Exam 1
A population is
the collection of all items of interest in a particular study
Z-Score
the standardized value
A researcher has collected the following sample data. 5 12 6 8 5 6 7 5 12 4 Refer to Exhibit 3-1. The 75th percentile is: (please don't use computer to calculate this question)
8
The variance of a sample of 81 observations equals 64. The standard deviation of the sample equals
8
A researcher has collected the following sample data. 5 12 6 8 5 6 7 5 12 4 Refer to Exhibit 3-1. The sample variance is (please don't use computer to calculate this question)
8.22
The empirical rule states that, for data having a bell-shaped distribution, the percentage of data values being within two standard deviations of the mean is approximately
95
Variable
A characteristic of interest for the elements
Random variable
A numerical description of the outcome of an experiment
A random variable that can assume only a finite number of values is referred to as a
discrete random variable
Quantitative data refers to data obtained with a
either interval or ratio scale
Probability distribution
for a random variable describes how probabilities are distributed over the values of the random variable
Coefficient of variation
how large the standard deviation is in relation to the mean
The number of hours worked (per week) by 400 statistics students are shown below. Number of Hours Frequency 0-9 20 10-19 80 20-29 200 30-39 100 The cumulative relative frequency for the class of 20-29
is 0.75
Can probability be negative?
no, the sum must also must equal 1
Refer to Exhibit 1-3. Employee Number is an example of ________ data.
nominal
Refer to Exhibit 1-3. Gender is an example of ________ data.
nominal
Some hotels ask their guests to rate the hotel's services as excellent, very good, good, and poor. This is an example of the
ordinal scale
Sample statistic
point estimator of the corresponding population parameter
pth percentile
pth percentile = (p/100)n
Five hundred residents of a city are polled to obtain information on voting intentions in an upcoming city election. The five hundred residents in this study is an example of a
sample
A random sample of 100 cars was selected from a population of 10,000 cars. Based upon that sample, the mean MPG of the cars was calculated determined to be 18. The mean based upon this sample is called a
sample statistic
A researcher has collected the following sample data. 5 12 6 8 5 6 7 5 12 4 Refer to Exhibit 3-1. What is the residual of the observation "4"?
-3
A life insurance company has determined that the number of claims filed follows a Poisson distribution in its Nashville branch. On average, seven claims are filed per week. What is the probability that during the next week at least seventeen claims will be filed? (keep 3 decimals)
0.001
During lunchtime, customers arrive at Bob's Drugs according to a Poisson distribution with on average 4 customers per minute. What is the probability of two arrivals in a two-minute period? (keep 3 decimals)
0.011
During lunchtime, customers arrive at Bob's Drugs according to a Poisson distribution with on average 4 customers per minute. During a one minute interval, determine the following probability: no arrivals (keep 3 decimals)
0.018
The following is a frequency distribution of the monthly expenditures for long distance telephone service of 200 households in Chattanooga. class 2: 20 and under 40, 64 what is the cumulative relative frequency?
0.53
During lunchtime, customers arrive at Bob's Drugs according to a Poisson distribution with on average 4 customers per minute. During a one minute interval, determine the following probability: three or more arrivals. (keep 3 decimals)
0.762
Exhibit 5-5 AMR is a computer-consulting firm. The number of new clients that they have obtained each month has ranged from 0 to 6. The number of new clients has the probability distribution that is shown below. Number of New Clients Probability 0 0.05 1 0.10 2 0.15 3 0.35 4 0.20 5 0.10 6 0.05 The variance is
2.0475
x is a random variable with the probability function: f(x) = x/6 for x = 1,2 or 3. The expected value of x is
2.333
Exhibit 5-10 The probability that Pete will catch fish on a particular day when he goes fishing is 0.8. Pete is going fishing 3 days next week. Refer to Exhibit 5-10. The expected number of days Pete will catch fish is
2.4
A researcher has collected the following sample data. The mean of the sample is 5. 3 5 12 3 2 Refer to Exhibit 3-2. The coefficient of variation is
81.24%
Ogive
A graph of a cumulative distribution
Sample
A subset of the population
Crosstabulation
A tabular summary of data for two variables
Frequency Distribution
A tabular summary of data showing the frequency of items in each of several non-overlapping classes
Data set
All the data collected in a particular study
Excel's BINOM.DIST function can be used to compute
Both binomial probabilities and cumulative binomial probabilities are correct
Excel's __________ function can be used to compute the mode.
MODE.SNGL
When using Excel's BINOM.DIST function, one should choose TRUE for the fourth input if
a cumulative probability is desired
Correlation
a measure of linear association and not necessarily causation
Covariance
a measure of the linear association between two variables
The total number of data items with a value less than the upper limit for the class is given by the
cumulative frequency distribution
The summaries of data, which may be tabular, graphical, or numerical, are referred to as
descriptive statistics
The number of hours worked (per week) by 400 statistics students are shown below. Number of Hours Frequency 0-9 20 10-19 80 20-29 200 30-39 100 The cumulative frequency for the class of 20-29
is 300
How to find the width of a class
(largest - smallest) / numbers of classes
Sample statistics
If the measure are computed for data from a sample
Population parameters
If the measures are computed for data from a population
Quantitative Data
Information about quantities (discrete and continuous)
Range
Largest number - Smallest number
Excel's __________ function can be used to compute the median.
