Stats exam 1
What is the cumulative relative frequency of the class "18 up to 21"?
0.6
What fraction of players weigh between 175 and 220 pounds?
0.7066
Find the probability that a randomly selected teacher receives a salary of more than $45,000. (Do not round your answer)
0.779
Refer to the Exhibit Teacher's Salary. Find the probability that a randomly selected teacher receives a salary of $45,000 or more. (Do not round your answer)
0.779
Airline Arrivals: What fraction of flights arrived on time or late?
0.8533
The variance of restaurant visits is calculated to be 0.75. What is the standard deviation of restaurant visits per week? (Please, round your solution to at least 2 decimal places).
0.87
What is the probability that 9 or less students will be accepted?
0.944
What is the cumulative relative frequency for the class of 30 - 39?
1
Refer to the Exhibit Restaurant Visits. What is the mean number of restaurant visits in the sample? (Please, do not round your answer).
1.25
Refer to the Exhibit Mother's Day Gifts. What is the value of the 1st quartile for this sample? (Round your answer to 4 decimal places)
129
Refer to the Exhibit Mother's Day Gifts. What is the 40th percentile for this sample? (Round your answer to 4 decimal places)
134.6
Refer to the Exhibit Mother's Day Gifts. What is the value of the median for this sample?
139
Refer to the Exhibit Mother's Day Gifts. What is the value of the mean for this sample? (Round your answer to 4 decimal places)
142
The following table shows a frequency distribution of the number of MacBook Air laptops sold per day at a particular Best Buy: Number of Laptops Frequency 0 2 1 1 2 4 3 5 4 2 5 2 What is the mean number of MacBook Air laptops sold per day? (Round your answer to 3 decimal places)
2.625
What is the expected number of CFA candidates who have a degree in economics? (Do not round your answer. Depending on which approach you take to calculate the expected value, shortcut or general formula, the answers may slightly differ because of rounding. Either solution will be accommodated in this question.)
2.64
Consider the following frequency distribution: Class Frequency 12 up to 15 3 15 up to 18 6 18 up to 21 3 21 up to 24 4 24 up to 27 4 The total number of observations to construct this frequency distribution is
20
What is the minimum weight of the top 5% of the players?
222.8971
What fraction of flights was at least half an hour late?
0.03
Refer to the Exhibit Mother's Day Gifts. Using the sample data, it was computed that the z-score for a data value of $166 is 0.96. Calculated z-score is best interpreted as:
Spending of $166 is 0.96 standard deviations above the mean spending
The standard deviation of a sample of 100 elements taken from a very large population is determined to be 60. The variance of the population
can be any value greater than zero
The cumulative relative frequency for the class "0 up to 10" is 0.66. This means that
66% of stocks have returns below 10%
If 69.5 percent of the students received grades of C or better, what is the minimum score of those who received C's?
67.3892
The following data represent the recent sales price (in $1,000s) of 24 homes in a Midwestern city:187 125 165 170 230 139 195 229239 135 188 210 228 172 127 139122 181 196 237 115 199 170 239Suppose the data are grouped into five classes, and one of them will be "165 up to 190." The frequency of this class is
7
What is the probability that less than 7 students will be accepted?
0.4167
What is the probability that less than 3 CFA candidates in the sample have a degree in economics? (Do not round your answer)
0.477
Consider the following probability distribution for the random variable x. xP(x) -2 0.2 -1 0.1 0 0.3 1 0.4 The expected value of this random variable is:
-0.1
Refer to the Exhibit Mother's Day Gifts. What is the z-score for the data value $137 in this sample? (Round your answer to 4 decimal places)
-0.2007
The covariance between the returns of stocks A and B is -0.112. The standard deviation of the rates of return is 0.26 for stock A and 0.81 for stock B. The correlation of the rates of return between A and B is the closest to
-0.53
What is the sample covariance for this data? (provide the answer below rounding it to 4 decimal places)
-0.5513
What is the sample coefficient of correlation for this data? (provide the answer below rounding it to 4 decimal places)
-0.917
In a standard normal distribution, the probability that z is greater than zero is
0.5
Refer to the Exhibit Student Grades. What faction of students scored above 73?
