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