Stats
A guidance counselor at a university is investigating demand for study abroad. The question before her is how engineering and humanities majors compare regarding interest in study abroad during summer. Random samples of 40 engineering and humanities majors each were interviewed. Twenty engineering majors and 24 humanities majors expressed interest in study abroad during the summer. The hypotheses to be tested are : H0:pE=pHH0:pE=pH vs Ha:pE<pHHa:pE<pH, where pEpE is the proportion of engineering majors interested in study abroad and pHpH is the proportion of humanities majors. The test statistic has the value:
-.8989
Birth weights at a local hospital have a Normal distribution, with a mean of 110 oz and a standard deviation of 15 oz. What is the proportion of infants with birth weights between 125 oz and 140 oz?
.1359
A statistician wishing to test a hypothesis that students score 75% on the final exam in a mathematics 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 78% and the standard deviation in the population is known to be σ=15%σ=15%. The P-value for the hypothesis H0:μ=75H0:μ=75 vs. Ha:μ≠75Ha:μ≠75 is: Select one: 0.814. 0.371. The answer cannot be determined with the information provided. 0.186.
0.371
It is reported that 75% of women use computers. Choose three women at random. Find the probability that (a) all three women use a computer (b) at least one woman does not use a computer. Hint: You may use the formula P(AP(A does not occur)=1−P(A)
0.42 0.58
A local board of education conducted a survey of residents in the community concerning a property tax levy on the coming local ballot. They randomly selected 850 residents in the community and contacted them by telephone. Of the 850 residents surveyed, 390 supported the property tax levy. Let pp represent the proportion of residents in the community that supports the property tax levy. A 90% confidence interval for pp is: Select one: 0.4489 to 0.5159. 0.4487 to 0.5161. 0.4307 to 0.4869. 0.4542 to 0.5105.
0.4307 to 0.4869.
At a small college, all entering freshmen must take a foreign language class, chosen from the languages Spanish, French, Swahili, Chinese, and Arabic. Because there is limited space in the foreign language courses, a student cannot simultaneously enroll in more than one course. The probability distribution for the language studied by a randomly selected freshman is summarized in the following table. Language Studied Spanish French Swahili Chinese Arabic Probability ? 0.13 0.09 0.19 0.12 The probability that the freshman is studying Spanish is: Select one: 0.47 The answer cannot be determined from the information given. 0.49 0.51
0.47
What is the area under the standard Normal curve corresponding to z<0.75z<0.75? (You may think of the RStudio command learned in Chapter 3)
0.7733
A company produces packets of soap powder labeled "Giant Size 32 Ounces." The actual weight of soap powder in such a box has a Normal distribution, with a mean of 33 oz and a standard deviation of 0.7 oz. To avoid having dissatisfied customers, the company says a box of soap is considered underweight if it weighs less than 32 oz. To avoid losing money, it labels the top 5% (the heaviest 5%) overweight. How heavy does a box have to be for it to be labeled overweight?
34.15
In a fish tank, there are 15 goldfish, 3 angelfish, and 17 guppies. If a fish is selected at random, find the probability that it is an angelfish or a guppy. Select one: 4/7 18/35 32/35 3/7
4/7
On a 35 point test, a sample of 11 students were selected. Their scores are: 28, 25, 32, 29, 12, 18, 15, 16, 15, 20, 17. What is the variance? what is the mean? What is the median? What is the standard deviation?
45.25 20.64 18 6.73
What is the difference between a histogram and a bar chart? Select one: A bar chart displays a categorical variable on the horizontal axis, whereas a histogram does not. A bar chart displays a quantitative variable on the horizontal axis, whereas a histogram does not. A histogram is a more accurate representation of a bar chart. There is no difference; they are exactly the same.
A bar chart displays a categorical variable on the horizontal axis, whereas a histogram does not.