MEDIAN
You are the manager of Warm Stone Creamery at Canal Park. The owner is interested in customers' spending in her shop. Today, you observed that the first four customers spent $5, $2, $9, and $4. You know that the average sales must be at least $4 for the shop to make a profit. What is the standard deviation of your sample?
$2.94
You are the manager of Warm Stone Creamery at Canal Park. The owner is interested in customers' spending in her shop. Today, you observed that the first four customers spent $5, $2, $9, and $4. You know that the average sales must be at least $4 for the shop to make a profit. What are the mean, median, and mode of your sample?
$5, $4.50, all observations occur exactly once
Exhibit 5-2 The probability distribution for the daily sales at Michael's Co. is given below. Daily Sales ($1,000s) Probability 40 0.1 50 0.4 60 0.3 70 0.2 Refer to Exhibit 5-2. The expected daily sales are
$56,000
Sample equation
(s/mean) * 100
You are the manager of Warm Stone Creamery at Canal Park. The owner is interested in customers' spending in her shop. Today, you observed that the first four customers spent $5, $2, $9, and $4. You know that the average sales must be at least $4 for the shop to make a profit. What is the residual of the $4 observation?
-$1
Exhibit 5-10 The probability that Pete will catch fish on a particular day when he goes fishing is 0.8. Pete is going fishing 3 days next week. Refer to Exhibit 5-10. The variance of the number of days Pete will catch fish is
.48
A life insurance company has determined that the number of claims filed follows a Poisson distribution in its Nashville branch. On average, seven claims are filed per week. What is the probability that during the next week fewer than four claims will be filed? (keep 3 decimals)
0.082
Exhibit 5-10 The probability that Pete will catch fish on a particular day when he goes fishing is 0.8. Pete is going fishing 3 days next week. Refer to Exhibit 5-10. The probability that Pete will catch fish on exactly one day is
0.096
Exhibit 5-10 The probability that Pete will catch fish on a particular day when he goes fishing is 0.8. Pete is going fishing 3 days next week. Refer to Exhibit 5-10. The probability that Pete will catch fish on one day or less is
0.104
A life insurance company has determined that the number of claims filed follows a Poisson distribution in its Nashville branch. On average, seven claims are filed per week. What is the probability that during the next week exactly seven claims will be filed? (keep 3 decimals)
0.149
A manufacturer of computer disk drives has a historical defective rate of .001. What is the probability that in a batch of 1000 drives, 2 would be defective? (keep 3 decimals) (hint: what is the number of trials? what is the 'success' rate?)
0.184
A life insurance company has determined that the number of claims filed follows a Poisson distribution in its Nashville branch. On average, seven claims are filed per week. What is the probability that during the next week there are either 4 or 5 claims will be filed? (keep 3 decimals)
0.219
Exhibit 5-5 AMR is a computer-consulting firm. The number of new clients that they have obtained each month has ranged from 0 to 6. The number of new clients has the probability distribution that is shown below. Number of New Clients Probability 0 0.05 1 0.10 2 0.15 3 0.35 4 0.20 5 0.10 6 0.05 The standard deviation is
1.431
A researcher has collected the following sample data. The mean of the sample is 5. 3 5 12 3 2 Refer to Exhibit 3-2. The range is
10
The following table shows the starting salaries of a sample of recent business graduates. Income (In $1,000s), # of Graduates 15 - 19 40 20 - 24 60 25 - 29 80 30 - 34 18 35 - 39 2 What percentage of graduates in the sample had starting salaries of at least $30,000? Of the graduates in the sample, what percentage had starting salaries of less than $25,000?
10 50
The number of hours worked (per week) by 400 statistics students are shown below. Number of Hours Frequency 0-9 20 10-19 80 20-29 200 30-39 100 Refer to Exhibit 2-1. The number of students who work 19 hours or less is
100
Exhibit 5-5 AMR is a computer-consulting firm. The number of new clients that they have obtained each month has ranged from 0 to 6. The number of new clients has the probability distribution that is shown below. Number of New Clients Probability 0 0.05 1 0.10 2 0.15 3 0.35 4 0.20 5 0.10 6 0.05 Refer to Exhibit 5-5. The expected number of new clients per month is
3.05
The following is a frequency distribution of the monthly expenditures for long distance telephone service of 200 households in Chattanooga. class 3: 40 and under 60, 34 class 4: 60 and under 80, 28 class 5: 80 and under 100, 20 Refer to Exhibit 1-5. What percentage of households have monthly expenditure for long distance service between $40 and $100?
