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