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=2.2σ=2.2. 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 Answer:
128
A food snack manufacturer samples 11 bags of pretzels off the assembly line and weighs their contents. If the sample mean is 14.2 oz. and the sample standard deviation is 0.70 oz., find the 95% confidence interval of the true mean. Select one: 14.5<μ<14.914.5<μ<14.9 13.7<μ<14.713.7<μ<14.7 11.6<μ<17.811.6<μ<17.8 14.2<μ<15.2
13.7<μ<14.7
Scores on a university exam are Normally distributed, with a mean of 78 and a standard deviation of 8. The professor teaching the class declares that a score of 70 or higher is required for a grade of at least C. What percent of students failed to earn a grade of at least C? (You may use RStudio with the command pnorm())
15.86
A sample of 40 employees from the local Honda plant was obtained, and the length of time (in months) that each employee has worked at the plant was recorded. A stemplot of these data follows. In the stemplot, 5|2 represents 52 months. 5|2 2 3 3 4 5 7 8 9 9 6|0 0 0 2 3 4 4 4 5 6 7 7 8 8 8 9 7|3 4 5 5 6 6 7 7 7 8 8 9 9 8| 9|8 The percentage of employees in the sample that has worked at the plant for less than five years is: Select one: 10%. 25%. approximately zero. 15%.
25%
A special diet is intended to reduce systolic blood pressure among patients diagnosed with stage 2 hypertension. If the diet is effective, the target is to have the average systolic blood pressure of this group be below 150. After six months on the diet, an SRS of 29 patients had an average systolic blood pressure of x¯=143x¯=143 with standard deviation s=21s=21. This is a hypothesis problem to check if there is a sufficient evidence that the diet is effective in meeting the target. Assume the distribution of the systolic blood pressure for patients in this group is approximately Normal with mean μμ. The appropriate degree of freedom for this test is: Select one: 27. 28. 149. 20.
28
The regression equation below relates the scores students in an advanced statistics course received for homework 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. The regression line that was obtained is given by y^=−84.4+0.91xy^=−84.4+0.91x. If a student had a homework score of 400, the midterm score would be predicted to be (rounded to an integer):
280
According to the National Institute on Alcohol Abuse and Alcoholism, and the National Institutes of Health, 41% of college students nationwide engage in binge drinking behavior—having five or more drinks on one occasion during the past two weeks. A college president wonders if the proportion of students enrolled at her college that binge drinks is lower than the national proportion. In a commissioned study, 462 students are selected randomly from a list of all students enrolled at the college. Of these, 166 admitted to having engaged in binge drinking. The college president is more interested in testing her suspicion that the proportion of students at her college that binge drinks is lower than the national proportion of 0.41. Her staff tests the hypotheses H0H0: p = 0.41, HaHa: p < 0.41. The P-value is: Select one: between 0.01 and 0.025. between 0.025 and 0.05. between 0.05 and 0.1. below 0.01.
between 0.01 and 0.025.
A student asks each person in one of his classes how many hours, on average, they spend studying each week. This is an example of: Select one: a double-blind experiment. a simple random sample. voluntary response sampling. convenience sampling
convenience sampling
A recent study of business travelers claims they spend an average of $41.00 per day on meals. As a test of this claim, a random sampling of 16 business travelers found they had spent an average of $44.00 per day with a sample standard deviation of $3.65. Use hypothesis testing to verify if there is enough evidence to reject this claim with α = 0.05 by answering the following questions? Is the z-test or t-test used? What is the null hypothesis? What is the alternative hypothesis? What is the test statistic? What is the range of the p-value? Is there enough evidence to reject the claim that travelers spend on average $41.00 on meals per day.
t-test The average cost on meal per day is $41.00 The average cost on meal is not $41.00 3.288 <0.001 Yes
In order to investigate treatments for morbid obesity, obese subjects satisfying fairly strict requirements were randomly assigned to one of three treatment groups: (1) gastric bypass surgery, (2) participation in a diet and exercise program, or (3) both gastric bypass surgery and participation in a diet and exercise program. Researchers observed the amount of weight lost five years after the study began. The response is: Select one: random assignment. the kind of program to which a subject was assigned. gastric bypass surgery. the amount of weight lost five years after the study began.
the amount of weight lost five years after the study began.
