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elementary statistics

Questions and Answers of Elementary Statistics

Using Continuity Correction There are many situations in which a normal distribution can be used as a good approximation to a random variable that has only discrete values. In such cases, we can use
Units of Measurement Weights of women are normally distributed with a mean of 143 lb and a standard deviation of 29 lb.a. If weights of individual women are expressed in units of pounds, what are the
Height Requirement for Rockettes Exercise 19 identified specific height requirements for Rockettes. Suppose that those requirements must be changed because too few women now meet them. What are the
Height Requirement for Rockettes In order to have a precision dance team with a uniform appearance, height restrictions are placed on the famous Rockette dancers at New York’s Radio City Music
Height Requirement for Women Soldiers The U.S. Army requires women’s heights to be between 58 in. and 80 in. Find the percentage of women meeting that height requirement. Are many women being
Beanstalk Club Height Requirement The Beanstalk Club, a social organization for tall people, has a requirement that women must be at least 70 in. (or 5 ft 10 in.) tall.What percentage of women meet
M&Ms Shown below is the Minitab display for the weights (in grams) of the 100 M&M candies listed in Data Set 19 of Appendix B. Although the mean and standard deviation are sample statistics, assume
CD Player Warranty Replacement times for CD players are normally distributed with a mean of 7.1 years and a standard deviation of 1.4 years (based on data from “Getting Things Fixed,” Consumer
TV Warranty Replacement times for TV sets are normally distributed with a mean of 8.2 years and a standard deviation of 1.1 years (based on data from “Getting Things Fixed,” Consumer Reports).a.
Designing Helmets Engineers must consider the breadths of male heads when designing motorcycle helmets. Men have head breadths that are normally distributed with a mean of 6.0 in. and a standard
SAT Test Requirement The combined math and verbal scores for females taking the SAT-I test are normally distributed with a mean of 998 and a standard deviation of 202 (based on data from the College
Lengths of Pregnancies The lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days.a. One classic use of the normal distribution is inspired by a
Body Temperatures Based on the sample results in Data Set 4 of Appendix B, assume that human body temperatures are normally distributed with a mean of 98.20°F and a standard deviation of 0.62°F.a.
Find the IQ score separating the top 55% from the others.
Find the IQ score separating the top 15% from the others.
Find P80, which is the IQ score separating the bottom 80% from the top 20%.
Find P20, which is the IQ score separating the bottom 20% from the top 80%.
Find the probability that a randomly selected adult has an IQ between 110 and 120(referred to as bright normal).
Find the probability that a randomly selected adult has an IQ greater than 131.5 (the requirement for membership in the Mensa organization).
Find the probability that a randomly selected adult has an IQ that is less than 115.
Sketch a graph representing a cumulative distribution for (a) a uniform distribution and (b) a normal distribution.
In a continuous uniform distribution, Find the mean and standard deviation for the uniform distribution represented in Figure 5-2.
Assume that z scores are normally distributed with a mean of 0 and a standard deviation of 1.a. If P(0 , z ,a) 5 0.3907, find a.b. If P(2b , z ,b) 5 0.8664, find b.c. If P(z .c) 5 0.0643, find c.d.
If a continuous uniform distribution has parameters of m 5 0 and s 5 1, then the minimum is 2 and the maximum is .a. For this distribution, find P(21 , x , 1).b. Find P(21 , x , 1) if you incorrectly
For a standard normal distribution, find the percentage of data that area. within 1 standard deviation of the mean.b. within 1.96 standard deviations of the mean.c. between m 2 3s and m 1 3s.d.
If 3.0% of the thermometers are rejected because they have readings that are too high and another 3.0% are rejected because they have readings that are too low, find the two readings that are cutoff
If 5% of the thermometers are rejected because they have readings that are too low, but all other thermometers are acceptable, find the reading that separates the rejected thermometers from the
Find P20, the 20th percentile.
Find P90, the 90th percentile. This is the temperature reading separating the bottom 90% from the top 10%.
a. Construct a graphic representation of the Table 12.1 data using six sideby-side dotplots.b. Visually estimate the mean commute time for each city and locate it with an X.c. Does it appear that the
a. Calculate the mean commute time for each city in Table 12.1.b. Does there seem to be a difference among the mean one-way commute times for these six cities?c. Calculate the standard deviation for
Draw a dotplot of the data in Table 12.2 (p.659). Represent the data using the integers 1, 2, and 3, indicating the level of test factor the data are from. Do you see a “difference” between the
Each department at a large industrial plant is rated weekly. State the hypotheses used to test that“the mean weekly ratings are the same in three departments.”
Refer to the following ANOVA table.Source df SS MS Factor 3 Error 40.4 Total 20 164.2a. Find the four missing values.b. Find the calculated value for F, F.
