Statistics Final Exam
Which of the following is the best description of a sample of size n from a population of size N
(b) Any method of sampling in which every group of individuals of size n is equally likely to be selected.
A political action committee sends out a questionnaire to randomly-selected mailing addresses, asking people to rate the importance of a variety of economic and social issues facing the country. At the end of the questionnaire is an (optional) invitation to donate money to the organization. Which of the following statements about this survey is true?
(d) The survey results will overestimate support for this political action committee in the entire population because people more likely to respond if they are prepared to donate money.
The five-number summary for the weights (in grams) of 1200 tomatoes grown in a certain greenhouse was 90 113.5 140 161 236. How many tomatoes weighed less than 161 grams?
(e) 900
. A forester studying oak trees finds that the correlation between x = the ages (measured in years) and y = height (in feet) of a sample of trees is 0.78. Which of the following statements must be true?
. If we measure the height in meters instead of feet, the correlation would still be 0.78.
In your top dresser drawer are 6 blue socks and 10 grey socks, unpaired and mixed up. One dark morning you pull two socks from the drawer (without replacement, of course!) What is the probability that the two socks match?
.500
Of people who died in the United States in a recent year, 86% were white, 12% were black, and 2% were Asian. ( we ignore the small number of deaths among other races). Diabetes cause 2.8% of deaths among whites, 4.4% among blacks, and 3.5% among Asians. The probability that a randomly chosen death was due to diabetes is about
0.030
if 10 people appear at random to give blood, what is the probability that at least 1 of them is a universal donor
0.5263
A special 20 sided die is constructed so that each face has either a 1,2,3, or 4 on it. The table below gives the probability of each value. Which of the following is the probability of rolling an odd number?
0.6
Gabriel has determined that if he gets to the bus stop by 7:30 am, there is a 0.15 probability that he misses the bus and that the consecutive days are independent. If he is at the bus stop three times consecutive days at 7:30, what is the approximate probability that he catches the bus all three days ?
0.614
All of the following small data sets have a mean of 5. Which one has the lowest standard deviation?
1 3 555 7 9
One flight—Philadelphia to West Palm Beach, FL—is 953 miles long and costs $110. Which of the following expressions correctly represents the residual for this data point?
110 − (101.24 + 0.02977 ⋅ 953)
In 1965, the mean price of a new car was $2,650 and the standard deviation was $1,000. In 2011, the mean was $30,500 and the standard deviation was $9,000. If a Ford Mustang cost $2,300 in 1965 and $28,000 in 2011, in which year was it more expensive relative to other cars?
1965, because the standardized score is greater than in 2011.
You randomly select one truck owner. What is the probability that he owns a chevy, given that he has four wheel drive.
32/80
Forty pound bags of bird seed do not have exactly 40 pounds of seed, but the weight of seed is approximately Normally distributed with a mean of 40 pounds and a standard deviation of 0.25 pounds. Which if the following is the best estimate of the 90th percentile for the weight of bags of seed?
40. 3 pounds
The cumulative relative frequency graph at right shows the distribution of lifespans for 39 U.S. presidents. Which of the following is closest to the 70th percentile of this distribution?
77
Randomly select one truck owner. What is the probability that he or she owns a Dodge or has four-wheel drive?
90/125
The same 1200 tomatoes from above have a mean weight of 143 grams and a standard deviation of 35 grams. If the weights are Normally distributed, approximately how many tomatoes weight between 73 grams and 178 grams?
978
Which of the two way tables below conveys the same information.
B-B
What is the principle purpose of control in a randomized comparative experiment.
Eliminating Bias
Which of the following is not true about the standard deviation?
If the units for the data are in inches, standard deviation is in square inches.
A track coach wants to test the effectiveness of a new training program for distance runners. He selects his two fastest runners and, using a coin flip, randomly chooses one to participate in the new program. The other will continue with the standard training regimen. He then picks the next two runners and randomly assigns one to each program. He repeats this process with all his runners, choosing the two fastest remaining each time. He then compares race times each group of two runners. What is the name for this kind of experimental design?
Matched Pair Designs
For the density curve shown, which letters correspond to the locations of the mean and median of the distribution?
Mean = A; Median = B
For the density curve shown at right, which letters correspond to the locations of the mean and median of the distribution?
Median=B; Mean=A
Which of the following statements about standard deviation is true?
Standard deviation is always a non-negative number
The bar graph at right shows the distribution of religious affiliation around the world. Which of the following statement best describes what is wrong with this graph?
Starting the vertical scale at 5 distorts the relative frequency of the religions
An airline has 10 daily flights from Philadelphia to Denver. To assess customer satisfaction, a random sample of 15 passengers from each flight on a single day is asked to fill out a survey about their experience on the flight. What type of sample is this?
Stratified random sample
Some studies of the relationship between car color and frequency of accidents have found that red cars are more likely to be in accidents than black cars, despite how visible they are. Some experts warn that we should not conclude that red cars are less safe than black cars, because of possible confounding. Which of the following best describes what this means?
Studies of this type are all observational, and it is not possible to separate the effect of car color from the type of people who choose to drive red cars.
One hundred people work at Lagtime Internet Services. Suppose after a particularly successful year, the president of the company decided to double his own salary and not change anyone else's. Assuming the president makes more than anyone else, which of the following statements about changes in measures of center and spread is true?
The mean and standard deviation will increase, but the median and interquartile range will stay the same
The time it takes people to finish a certain kind of puzzle is strongly skewed right. Which of the following statements is true about the mean and median of this distribution?
The mean will be greater than the median.
Shown below are box plots describing the distribution of prices paid for homes in two suburbs of Columbus, Ohio over a single 30-day period in 2016. Which of the following statements is supported by the information in this graph?
The median house price in Dublin is higher than the 75th percentile of house price in Westerville.
. The weights of adult male Labrador Retrievers are approximately Normally distributed with a mean of 87 pounds and a standard deviation of 8 pounds. Which of the following statements is true?
The proportion of adult male Labrador Retrievers that weigh less than 80 pounds is approximately equal to the proportion that weigh more 94 pounds.
A recent investigation of prices for five-year-old Toyota Camrys in Montgomery, Alabama, and New York, New York, revealed that the mean price in Montgomery was $13,200 with a standard deviation of $1000. In New York, the mean price was $12,800 with a standard deviation of $1800. Which of the following statements is true?
The standard score for a car priced at $15,000 would be higher in Montgomery than in New York.
Randomly select one truck owner. Which one of the followings true about the events "Owner has a Chevy" and "Owner's truck has four-wheel drive"?
These two events are not mutually exclusive, but they are independent
For the track coaches study described in the previous question, which of the following best describes the conclusion that can be drawn.
We can determine whether the new training program improves race times more than the standard program for the distance runners in this study.
The unusual point in the upper left part of the plot is for navy beans, with 15.8 grams of protein and 15.8 grams of carbs. Which of the following best describes how correlation would change if we removed navy beans from the data set?
a) (0.84)(5.3)/(15.7)
Which of the following best describes what S=20.7237 measures?
c) the standard deviation of the residuals
If you flip three coins, the probability of getting three heads is 0.125. Which of the following statements follows this?
d) if you flip three coins 5000 times, the percentage of time you get three heads will be very close to 12.5%
The least squares regression line minimizes the sum of the
squared differences between actual and predicted Y values
Which of the following is closest to the 61st percentile of the standard Normal distribution?
z = 0.28