The correlation between the height and weight of children aged 6 to 9 is found to be about r=0.8r=0.8. Suppose we use the height x of a child to predict the weight y of the child. We conclude that: Select one: the fraction of variation in weights explained by the least-squares regression line of weight on height is 0.64. the least-squares regression line of y on x would have a slope of 0.8. height is generally 80% of a child's weight. about 80% of the time, age will accurately predict weight.
the fraction of variation in weights explained by the least-squares regression line of weight on height is 0.64.
Use lm() in R to find the least square regression line by first assigning HW<- c(380,270,281,457,390,310,430,370,418,220) and EX<-c(190,200,108,323,315,256,341,236,285,125). You can write down your answer as y=a+bxy=a+bx instead of y^=a+bxy^=a+bx.
y=70.74+.88x
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 10 selected survey participants. Income Grocery 98 52 201 78 298 108 398 121 481 100 600 99 738 162 805 71 890 105 1023 173 What is the slope of the regression line for these data? You may use R and round your answer to four decimal point. You may assign x <- c(98,201,298,398,481,600,738,805,890,1023), and y <- c(52,78,108,121,100,99,162,71,105,173) and use lm() to find the slope. Note that you have to pay attention to which is the explanatory variable and which is the response variable. (please round your answer to the fifth decimal place).
.25243
A single card is drawn from a deck of 52 cards. Find the probability of selecting the following. A 6 or a diamond. A club or a diamond.
0.31 0.5
An SRS of 36 recent birth records at the local hospital was selected. In the sample, the average birth weight was x=119.6x=119.6 ounces. Suppose the standard deviation is known to be σ=6.6σ=6.6 ounces. Assume that in the population of all babies born in this hospital, the birth weights follow a Normal distribution, with mean μμ. The standard deviation of the sampling distribution of the mean is:
1.1
A baseball player has a batting average of 0.325 each week of the season, with a standard deviation of 0.065. What is the z score when he bats 0.410 one week?
1.31
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¯=$15x¯=$15. Based on previous surveys, the restaurant informs the marketing manager that the standard deviation is σ=$3.50σ=$3.50. To address the CEO's conjecture, the marketing manager carried out a test of the hypothesis H0:μ=13.50H0:μ=13.50 vs. Ha:μ>13.50Ha:μ>13.50. What is the test statistic the marketing manager calculated using the survey of 25 customers?
2.14
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. Select one: Approximately 25% of the tornadoes caused less than $10 million in damage. Approximately 25% of the annual reports of property damage were less than $10 million. Approximately 50% 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.
A survey of radio stations was conducted following the attacks on the World Trade Center in 2001. The station rankings were included in the survey. The attached histogram has the interval limits 0 ≤ X < 50; 50 ≤ X < 100, 100 ≤ X < 150; 150 ≤ X < 200; and 200 ≤ X < 250. Select one: left-skewed. bimodal. right-skewed. symmetric.
right-skewed
An SRS of 100 flights of a large airline (airline 1) showed that 64 were on time. An SRS of 100 flights of another large airline (airline 2) showed that 80 were on time. Let p1p1 and p2p2 be the proportion of all flights that are on time for these two airlines. Is there evidence the the on-time rate for airline 1 is smaller than the on-time rate for airline 2? To determine this, you test the following hypotheses: Select one: H0:p1=p2H0:p1=p2 vs Ha:p1≠p2Ha:p1≠p2 H0:p1=p2H0:p1=p2 vs Ha:p1<p2Ha:p1<p2 H0:p1≠p2H0:p1≠p2 vs Ha:p1=p2Ha:p1=p2 H0:p1=p2H0:p1=p2 vs Ha:p1>p2
H0:p1=p2H0:p1=p2 vs Ha:p1<p2
The t-distribution must be used to find the confidence interval for a population mean when the variable is normally or approximately normally distributed, and the population standard deviation is known. Select one: True False
False
A random sample of n = 16 flights was taken, along with the time recorded to board each flight. It was found that x¯=42x¯=42 minutes. Previous studies had determined boarding times to be Normally distributed, with μ=38μ=38 minutes and σ=36σ=36 minutes. The sampling distribution of x¯x¯, the sample average in samples of size n = 16 is: Select one: N (38, 36), the normal distribution with the mean 38 and the standard deviation 36. N (38, 7.2), the normal distribution with the mean 38 and the standard deviation 7.2. N (38, 9), the normal distribution with the mean 38 and the standard deviation 9. N (42, 36), the normal distribution with the mean 42 and the standard deviation 36.
