of horses. She suspected that a diet of mostly alfalfa could be a cause. In a study conducted at a veterinary research facility, she examined the records of 62 horses with enteroliths (cases) and compared them with the records of 75 horses free of enteroliths (controls). She found that 42 case horses were fed mostly alfalfa, compared with 17 control horses. She decided to base her statistical procedures on 𝑝𝑐𝑎𝑠𝑒pcase , the proportion of horses with enteroliths that are fed mostly alfalfa, and 𝑝𝑐𝑜𝑛𝑡𝑟𝑜𝑙pcontrol , the proportion of control horses mostly fed alfalfa. She is told by a statistician colleague that she can proceed with a large sample confidence interval for 𝑝𝑐𝑎𝑠𝑒−𝑝𝑐𝑜𝑛𝑡𝑟𝑜𝑙pcase−pcontrol because: the two sample sizes combined (at 137) exceed 30. the numbers of successes and failures exceed 10 in both samples. each sample (at 𝑛𝑐𝑎𝑠𝑒=62ncase=62 and 𝑛𝑐𝑜𝑛𝑡𝑟𝑜𝑙=75ncontrol=75) exceeds 30. None of the answer options are correct; sample size does not matter for inference about proportions.
the numbers of successes and failures exceed 10 in both samples.
Enteroliths are calcifications that form in the gut of a horse. The stones can cause considerable morbidity and mortality. A study was conducted to investigate factors (such as diet and environment) that may be related to the formation of enteroliths. The study contained 62 horses with enteroliths (cases) and 75 horses without (controls). The graph below contains side-by-side boxplots of the percent of alfalfa in the diet for cases and controls. Based on the boxplot cases, the median amount of alfalfa in the diet of cases is: twice the amount as for controls. the same as for controls. half the amount as for controls. None of the answer options is correct.
twice the amount as for controls.
An insurance underwriter wonders whether sports cars "cause" people to drive too fast or whether those with a propensity for speeding are drawn to sports cars. She secures some research funds and recruits 100 car buyers to her study. She randomly assigns 25 drivers to each of four groups: 1) sports car white, 2) sports car red, 3) sedan white, and 4) sedan red. The primary research questions are: 1) Do sports cars make people drive faster? 2) Does color make a difference? The result shows that people driving red cars drive faster than those driving white cars. There is no statistically significant difference by type. This conclusion is: wrong because you cannot study two different things, like type and color, at once. valid because sports cars obviously make people drive fast. valid because this was a randomized study and drivers were randomized on color and type. wrong because the stated purpose was to study type, not color.
valid because this was a randomized study and drivers were randomized on color and type.
Suppose the time that it takes a certain large bank to approve a home loan is Normally distributed, with mean (in days) 𝜇μ and standard deviation 𝜎=1. The bank advertises that it approves loans in 5 days, on average, but measurements on a random sample of 500 loan applications to this bank gave a mean approval time of 𝑥¯=5.3days. Is this evidence that the mean time to approval is actually longer than advertised? To answer this, test the hypotheses 𝐻0:𝜇=5, 𝐻𝛼:𝜇>5Hα:μ>5 at significance level 𝛼=0.01 You conclude that:𝐻𝑎Hshould be rejected. there is a 5% chance that the null hypothesis is true. 𝐻0should not be rejected. 𝐻0 should be rejected.
𝐻0 should be rejected.
An instructor at a major research university occasionally teaches summer session and notices that that there are often students repeating the class. Out of curiosity, she designs a random sample of students enrolled in summer sessions and counts the number repeating a class. She counts 105 students in the sample, of which 19 are repeating the class. She hypothesizes that, in general, 10% of students repeat a course. The hypotheses to be tested are: 𝐻0:𝑝=0.1H0: vs. 𝐻𝛼:𝑝≠0.1 .𝐻0:𝑝=0.1vs. 𝐻𝛼:𝑝≥0.18 .𝐻0:𝑝̂ =0.181vs. 𝐻𝛼:𝑝=0.1 𝐻0:𝑝=0.1 vs. 𝐻𝛼:𝑝̂ =0.181 .
𝐻0:𝑝=0.1H0: vs. 𝐻𝛼:𝑝≠0.1
Is the mean age at which American children first read now under four years? If the population of all American children has a mean age of 𝜇μ years until they begin to read, which of the given null and alternative hypotheses would be tested to answer this question? H0:μ=4 and 𝐻𝑎:𝜇≠4 .𝐻0:𝜇=4and Ha:μ>4 . 𝐻0:𝜇=4and Ha:μ<4 . 𝐻0:𝜇=4 and 𝐻𝑎:𝜇<4±, assuming our sample size is 𝑛n .
𝐻0:𝜇=4 and 𝐻𝑎:𝜇<4±,
A statistics teacher taught a large introductory statistics class, with 500 students having enrolled over many years. The mean score over all those students on the first midterm was 𝜇=78 with standard deviation 𝜎=10 . One year, the teacher taught a much smaller class of only 25 students. The teacher wanted to know if teaching a smaller class was more effective and students performed better. We can consider the small class as an SRS of the students who took the large class over the years. The average midterm score was 𝑥¯=83 . The hypothesis should be: 𝐻0:𝜇=78vs. 𝐻𝑎:𝜇>78 𝐻0:𝜇=88 vs. 𝐻𝑎:𝜇=78 H0:μ=88 vs. Ha:μ<88 H0:μ=78 vs. Ha:μ=88 .
𝐻0:𝜇=78vs. 𝐻𝑎:𝜇>78
In their advertisements, the manufacturers of a certain brand of breakfast cereal would like to claim that eating their oatmeal for breakfast daily will produce a mean decrease in cholesterol of more than 10 points in one month for people with cholesterol levels over 200. To determine if this is a valid claim, they hire an independent testing agency, which then selects 25 people with cholesterol levels over 200 to eat the manufacturer's cereal for breakfast daily for a month. The agency should be testing the null hypothesis 𝐻0:𝜇=10 and the alternative hypothesis: 𝐻𝑎:𝜇≠10 .𝐻𝑎:𝜇<10 𝐻𝑎:𝜇≠10±𝜎𝑛√ .𝐻𝑎:𝜇>10
𝐻𝑎:𝜇>10