An analysis of variance experiment with level A containing 10 data values; level B, 12 data values;level C, 10 values; level D, 12 values; level E, 9 values; and level F, 10 values was analyzed using
Referring to Applied Example 12.4:a. Does the category appear to have an effect on the average number of students per computer?Explain.b. The graphic shows three categories. Explain how these three
The amount of monthly rainfall varies from month to month and from city to city. Applied Example 12.5 suggests that the average monthly rainfall is affected by both the month and the location.a. What
Consider the following table for a single-factor ANOVA. Find the following: a. X1,2 b. x2, c. 1 c. C G d. x e. (C) Level of Factor Replicates 1 1 3 2 3 2 0 25 2 7 5 4 3. 1 4 5
The following table of data is to be used for single-factor ANOVA. Find each of the following: a. X3, 2 b. X4, 3 c. C d. x x e. (C) Level of Factor Replicates 1 2 3 4 1 13 12 16 14 2 17 8 18 11 3 9
Find the p-value for each of the following situations:a. F 3.852, df(factor) 3, df(error) 12b. F 4.152, df(factor) 5, df(error) 18c. F 4.572, df(factor) 5, df(error) 22
For the following ANOVA experiments, determine the critical region(s) and critical value(s)that are used in the classical approach for testing the null hypothesis.a. Ho : 1 2 3 4, with n
Why does df(factor), the number of degrees of freedom associated with the factor, always appear first in the critical value notation F[df(factor), df(error), ]?
Two new drugs are being tested for their effect on the number of days a patient must remain hospitalized after surgery. A control group is receiving a placebo, and two treatment groups are each
The article “An Investigation of High School Preparation as Predictors of the Cultural Literacy of Developmental, Nondevelopmental and ESL College Students” (RTDE) reported on a study that
An article titled “The Effectiveness of Biofeedback and Home Relaxation Training on Reduction of Borderline Hypertension” (Health Education)compared different methods of reducing blood pressure.
“The NBA is a big man’s game.Average height for the league is about 6 feet 7 inches, with guards averaging 6 ft 4 in, forwards averaging 6 ft 9 in and centers 7 feet,” as reported in a USA
A new operator was recently assigned to a crew of workers who perform a certain job. From the records of the number of units of work completed by each worker each day last month, a sample of size
An employment agency wants to see which of three types of ads in the helpwanted section of local newspapers is the most effective.Three types of ads (big headline, straightforward, and bold print)
Cities across the United States have restaurants that offer themes associated with foreign countries. German-style food and drink have become popular since many communities started hosting
Thirty-nine counties from the six-state upper Midwest area of the United States were randomly selected from the USDA-NASS website and the following data on oat-production yield per acre were
A number of sports enthusiasts have argued that major league baseball players from teams in the Central Division have an unfair advantage over coastal players in the Western and Eastern Divisions.
Does the position of a suburb with respect to a city have an effect on school population?The following table lists 2004–2005 student enrollment in the suburbs of Rochester as shown in the May 9,
A study was conducted to assess the effectiveness of treating vertigo (motion sickness)with the transdermal therapeutic system(TTS; a patch worn on the skin). Two other treatments, both oral (one
Tracy works in a drugstore photo-developing department. Over time, Tracy felt that the number of rolls of film brought in for development varied among the days of the week.Were the weekends having an
Let x a person’s “ideal age” in years. Independent and random samples were obtained from U.S. adults in each of six different age groups.18–24 25–29 30–39 40–49 50–64 6521 28 30 38
Albert Michelson, the first American citizen to be awarded a Nobel Prize in Physics, conducted many experiments in determining the velocity of light in air. Following is an excerpt of five trials of
The U.S. Department of Labor Bureau of Labor Statistics posts a table of average hourly wages paid to production workers on private nonfarm payrolls by major industry. The following data were taken
Mr. B, the manager of the retail store in Exercise 12.36, has seen that the mean number of customers per day and the mean number of items purchased (Exercise 12.37) are affected by the month, and he
Samples of peanut butter produced by three different manufacturers were tested for salt content (in milligrams), with the following results:Brand 1 2.5 8.3 3.1 4.7 7.5 6.3 Brand 2 4.5 3.8 5.6 7.2 3.2
A new all-purpose cleaner is being test-marketed by placing sales displays in three different locations within various supermarkets.The number of bottles sold from each location within each of the
Does it really matter where you grocery shop financially? Are the prices at one grocery store consistently higher or lower than those at another?“Shopping the grocers,” an article in the December
An experiment was designed to compare the lengths of time that four different drugs provided pain relief after surgery. The results (in hours) follow.Drug Drug A B C D A B C D 8 6 8 4 2 4 10 6 6 10 4
The distance required to stop a vehicle on wet pavement was measured to compare the stopping power of four major brands of tires. A tire of each brand was tested on the same vehicle on a controlled
Every time you fill your car’s gas tank, consider the federal tax that is charged.That money goes for the repair of roads and bridges. Not all things are equal according to“Alaska thanks you,”
A certain vending company’s soft-drink dispensing machines are supposed to serve 6 oz of beverage. Various machines were sampled, and the resulting amounts of dispensed drink (in ounces) were
