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statistics

Elementary Statistics 11th Edition Robert R. Johnson, Patricia J. Kuby - Solutions

a. What proportion of the probability distribution is in the critical region, provided the null hypothesis is correct? b. What error could be made if the test statistic falls in the critical region? c. What proportion of the probability distribution is in the noncritical region, provided the null
The following computer output was used to complete a hypothesis test.a. State the null and alternative hypotheses. b. If the test is completed using , what decision and conclusion are reached? c. Verify the value of the standard error of the mean.
Using the computer output and information in Exercise 8.153, determine the value of the following: a. Hypothesized value of population mean b. Sample mean c. Population standard deviation d. Test statistic
The following computer output was used to complete a hypothesis test.a. State the null and alternative hypotheses. b. If the test is completed using a = 0.05 , what decision and conclusion are reached? c. Verify the value of the standard error of the mean.
Using the computer output and information in Exercise 8.155, determine the value of the following: a. Hypothesized value of population mean b. Sample mean c. Population standard deviation d. Test statistic
The Texas Department of Health published the statewide results for the Emergency Medical Services Certification Examination. Data for those taking the paramedic exam for the first time gave an average score of 79.68 (out of a possible 100) with a standard deviation of 9.06. Suppose a random sample
According to the Center on Budget and Policy Priorities’ article “Curbing Flexible Spending Accounts Could Help Pay for Health Care Reform” (revised June 10, 2009), flexible-spending accounts encourage the overconsumption of health car e. People buy things they do not need; otherwise they
Women own an average of 15 pairs of shoes. This is based on a survey of female adults by Kelton Research for Eneslow, the New York City–based Foot Comfort Center. Suppose a random sample of 35 newly hired female college graduates was taken and the sample mean was 18.37 pairs of shoes. If σ =
Find the level of confidence assigned to an interval estimate of the mean formed using the following intervals:
A fire insurance company thought that the mean distance from a home to the nearest fire department in a suburb of Chicago was at least 4.7 miles. It set its fire insurance rates accordingly. Members of the community set out to show that the mean distance was less than 4.7 miles. This, they thought,
The length of Major League Baseball games is approximately normally distributed and averages 2 hours and 50.1 minutes, with a standard deviation of 21.0 minutes. It has been claimed that New York Yankees baseball games last, on the average, longer than the games of the other Major League teams. To
The manager at Air Express believes that the weights of packages shipped recently are less than those in the past. Records show that in the past, packages have had a mean weight of 36.5 lb and a standard deviation of 14.2 lb. A random sample of last month€™s shipping records yielded the
Do you drink the recommended amount of water each day? Most Americans don’t! On average, Americans drink 4.6 eight-oz servings of water a day. A sample of 42 education professionals was randomly selected and their water consumption for a 24-hour period was monitored; the mean amount consumed was
The recommended amount of water a person should drink is eight 8-oz servings per day. a. Does the sample of educational professionals in Exercise 8.163 show sufficient evidence that the education professionals consume, on average, significantly less water daily than the recommended amount? Use a =
A sample of 64 measurements is taken from a continuous population, and the sample mean is found to be 32.0. The standard deviation of the population is known to be 2.4. An interval estimation is to be made of the mean with a level of confidence of 90%. State or calculate the following items.g. E
The average volunteer ambulance member is 45 years old and has 8 years of service, according to the Democrat & Chronicle article “Unpaid ambulance workers could get ‘pension’” (January 23, 2005). The quoted statistics were based on the Penfield Volunteer Ambulance Squad of 80 members. If
“Population requirement for primary hip-replacement surgery: a cross-sectional study” was conducted by the University of Bristol in the United Kingdom. The findings resulted in the following statement:“The prevalence of selfreported hip pain was 107 per 1000 (95% CI 101–113) for men and 173
The standard deviation of a normally distributed population is equal to 10. A sample size of 25 is selected, and its mean is found to be 95. a. Find an 80% confidence interval for m. b. What would the 80% confidence interval be for a sample of size 100? c. What would be the 80% confidence
The weights of full boxes of a certain kind of cereal are normally distributed with a standard deviation of 0.27 oz. A sample of 18 randomly selected boxes produced a mean weight of 9.87 oz. a. Find the 95% confidence interval for the true mean weight of a box of this cereal. b. Find the 99%
Waiting times (in hours) at a popular restaurant are believed to be approximately normally distributed with a variance of 2.25 during busy periods. a. A sample of 20 customers revealed a mean waiting time of 1.52 hours. Construct the 95% confidence interval for the population mean. b. Suppose
A random sample of the scores of 100 applicants for clerk-typist positions at a large insurance company showed a mean score of 72.6. The preparer of the test maintained that qualified applicants should average 75.0. a. Determine the 99% confidence interval for the mean score of all applicants at
The length of time it takes to play a Major League Baseball game is of interest to many fans. To estimate the mean “time of game,” a random sample of 48 National League games was identified and the “time of game” (in minutes) obtained for each. The resulting sample mean was 2 hours and 49.1
A large order of the no. 9 corks described in Applied Example 6.13 (p. 285) is about to be shipped. The final quality-control inspection includes an estimation of the mean ovality (ovalization; out-ofroundness) of the corks. The diameter of each cork is measured in several places, and the
Use a computer and generate 50 random samples each of size n = 25 from a normal probability distribution with µ = 130 and σ _ 10 a. Calculate the 95% confidence interval based on each sample mean. b. What proportion of these confidence intervals contains µ _ 130? c. Explain what the
A pharmaceutical company wants to estimate the mean response time for a supplement to reduce blood pressure. How large of a sample should be taken to estimate the mean response time to within 1 week at 99% confidence. Assume σ = 3.7 weeks.