0.5
What fraction of flights was 5 to 10 minutes early?
0.04
What is the probability that exactly 10 students will be accepted?
0.0442
Refer to the Exhibit Hours Worked. What is the relative frequency of students working 9 hours or less?
0.05
What is the probability of a player weighing more than 220 pounds?
0.0668
Suppose, you obtained the following probability distribution for the random variable x: xP(x)00.04110.16020.27630.27240.16750.06660.01670.00280.000 What is the probability that at least 5 CFA candidates in the sample have a degree in economics? (Do not round your answer)
0.084
Students who made 57.93 or lower on the exam failed the course. What fraction of students failed the course?
0.0853
The following table shows the probability distribution for the number of boats sold daily at Boats Unlimited. What is the probability that exactly 3 boats are sold? x f(x) 0 0.20 1 0.30 2 0.32 3 ? 4 0.05 5 0.02
0.11
What fraction of flights arrived early during this time?
0.1467
What fraction of flights was 5 to 10 minutes late?
0.17
What is the fraction of students working 19 hours or less?
0.25
What is the relative frequency of the class "15 up to 18"?
0.3
Refer to the Exhibit University Applications. What is the probability that at least 8 students will be accepted?
0.3557
What is the probability that more than 7 students will be accepted?
0.3557
Twenty percent of the students in a class of 100 are planning to go to graduate school. The standard deviation of this binomial distribution is
4
The statistics professor has kept attendance records and recorded the number of absent students per class. The recorded data is displayed in the following bar chart with the frequency of each number of absent students shown above the bars.
43
Assume that you have a binomial experiment with p = 0.5 and a sample size of 100. The expected value for this distribution is
50
Refer to the Exhibit Condo Price. The city government exempts the cheapest 6% of the condos from city taxes. What is the maximum price of the condos that will be exempt from city taxes?
50.2472
Suppose the wait through immigration at JFK Airport in New York is thought to be bell-shaped and symmetrical distributed with a mean of 22 minutes. It is known that 68 percent of travelers will spend between 16 and 28 minutes waiting to pass through immigration. The standard deviation for the wait time through immigration is
6 minutes
Determine the expected number of acceptances.
6.84
Refer to the Exhibit Mother's Day Gifts. Using the sample data, it was computed that the 60th percentile for this data is $143.4. Calculated 60th percentile is best interpreted as:
60% of all gift spending for the Mother's Day are below $143.4
Due to budget limitations, it has been decided that the teachers who are in the top 2.5% of the salaries would not get a raise. What is the salary level that divides the teachers into one group that gets a raise and one that doesn't? (Do not round your answer). Assume that the value of z 0 such that P ( z ≥ z 0 ) = 0.025 is equal to 1.96.
62,740
Refer to the Exhibit Mother's Day Gifts. What is the value of the variance for this sample? (Round your answer to 4 decimal places)
620.9091
The following data represent the recent sales price (in $1,000s) of 24 homes in a Midwestern city:187 125 165 170 230 139 195 229239 135 188 210 228 172 127 139122 181 196 237 115 199 170 239Suppose the data are grouped into five classes, and one of them will be "115 up to 140." The relative frequency of this class is
7/24
Refer to the Exhibit Mother's Day Gifts. Using the sample data, it was computed that the 3d quartile for this sample equals $161.5. This is best interpreted as:
75% of spending for the Mother's Day are below $161.5
The professor has informed the class that 7.93 percent of her students received grades of A. What is the minimum score needed to receive a grade of A?
88.5078
Refer to the Exhibit Wait Times. Comparing values of the mean, the median and the standard deviation for the offices with and without a tracking system, what would you say about efficiency in accommodating patients of the offices with a wait tracking system (compared to the offices without a tracking system)?