Suburbs, each with its own attributes, are located around every metropolitan area. There is always the “rich” one (the most expensive one), the least expensive one, and so on.The dollar amount of
Each year when the National Football League playoffs begin, the question arises,“Which division’s teams are the toughest, East, North, South, or West?” Two ways to measure the strength of the
Contact lenses are big business.From 25 to 27 million Americans wear contact lenses according to the University of Michigan Kellogg Eye Center website
The following table gives the number of arrests made last year for violations of the narcotic drug laws in 24 communities. The data given are rates of arrest per 10,000 inhabitants.Cities Cities
Seven golf balls from each of six manufacturers were randomly selected and tested for durability. Each ball was hit 300 times or until failure occurred, whichever came first.A B C D E F 300 190 228
The U.S. Department of Labor Bureau of Labor Statistics posts a table of average weekly hours worked by production workers on private nonfarm payrolls by major industry. The following data were
Mr. B, the manager of the retail store in Exercise 12.36, has seen the effect month has on the mean number of customers per day and is now wondering about the effect day of the week has on the mean
Mr. B, the manager of the retail store in Exercise 12.55, has seen the effect day has on the mean number of customers per day and is now wondering if day has a similar effect on number of items
Mr. B, the manager of the retail store in Exercise 12.55, has seen the effect day has on the mean number of customers per day and is now wondering if day has a similar effect on total cost of items
For the following data, find SS(error) and show that SS(error) (k1 1)s2 1 (k2 1)s2 2 (k3 1)s2 3where s2 i is the variance for the ith factor level. 1 Factor Level 2 3 8 4 6 6 6 10 6 12 2 4 14
For the following data, show that SS(factor) k1(x1 x)2 k2(x2 x)2 k3(x3 x)2 where x1, x2, x3 are the means for the three factor levels and x is the overall mean. Factor Level 1 6 8 232 3 13 9 12
An article in the Journal of Pharmaceutical Sciences discusses the change of plasma protein binding of diazepam at various concentrations of imipramine. Suppose the results were reported as
[EX12-01] Let x one-way travel to work in minutes. Independent and random samples were obtained in each of the six different U.S.cities from workers who commute to work during the 8:00 AM rush
Design your own “commute time” study.a. Define a specific population that you will sample based on four age groupings, describe your sampling plan, and collect a random sample of at least 25
To partition the sum of squares for the total is to separate the numerical value of SS(total)into two values such that the sum of these two values is equal to SS(total). True or False
A sum of squares is actually a measure of variance. True or False
Experimental error is the name given to the variability that takes place between the levels of the test factor. True or False
Experimental error is the name given to the variability that takes place among the replicates of an experiment as it is repeated under constant conditions. True or False
Fail to reject Ho is the desired decision when the means for the levels of the factor being tested are all different. True or False
The mathematical model for a particular problem is an equational statement showing the anticipated makeup of an individual piece of data. True or False
The degrees of freedom for the factor are equal to the number of factors tested. True or False
The measure of a specific level of a factor being tested in an ANOVA is the variance of that factor level. True or False
We need not assume that the observations are independent to do analysis of variance. True or False
The rejection of Ho indicates that you have identified the level(s) of the factor that is (are) different from the others. True or False.
Determine the truth (T/F) of each statement with regard to the one-factor analysis of variance technique.a. The mean squares are measures of variance.b. “There is no difference between the mean
Consider this table:Find the values:a. Ab. Bc. Cd. De. E Part III: Understanding the Concepts SS MS F Factor A 4 18 E Error B 18 D Total 144 C
In 50 words or less, explain what a singlefactor ANOVA experiment is.
A state environmental agency tested three different scrubbers used to reduce the resulting air pollution in the generation of electricity. The primary concern was the emission of particulate matter.
Refer to the wheat crop data above.a. Construct a scatter diagram for Planted (x) and Harvested (y).b. Construct a scatter diagram of Harvested (x)and Production (y).c. Construct a histogram of
Refer to the wheat crop data on page 696.a. Find the linear correlation coefficient and the equation for the line of best fit for Planted (x)and Harvested (y). What does the correlation coefficient
Consider a set of paired bivariate data.a. Explain why (x x) 0 and (y y) 0.b. Describe the effect that lines x x and y yhave on the graph of these points.c. Describe the
Skillbuilder Applet Exercise matches correlation coefficients with their scatterplots. After several practice rounds using “New Plots,” explain your method of matching. PlotA Plot C r=0.56 CA
Aerial photographs are one of many techniques used to monitor wildlife populations.Knowing the number of animals and their location relative to areas inhabited by the human population is very useful.
a. Construct a scatter diagram of the following bivariate data.Point A B C D E F G H I J x 1 1 3 3 5 5 7 7 9 9 y 1 2 2 3 3 4 4 5 5 6b. Calculate the covariance.c. Calculate sx and sy.d. Calculate r
a. Draw a scatter diagram of the following bivariate data. Point A B C D E F G H I J X 0 1 1 2 3 4 5 6 6 7 y 6674 4 5 2 3 0 1 1 b. Calculate the covariance. c. Calculate s, and Sy d. Calculater using

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