41%
The median of a sample will always equal the
50th percentile
You are the manager of Warm Stone Creamery at Canal Park. The owner is interested in customers' spending in her shop. Today, you observed that the first four customers spent $5, $2, $9, and $4. You know that the average sales must be at least $4 for the shop to make a profit. What is the coefficient of variation?
58.8%
In many universities, students evaluate their professors by means of answering a questionnaire. Assume a questionnaire is distributed to a class of 45 students. Students are asked to answer the following: 1. Sex 2. Race (Black, White, Other) 3. Age 4. Number of hours completed 5. Grade point average 6. My instructor is a very effective teacher How many variables are in this data set?
6
Excel's __________ function can be used to compute the sample correlation coefficient.
CORREL
Cross-sectional data
Collected at the same or approximately the same point in time
Census
Collecting data for the entire population
Nominal
Data are labels or names used to identify an attribute of the element ex: Names of where students are enrolled in (education, science, business)
3 types of data sources
Existing, Experimental, Observational
You are the manager of Warm Stone Creamery at Canal Park. The owner is interested in customers' spending in her shop. Today, you observed that the first four customers spent $5, $2, $9, and $4. You know that the average sales must be at least $4 for the shop to make a profit. Based on this sample can we be sure the shop will make a profit during the entire day?
No, we cannot be sure how much the other customers will spend.
If we only have the relative frequency table for the outcomes of a discrete random variable, Excel's __________ function can be used to compute the expected value of this discrete random variable.
SUMPRODUCT
Expected value
Same thing as a mean
Descriptive statistics
Summaries of data, which may be tabular, graphical, or numerical
Ratio
The data have all the properties of interval data and the ratio of two values is meaningful ex: Yufei- 36 credit hours Kevin- 72 credit hours - Kevin has 2x as many hours as Yufei
Ordinal
The data have the properties of nominal data and the order or rank of the data is meaningful ex: classified as freshman, sophomore, etc.
Interval
The data have the properties of ordinal data, and the interval between observations is expressed in terms of a fixed unit of measure *always numeric ex: SAT scores
Elements
The entities on which data are collected
Inferential statistics
The process of using data obtained form a sample to make estimates and test hypotheses about the characteristics of a population
Population
The set of all elements of interest in a particular study
Observation
The set of measurements obtained for a particular element
Which of the following is a characteristic of a binomial experiment?
The trials are independent
Categorical Data
Uses nominal or ordinal scale of measurement
Statistical Inference
Using data obtained from a sample to make estimates and test hypotheses about the characteristics of a population
A frequency distribution is
a tabular summary of a set of data showing the frequency of items in each of several nonoverlapping classes
Percent frequency distribution
a tabular summary of a set of data showing the percent frequency for each class
Relative frequency distribution
a tabular summary of a set of data showing the relative frequency for each class
Cumulative relative frequency distribution
shows the proportion of items with values less than or equal to the upper limit of each class. The last entry equals 1
The correlation coefficient
cannot be larger than 1
Time series data
collected over several time periods
A discrete probability distribution for which the relative frequency method is used to assign probabilities is the
empirical discrete distribution
Histogram chart
graphical presentation of quantitative data
The number of hours worked (per week) by 400 statistics students are shown below. Number of Hours Frequency 0-9 20 10-19 80 20-29 200 30-39 100 The class width for this distribution
is 10
Continuous random variable
may assume any numerical value in an interval or collection of intervals
Discrete random variable
may assume either a finite number of values or an infinite sequence of values
A sample of 9 mothers was taken. The mothers were asked the age of their oldest child. You are given their responses below 3 12 4 7 14 6 2 9 11 What is the mean, standard deviation and 75th percentile?
mean: 7.56 standard deviation: 4.22 75th percentile: 11
After the data has been arranged from smallest value to largest value, the value in the middle is called the
median
During a cold winter, the temperature stayed below zero for 10 days. The variance of the temperatures of the 10 day period
must be at least zero
Cumulative frequency distribution
shows the number of items with values less than or equal to the upper limit of each class
Cumulative percent frequency distribution
shows the percentage of items with values less than or equal to the upper limit of each class. the last entry equals 100
Discrete uniform probability distribution
simplest example of a discrete probability distribution given by a formula f(x)= 1/n
As one of its major contributions, statistics uses data from a sample to make estimates and test hypotheses about the characteristics of a population through a process referred to as
statistical inference
Statistics
the art and science of collecting , analyzing, presenting, and interpreting data
Data
the facts and figures collected, analyzed, and summarized for presentation and interpretation
Relative Frequency
the fraction or proportion of the total number of data items belonging to the class Relative frequency= frequency/total number
Percent frequency
the relative frequency multiplied by 100
Which of the following is not a characteristic of an experiment where the binomial probability distribution is applicable?
the trials are dependent
Outlier
z-score less than -3 or greater than 3
Which of the following is not a required condition for a discrete probability function?
∑f(x) = 0