A tracking system helps accommodating patients in a more efficient way which is supported by the lower average and median wait times, as well as the lower standard deviation of the waiting times
The Boom company has recently decided to raise the salaries of all employees by 10%. Which of the following is(are) expected to be affected by this raise?
Mean, median, and mode
The accompanying chart shows the numbers of books written by each author in a collection of cookbooks. What type of chart is this?
Bar chart for qualitative data
Based on the sample coefficient of correlation, what can you say about the strength of the relationship between variables?
Because the coefficient of correlation is close to -1, there is a strong relationship between smoke detectors and death rate
Based on the coefficient of correlation, what can you say about the direction of the relationship between variables?
Because the correlation coefficient is negative, there is a negative relationship between variables. I.e. more smoke detectors is associated with less death.
Based on the sample covariance, what can you say about the direction of the relationship between variables?
Because the covariance is negative, there is a negative relationship between variables. I.e. more smoke detectors is associated with less death.
Refer to the Exhibit CFA Candidates. What is the the probability distribution of the random variable x?
Binomial
How do we find the median if the number of observations in a data set is odd?
By taking the middle value in the sorted data set
Based on the sample covariance, what can you say about the strength of the relationship between variables?
Covariance is not used to determine the strength of the relationship between variables. So, nothing can be inferred about the strength of the relationship between smoke detectors and death rate from the sample covariance.
Refer to the Exhibit Wait Times. Consider patients with a wait time of 37 minutes in the samples of offices with and without a wait tracking system (10th and 6th patient in the data, respectively). Comparing the z-scores for these two patients, what would you conclude?
Even though the wait time is the same for these patients, the z-scores are different because the patients belong to the samples with different means and standard deviations
Which of the following variables is qualitative?
Gender
Which scales of data measurement are associated with quantitative data?
Interval and ratio
In the following pie chart representing a collection of cookbooks, which author has more titles?
Julia Child
Suppose that you conduct a study in which you observe parents and their children interacting at home. You find that the more supportive parents are, the less aggressive their children are. What conclusion can you make?
Level of support and aggression are negatively correlated.
Which of the following is an example of cross-sectional data?
Results of market research conducted in 2012 testing consumer preferences for soda
Frequency distributions may be used to describe which of the following types of data?
Nominal, ordinal, interval, and ratio data
If two groups of numbers have the same mean, then
None of the suggested alternatives is correct
The mean of the sample is always smaller than the mean of the population from which the sample was taken can never be negative can never be zero None of the suggested alternatives is correct
None of the suggested alternatives is correct
It is known that the length of a certain product x is normally distributed with µ = 20 inches. How is the probability P ( x > 16 ) related to P ( x < 16 )?
P ( x > 16 )is greater than P ( x < 16 )
If x has a normal distribution with µ = 100 and σ = 5, then the probability P ( 90 ≤ x ≤ 95 ) can be expressed in terms of a standard normal variable z as
P ( − 2 ≤ z ≤ − 1 )
The accompanying chart shows the numbers of books written by each author in a collection of cookbooks. What type of data is being represented?
Qualitative, nominal
Which one of the following statements is true for a right-skewed distribution?
The mean is greater than the median.
Refer to the Exhibit Mother's Day Gifts. What is the value of the mode for this sample?
The mode does not exist
Which of the following can be represented by a discrete random variable?
The number of obtained spots when rolling a six-sided die
Refer to the Exhibit Smoke Detectors. In the scatter plot, which of the following do you use as an independent variable on the horizontal axis?
The percentage of homes with smoke detectors
Which of the following is NOT a characteristic of a binomial experiment?
The probability of a success must exceed the probability of a failure.
Which of the following is NOT a characteristic of the normal probability distribution?
The standard deviation must be 1
Which of the following can be represented by a continuous random variable?