N (38, 9), the normal distribution with the mean 38 and the standard deviation 9.
When two events A and B are independent, then the probability of both occurring is P(A and B)=P(A)P(B). What is the probability of both occurring if A and B are not assumed to be independent? Select one: P(A and B)=P(A)P(B) P(A and B)=P(A)P(B|A) P(A and B)=P(A)+P(B) P(A and B)=1-P(A)P(B)
P(A and B)=P(A)P(B|A)
The range of the values of the probability of an event is 0 to 1 inclusive. Select one: True False
True
The survey results from 12 parks in a city show the mean height of 60 ft of mature oak trees. The mean height of 60 ft is a statistic. Select one: True False
True
When two events A and B are disjoint, then P(A or B)=P(A)+P(B), where P(A), P(B), and P(A or B) represent the probabilities of A, B, and the event A or B. Select one: True False
True
To assess the opinion of students at The Ohio State University about campus safety, a reporter for the student newspaper interviews 15 students that she meets walking on the campus late at night who are willing to give their opinion. The sample obtained is: Select one: probably biased. a probability sample of students with night classes. a simple random sample of students feeling safe. a stratified random sample of students feeling safe.
probably biased
A Type I error is: Select one: accepting the null hypothesis when it is false. incorrectly specifying the alternative hypothesis. incorrectly specifying the null hypothesis. rejecting the null hypothesis when it is true.
rejecting the null hypothesis when it is true.
The management for a chain of restaurants recorded the number of appetizers, X, ordered by tables dining. They observed that X had the following probability distribution. Value of X 0 1 2 3 or more Probability 0.65 0.3 0.04 0.01 The probability that a randomly chosen table orders at least one appetizer is:
.35
If a die is rolled, find the probability of getting a number greater than or equal to 4.
.5
A group of college DJs surveyed students to find out what music to plan for their upcoming parties. Thirty percent of the students preferred dubstep, 25% of the students liked trance music, and 20% wanted to hear only house music. Eighteen percent of the respondents selected both dubstep and trance. The conditional probability that a student likes dubstep, given that he or she likes trance music, is:
.72
A candidate for one of Ohio's two U.S. Senate seats wishes to compare her support among registered voters in the northern half of the state with her support among registered voters in the southern half of the state. A random sample of 2000 registered voters in the northern half of the state is selected, of which 1062 support the candidate. Additionally, a random sample of 2000 registered voters in the southern half of the state is selected, of which 900 support the candidate. A 90% confidence interval for the difference in the proportion of registered voters that support this candidate between the northern and southern halves of the state is: Select one: 0.0325 to 0.1237. 0.0434 to 0.1232. 0.0501 to 0.1118. 0.0550 to 0.1069.
0.0550 to 0.1069.
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¯x¯ of these residents is to be computed. What is the probability that the average age, x¯x¯, of the 100 residents selected is less than 68.3? Round your answer to three decimal places.