The time of a flight between Chicago and New York
Refer to the Exhibit Wait Times. Do the data for offices with and without a tracking system contain outliers? Hint: that's where you want to use the z-scores.
There are no outliers in the data
Based on the scatter plot, what would you conclude about the direction of the relationship between analyzed variables?
There is a negative linear relationship because the fitted line which describes this relationship is negatively sloped
Based on the scatter plot, what would you conclude about the strength of the relationship between analyzed variables?
There is a strong linear relationship because the dots (observations) come close to the fitted line on the graph
Which of the following characteristics does the interval scale NOT have?
There is a true zero point.
The data represents the stock price for Google at the end of the past four quarters. Which of the following types of data best describes these values?
Time series
Is it possible for a data set to have more than one mode?
Yes, if two or more values in a data set occur with the most frequency.
Positive values of the correlation coefficient indicate
a positive relation between the independent and the dependent variables
A population consists of
all items of interest in a study
Which of the following is a quantitative variable? house size house prize house age all of the suggested choices
all of the suggested choices
The random variable x can take
any integer value between 0 and 8 (including 0 and 8)
A continuous random variable may assume
any value in an interval or collection of intervals
In inferential statistics, we calculate sample statistics to
estimate unknown population parameters
The Fahrenheit scale for measuring temperature would be classified as a(n)
interval scale
If a data set has an even number of observations, the median
is the average value of the two middle items when all items are arranged in ascending order
The center of a normal curve
is the mean of the distribution
When outliers are present in the data set, which measure is the best to describe central tendency in the data?
median
The median is defined as the
middle point in a data set
The covariance ranges between
minus infinity and plus infinity
Which measure would you use to describe central tendency for qualitative data?
mode
During a cold winter, the temperature stayed below zero for ten days (ranging from -20 to -5). The variance of the temperatures of the ten-day period
must be positive
The normal distribution can well approximate the binomial distribution as long as
n p ≥ 5 , n q ≥ 5
The following graph shows the curb weight of seven cars, in pounds, along with their corresponding highway miles per gallon: miles per gal on y-axis curb weight on x-axis
scatter plot, and miles per gallon is the dependent variable in the graph
A smaller standard deviation for the normal probability distribution results in a
skinnier curve that is tighter and taller around the mean
Data that describe a characteristic about a sample is known as a
statistic
If the variance of a data set is correctly computed with the formula using n - 1 in the denominator, which of the following is true?
the data set is a sample
For a continuous random variable x, the probability density function f(x) represents
the height of the function at x
Compute the standard deviation of the distribution.
1.715
Suppose the dealer incentive per vehicle for Honda's Acura brand is thought to be bell-shaped and symmetrical with a mean of $2,500 and a standard deviation of $300. Based on this information, what interval of dealer incentives would we expect approximately 99.7% of vehicles to fall within?
$1,600 to $3,400
Refer to the Exhibit Mother's Day Gifts. What is the unit of measurement for the variance you calculated above?
$^2
For any continuous random variable, the probability that the random variable takes on exactly a specific value is
0
The professor has informed the class that students who scored over 98% on the exam (out of 100 points) demonstrated exceptional performance on the exam. What fraction of students fall into this category?
0.0115
Find the probability that a randomly selected teacher receives a salary greater than $45,000 but less than or equal to $53,000. (Do not round your answer)
0.457
For the standard normal probability distribution, the area under the probability density function to the left of the mean is
0.5
Refer to the Exhibit Football Players. What is the probability of a player weighing less than 230 pounds?
0.9772
Find the variance of x or the number of cups of coffee. (Do not round intermediate steps but round your final answer to 4 decimal places)
0.9899
What is the median number of restaurant visits in the sample? (Please, do not round your answer).
1.5
Refer to the Exhibit Coffee Consumption. Find the expected value of x or the expected number of morning cups of coffee. (Do not round your final answer and intermediate steps if you are doing calculations step-by-step)
1.51
What is the variance in the number of CFA candidates with economics degree? (Do not round your answer. Depending on which approach you take to calculate the variance, shortcut or general formula, the answers may slightly differ because of rounding. Either solution will be accommodated in this question.)
1.7688
What is the minimum weight of the middle 95% of the players? (Please, use Excel to find the value rather than statistical tables to avoid rounding errors)
150.8007
What is the minimum weight of the middle 92% of the players?
154.9863
What is the maximum weight of the bottom 10% of the players?
164.369
If 2% of the most expensive condos are subject to a luxury tax, what is the minimum price of condos that will be subject to the luxury tax?
165.72
What is the mode in the sample? (Please, do not round your answer).
2
What is the range of restaurant visits per week? (Please, do not round your answer).
2
x is a random variable with the probability function P(x) = x/6 for x = 1, 2 or 3. The expected value of x is
2.333
In 2009, the average donation to the Help Way was $225 with a standard deviation of $45. In 2010, the average donation was $400 with a standard deviation of $60. In which year did the donations show a more dispersed distribution? Hint: to answer this question, you need to calculate the coefficient of variation for each year. The donations show a more dispersed distribution in _______ because the coefficient of variation is ________ for that year.
2009 larger
What is the maximum weight of the middle 98% of the players?
236.527
Which of the following is an example of time series data?
Quarterly housing starts collected over the last 60 years
What is the scale of measurement of the distance between any two locations?
Ratio
Which of the following represents a population and a sample from that population?
Residents of Albany, New York, and registered voters in Albany, New York
Population parameters are difficult to calculate due to
both cost prohibitions on data collection and the infeasibility of collecting data on the entire population
Comparing the consistency (variability) between two data sets when their means are very different is best done with the
coefficient of variation
The following data shows the number of students who came to office hours per day for a particular faculty member. 0 0 0 1 3 0 0 3 4 0 1 1 3 1 1 1 1 4 2 2 2 0 2 3 1 2 0 4 The next several questions refer to this exhibit. You can either type this data in Excel or use the Excel file 'HW1 - Questions - Excel Files' under the Files link on Canvas (folder HWs ⟶ HW1).
comment on histogram: For a majority of the 28 days observed, 0 or 1 student went to office hours. As the number of students goes up, the number of days that many students visited office hours goes down. The trendline of this histogram would be downward sloping.
Since the population is always larger than the sample, the value of the sample mean
could be larger, equal to, or smaller than the true value of the population mean
Which of the following measures the direction of the linear relationship between two variables but does not measure the strength of the relationship?
covariance
Suppose that you obtained the following scatter plot for the relationship between variables x and y. (negative slope scatter plot) What would you conclude about sample covariance for this data?
covariance is negative
Your business statistics class had a test last week. The average score for the class is an example of
descriptive statistics
A recent survey of 200 small firms (annual revenue less than $10 million) asked whether an increase in the minimum wage would cause the firm to decrease capital spending. Possible responses to the survey question were: "Yes," "No," or "Don't Know." The scale of measurement for the data generated by this survey question is best classified as
nominal
The covariance between the returns on two assets is negative. This occurs when
on average, the return on one asset increases while the return on the other asset decreases
The sum of the relative frequencies for all classes will always equal to
one
What kind of data assumes that the differences between categories are meaningless?
ordinal
μ is an example of a
population parameter
Which of the following indicates the strongest relationship between two variables?
r = -0.6
An analyst constructed the following frequency distribution on the monthly returns for 50 selected stocks: Class (in percent) Frequency -10 up to 0 8 0 up to 10 25 10 up to 20 15 20 up to 30 2 The frequency for the class "0 up to 10" is 25. This means that
the number of stocks with returns between 0% and 10% is 25.
Which of the following symbols represents the mean of the sample?
x ¯ x-bar
Which of the following statements is NOT true concerning the attributes of z-scores?
z-scores can be positive or negative for data values above the mean of the distribution
Which of the following symbols represents the standard deviation of the population?
σ