0.114
In the past decades, there have been intensive antismoking campaigns sponsored by both federal and private agencies. In one study of national smoking trends, two random samples of U.S. adults were selected in different years. The first sample, taken in 1995, involved 4276 adults, of which 1642 were smokers. The second sample, taken in 2010, involved 3908 adults, of which 1515 were smokers. The samples are to be compared to determine whether the proportion of U.S. adults that smokes declined during the 15-year period between the samples. Let p1p1 be the proportion of all U.S. adults that smoked in 1995. Let p2p2 denote the proportion of all U.S. adults that smoked in 2010. The value of the z statistic for testing equality of the proportion of smokers in 1995 and 2010 is:
0.34
At a large Midwestern college, 4% of the students are Hispanic. A random sample of 20 students from the college is selected. Let XX denote the number of Hispanics among them. Note that the formulas for the mean and standard deviation of a binomial distribution is μ=npμ=np and σ=np(1−p)−−−−−−−−√σ=np(1−p). The mean of XX is: The standard deviation of XX is:
0.8 0.88
Frequent food questionnaires (FFQ) are a simple way to obtain information on the foods individuals consume by asking them questions about typical amounts of food consumed in a day, a week, or a month. A more accurate picture is obtained by obtaining a detailed food diary (DR) for several days that are randomly chosen over a certain time period. The data obtained from a frequent food questionnaire can be compared with the food diary to assess the validity of the questionnaire. The data below are for seven individuals who participated in such a study on alcohol consumption. DR FFQ 8.26 1.68 0.83 0 20.13 15.10 11.16 7.49 7.18 12.84 1.76 0 22.66 25.06 Use R by assigning DR <- c(8.26, 0.83, 20.13, 11.16, 7.18, 1.76, 22.66) and FFQ<- c(1.68, 0, 15.10, 7.49, 12.84, 0, 25.06), and use cor() to find the correlation for these data.
0.8898
A random variable xx has a Normal distribution with an unknown mean μμ and a standard deviation σ=12σ=12. Suppose that we take a random sample of size n=36n=36 and find a sample mean of x¯=98x¯=98. Compute the 90% confidence interval for μμ and provide the following numbers: The critical value z∗z∗ for the confidence interval is ___ The margin of error of the confidence interval is ___ . A 95% confidence interval for μμ is _____
1.645 3.29 (94.71, 101.29)
A sports writer wished to see if a football filled with helium travels farther, on average, than a football filled with air. To test this, the writer used 20 adult male volunteers. These volunteers were randomly divided into two groups of 10 subjects each. Group 1 kicked a football that was filled with helium to the recommended pressure. Group 2 kicked a football that was filled with air to the recommended pressure. The mean yardage for group 1 was x¯1=32x¯1=32 yards with a standard deviation s1=9s1=9 yards. The mean yardage for group 2 was x¯2=26x¯2=26 yards with a standard deviation s2=6s2=6 yards. Assume the two groups of kicks are independent. Let μ1μ1 and μ2μ2 represent the mean yardage we would observe for the entire population represented by the volunteers if all members of this population kicked, respectively, a helium-filled and an air-filled football. Assume that two-sample t procedures are safe to use. Suppose the researcher had wished to test the hypotheses : μ1=μ2μ1=μ2 : μ1>μ2μ1>μ2. The numerical value of the two-sample t statistic is: Select one: 1.46. 0.36. 2.57. 1.75
1.75
A randomly sampled group of patients at a major U.S. regional hospital became part of a nutrition study on dietary habits. Part of the study consisted of a 50-question survey asking about types of foods consumed. Each question was scored on a scale from one (most unhealthy behavior) to five (most healthy behavior). The answers were summed and averaged. The population of interest is the patients at the regional hospital. A prior survey of patients had found the mean score for the population of patients to be μ=2.9μ=2.9. After careful review of these data, the hospital nutritionist decided that patients could benefit from nutrition education. The current survey was implemented after patients were subjected to this education, and it produced the following sample statistics for the 15 patients sampled: x¯=3.5x¯=3.5 and s=1.2s=1.2. We would like to know if the education improved nutrition behavior. We test the hypotheses H0:μ=2.9H0:μ=2.9 versus Ha:μ>2.9Ha:μ>2.9. The tt test to be used has the test statistic: Answer:
1.94
In a particular game, a six-sided fair die is tossed. If the number of spots showing is six, you win $6; if the number of spots showing is five, you win $3. If the number of spots showing is one, or two, or three, or four, you win nothing. You are going to play the game three. The probability that you win something on each of the three plays of the game is: Select one: 1/6 1/9 1/3 1/27
1/27
A student looked up the number of years served by 35 of the more than 100 Supreme Court justices. The average number of years served by those 35 justices was 13.8. If the standard deviation of the entire population is 7.3 years, find the 99% confidence interval for the average number of years served by all Supreme Court justices. Select one: 10.61<μ<16.9810.61<μ<16.98 11.38<μ<16.2211.38<μ<16.22 11.76<μ<15.8311.76<μ<15.83 12.21<μ<15.45
10.61<μ<16.98
The scores on the Wechsler Adult Intelligence Scale are approximately Normal, with μ=100μ=100 and σ=15σ=15. What is the score needed to be among the highest 10% of all scores?
119.2
A veterinarian collects data on the number of times race horses are raced during their careers. The veterinarian finds that the average number of races a horse enters is x¯=15.3x¯=15.3, with a standard deviation of s=6.8s=6.8 in a sample of n=33n=33 horses. A 95% confidence for μμ, the average number of times a horse races, is given by Select one: 12.118≤μ≤18.48312.118≤μ≤18.483. 10.935≤μ≤19.62510.935≤μ≤19.625. 11.338≤μ≤19.23211.338≤μ≤19.232. 12.203≤μ≤18.39712.203≤μ≤18.397.
12.203≤μ≤18.397
A high-profile consulting company chooses its new entry-level employees from a pool of recent college graduates using a five-step interview process. Unfortunately, there are usually more candidates who complete the interview process than the number of new positions that are available. As a result, cumulative GPA is used as a tie-breaker. GPAs for the successful interviewees are Normally distributed, with a mean of 3.3 and a standard deviation of 0.4. Out of the163 people who made it through the interview process, only 121 can be hired. What cut-off GPA should the company use?
3.04
A violin student records the number of hours she spends practicing during each of nine consecutive weeks: 6.2 5.0 4.3 7.4 5.8 7.2 8.4 1.2 6.3 Use R or RStudio to find the following by assigning x <- c(6.2, 5.0, 4.3, 7.4, 5.8, 7.2, 8.4,1.2, 6.3) and using appropriate commands. Please drag and drop your answers. mean median standard deviation the first quartile
5.756 6.2 2.113 5.0
An economics professor randomly selected 100 millionaires in the United States. The average age of these millionaires was 55.8 years. If the standard deviation of the entire population of millionaires is 7.9 years, what is the 95% confidence interval for the mean age of all United States millionaires? Select one: 53.3<μ<56.353.3<μ<56.3 54.3<μ<57.454.3<μ<57.4 54.0<μ<55.654.0<μ<55.6 52.8<μ<56.8
54.3<μ<57.4
A local board of education conducted a survey of residents in the community concerning a property tax levy on the coming local ballot. They randomly selected 850 residents in the community and contacted them by telephone. Of the 850 residents surveyed, 410 supported the property tax levy. Let pp represent the proportion of residents in the community that supports the property tax levy. How large a sample n would you need to estimate p with margin of error 0.03 with 90% confidence?
753
An instructor at a major research university occasionally teaches summer session and notices 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 a class. She hypothesizes that, in general, more than10% of students repeat a course. The hypotheses to be tested are: Select one: H0:p=0.1H0:p=0.1 vs. Ha:p≠0.1Ha:p≠0.1 H0:p=0.1H0:p=0.1 vs. Ha:p>0.1Ha:p>0.1 H0:p=0.1H0:p=0.1 vs. Ha:p>0.18Ha:p>0.18 H0:p=0.1H0:p=0.1 vs. Ha:p=0.18
H0:p=0.1H0:p=0.1 vs. Ha:p>0.1
For the statement "The average weight μ of fish in Lake Superior is greater than 1.9 pounds", the null and alternative hypotheses are: Select one: \H0:μ=1.9; H1:μ>1.9 H0:μ≤1.9; H1:μ>1.9 H0:μ<1.9; H1:μ>1.9 H0:μ>1.9; H1:μ>1.9
H0:μ=1.9; H1:μ>1.9
An SRS of size 26 was taken to estimate mean body mass index (BMI) for girls between 13 and 19 years of age. The 95% confidence interval obtained had the lower limit 19.5 and upper limit 26.3. Which of the following is true? Select one: There is 95% chance that a randomly selected teenage girl between 13 and 19 has BMI between 19.5 and 26.3. A total of 95% of all teenage girls have BMI between 19.5 and 26.3. We are 95% confident that the true mean BMI of all teenage girls between 13 and 19 is between 19.5 and 26.3. A total of 95% of 36 sampled teenage girls have BMI between 19.5 and 26.3.
We are 95% confident that the true mean BMI of all teenage girls between 13 and 19 is between 19.5 and 26.3.
Randomly assigning all subjects to treatment groups is called: Select one: a completely randomized design. a randomized complete block design. a randomized comparative experiment. None of the answer options is correct.
a completely randomized design.
A group of veterinarians at a major veterinary hospital was interested in investigating a possible link between enteroliths (stones that form in the colon of horses) and diet. They decided to conduct a survey of the feeding practices for horses in the hospital's state. They created a survey questionnaire and decided to administer it to the owners of every fifth horse being treated at the hospital. The sample is: The population of interest is:
a convenience sample all horses in the state
In a study using 15 samples, and in which the population standard deviation is unknown, the distribution that should be used to calculate confidence intervals of the mean is Select one: a t distribution with 15 degrees of freedom. a t distribution with 14 degrees of freedom. a t distribution with 16 degrees of freedom. a standard normal distribution.
a t distribution with 14 degrees of freedom.
In a test of hypothesis, a small P-value provides evidence: Select one: against the null hypothesis and the alternative hypothesis. against the alternative hypothesis in favor of the null hypothesis. against the null hypothesis in favor of the alternative hypothesis. for the null hypothesis and the alternative hypothesis.
against the null hypothesis in favor of the alternative hypothesis.
Each month, the census bureau mails survey forms to 250,000 households asking questions about the people living in the household and about such things as motor vehicles and housing costs. Telephone calls are made to households that don't return the form. In one month, responses were obtained from 240,000 of the households contacted. The population of interest is: A household that does not return the form and cannot be contacted by telephone is an example of: The sample is:
all U.S. households nonresponse the 240,000 households that responded
A veterinarian interested in studying the causes of enteroliths (stones that form in the gut of horses) decided to compare the diets of horses with enteroliths and horses without that were admitted to the veterinary hospital. This study is an example of: Select one: an experimental study. a survey. an observational study. None of the above.
an observational study.
A veterinarian is interested in studying the causes of enteroliths (stones that form in the gut of horses). An observational study comparing the diet of horses admitted to the veterinary hospital with enteroliths and the diet of horses admitted for other reasons does not allow causal conclusions to be drawn because: Select one: the study does not match horses. associations in observational studies can be confounded by lurking variables. an observational study can only establish correlations, unless the investigator is double blinded. All of the answer options are correct.
associations in observational studies can be confounded by lurking variables.
A statistician wishing to test a hypothesis that students score at most 74% on the final exam in a mathematics 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%. The statistician calculates the test statistic to be −0.8944. The P-value would be calculated by: Select one: 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 under the standard normal curve. finding the area to the right of −0.8944 under the standard normal curve and doubling it. finding the area to the left of −0.8944 under the standard normal curve and doubling it.
finding the area to the left of −0.8944 under the standard normal curve.
Suppose the least-squares regression line for a set of data has slope 72.4. Now suppose we remove a point from the data, compute the least-squares regression line, and find that the new slope is 8.7. The point removed would be considered: Select one: robust. influential. a response. a residual.
influential
Consider the following scatterplot, which depicts the tread depth (measured in mils, where 1 mil = 0.001 inch) versus the number of miles driven on the tire (measured in thousands of miles). The correlation between x and y Select one: is approximately 0. is approximately -0.97. cannot be computed because the trend is curved. is approximately 0.97.
is approximately -0.97
Scientists examined how mean sea surface temperatures (in degrees Celsius) affects mean coral growth (in centimeters per year) over a several-year period at locations in the Gulf of Mexico and the Caribbean. Here are the data for the Gulf of Mexico: Sea surface temperature 26.7 26.6 26.6 26.5 26.3 26.1Growth 0.85 0.85 0.79 0.86 0.89 0.92 You can download the data in R format: R Data 1. What is the explanatory variable 2. Use RStudio to find the correlation coefficient:
mean sea surface temperature -0.8111
A small math department has seven faculty members and 35 students. The department can send six people to a national convention, and it would like to send four students and two faculty members. Of the 35 students, four are selected randomly. Two faculty members are randomly selected from the seven. This is an example of: Select one: voluntary response sampling. stratified random sampling. a census. simple random sampling.
stratified random sampling
An introductory statistics class decides to investigate whether there is a relationship between the performance on midterms 1 and 2. The instructor creates a scatterplot of midterm 2 scores (y) versus midterm 1 scores (x). Based on the plot, which of the following is likely true? Select one: The correlation between midterm 1 and midterm 2 scores is positive. Students who did well on midterm 1 did not do so well on midterm 2. Students who did well on midterm 2 did not do so well on midterm 1. None of the answer options is correct.
the correlation between midterm 1 and midterm 2 scores is positive.
A company has three divisions and three conference rooms for meetings. To keep track of the use of their facilities, for each meeting the company records the name of the division holding the meeting, the conference room used, and the length of time of the meeting. Which of the variables is quantitative? Select one: the name of the division holding the meeting the conference room used the length of time of the meeting All of the answer options are correct.
the length of time of the meeting
Which of the following is likely to have a mean that is smaller than the median? Select one: the scores of students (out of 100 points) on a very difficult exam, in which most scores are low but a few scores are high the scores of students (out of 100 points) on a very easy exam, in which most scores are high but a few scores are low the prices of homes in a large city, where there are lots of relatively inexpensive homes and a few very expensive homes the salaries of all National Football League players, where a few players make much more than most players
the scores of students (out of 100 points) on a very easy exam, in which most scores are high but a few scores are low
A researcher has developed a new drug designed to reduce blood pressure. In an experiment, 22 subjects were assigned randomly to the treatment group and received the new experimental drug. The other 24 subjects were assigned to the control group and received a standard, well-known treatment. After a suitable period, the reduction in blood pressure for each subject was recorded. A summary of these data is: nn x¯x¯ ss Treatment group (new drug) 22 23.48 8.01 Control group (old drug) 24 18.52 7.15 Without using software, how would you estimate the number of degrees of freedom for this problem? Select one: use the smaller value, 22, chosen from the two options 22 and 24 use the larger value, 23, chosen from the two options 21 and 23 use the larger value, 24, chosen from the two options 22 and 24 use the smaller value, 21, chosen from the two options 21 and 23
use the smaller value, 21, chosen from the two options 21 and 23
The magazine High Times has a website that once asked visitors whether recreational marijuana use should be legal. This is an example of: Select one: a survey with little bias, because a large simple random sample was used. voluntary response sampling. a survey with little bias, because someone who responded would know his or her opinion. All of the answer options are correct.
voluntary response sampling
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 to 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. The explanatory variable is: Select one: weekly income. gender weekly expenditure. All of the answer options are correct.
weekly income
Is there a difference in the amount of airborne bacteria between carpeted and uncarpeted rooms? In an experiment, seven rooms were carpeted and seven were left uncarpeted. The rooms were similar in size and function. After a suitable period, the concentration of bacteria in the air was measured (in units of bacteria per cubic foot) in all of these rooms. The data and summaries are provided: x¯x¯ ss Carpeted rooms 184 22.0 Uncarpeted rooms 170 16.9 A 95% confidence interval for the difference in mean bacterial concentration in the air of carpeted rooms versus uncarpeted rooms (using the conservative value for the degrees of freedom) is: Select one: −16.66 to 34.66. −7.47 to 31.47. −11.7 to 39.7. −18.89 to 42.89.
−11.7 to 39.7.