An automobile manufacturer wants to estimate the mean gasoline mileage of its new compact model. How many sample runs must be performed to ensure that the estimate is accurate to within 0.3 mpg at 95% confidence?
A fish hatchery manager wants to estimate the mean length of her 3-year-old hatchery-raised trout. She wants to make a 99% confidence interval accurate to within 1\3 of a standard deviation. How large a sample does she need to take?
A sample of 25 of 174 funded projects revealed that 19 were valued at $17,320 each and 6 were valued at $20,200 each. From the sample data, estimate the total value of the funding for all the projects.
We are interested in estimating the mean life of a new product. How large a sample do we need to take to estimate the mean to within 1/10 of a standard deviation with 90% confidence?
Suppose a hypothesis test is conducted using the pvalue approach and assigned a level of significance of a = 0.01a. How is the 0.01 used in completing the hypothesis test? b. If a is changed to 0.05, what effect would this have on the test procedure?
Suppose a hypothesis test is conducted using the pvalue approach and assigned a level of significance of a = 0.01 a. How is the 0.01 used in completing the hypothesis test? b. If a is changed to 0.05, what effect would this have on the test procedure?
Suppose a hypothesis test is conducted using the classical approach and assigned a level of significance of a = 0.01. a. How is the 0.01 used in completing the hypothesis test? b. If a is changed to 0.05, what effect would this have on the test procedure?
The expected mean of a continuous population is 100, and its standard deviation is 12. A sample of 50 measurements gives a sample mean of 96. Using a 0.01 level of significance, a test is to be made to decide between €œthe population mean is 100€ and €œthe population
The expected mean of a continuous population is 200, and its standard deviation is 15. A sample of 80 measurements gives a sample mean of 205. Using a 0.01 level of significance, a test is to be made to decide between “the population mean is 200” and “the population mean is different from
A lawn and garden sprinkler system is designed to have a delayed start; that is, there is a delay from the moment it is turned on until the water starts. The delay times form a normal distribution with mean 45 seconds and standard deviation 8 seconds. Several customers have complained that the
The college bookstore tells prospective students that the average cost of its textbooks is $90 per book with a standard deviation of $15. The engineering science students think that the average cost of their books is higher than the average for all students. To test the bookstore’s claim against
A manufacturing process produces ball bearings with diameters having a normal distribution and a standard deviation of σ = 0.04 cm. Ball bearings that have diameters that are too small or too large are undesirable. To test the null hypothesis that µ _ 0.50 cm, a sample of 25 is randomly selected
After conducting a large number of tests over a long period, a rope manufacturer has found that its rope has a mean breaking strength of 300 lb and a standard deviation of 24 l b. Assume that these values are m and s. It is believed that by using a recently developed highspeed process, the mean
A worker honeybee leaves the hive on a regular basis and travels to flowers and other sources of pollen and nectar before returning to the hive to deliver its cargo. The process is repeated several times each day in order to feed younger bees and support the hive’s production of honey and wax.
Using the Old Faithful eruption information in Applied Example 8.1 on page 344: a. What does “3:19 PM +-10 min mean? Explain. b. Did this eruption occur during the predicted time interval? c. What does “90% of the time” mean? Explain.
In a large supermarket the customer’s waiting time to check out is approximately normally distributed with a standard deviation of 2.5 minutes. A sample of 24 customer waiting times produced a mean of 10.6 minutes. Is this evidence sufficient to reject the supermarket’s claim that its customer
At a very large firm, the clerk-typists were sampled to see whether salaries differed among departments for workers in similar categories. In a sample of 50 of the firm’s accounting clerks, the average annual salary was $16,010. The firm’s personnel office insists that the average salary paid
Jack Williams is vice president of marketing for one of the largest natural gas companies in the nation. During the past 4 years, he has watched two major factors erode the profits and sales of the company. First, the average price of crude oil has been virtually flat, and many of his industrial
With a nationwide average drive time of about 24.3 minutes, Americans now spend more than 100 hours a year commuting to work, according to the U.S. Census Bureau’s American Community Survey. Yes, that’s more than the average 2 weeks of vacation time (80 hours) taken by many workers during a
A manufacturer of automobile tires believes it has developed a new rubber compound that has superior antiwearing qualities. It produced a test run of tires made with this new compound and had them roadteste d. The data values recorded were the amount of tread wear per 10,000 miles. In the past, the
From a population of unknown mean µ and a standard Deviation σ = 5.0 a sample of n = 100 is selected and the sample mean 40.6 is found. Compare the concepts of estimation and hypothesis testing by completing the following: a. Determine the 95% confidence interval for µ. b. Complete the
From a population of unknown mean µ and a standard Deviation σ = 5.0 a sample of n = 100 is selected and the sample mean 41.5 is foun d. Compare the concepts of estimation and hypothesis testing by completing the following: a. Determine the 95% confidence interval for µ . b. Complete the
From a population of unknown mean µ and a standard Deviation σ = 5.0 a sample of n = 100 is selected and the sample mean 40.9 is found. Compare the concepts of estimation and hypothesis testing by completing the following: a. Determine the 95% confidence interval for µ . b. Complete the
A manufacturer of stone-ground, deli-style mustard uses a high-speed machine to fill jars.The amount of mustard dispensed into the jars forms a normal distribution with a mean 290 grams and a standard deviation 4 grams. Each hour a random sample of 12 jars is taken from that hour’s production. If
All drugs must be approved by the U.S. Food and Drug Administration (FDA) before they can be marketed by a drug company. The FDA must weigh the error of marketing an ineffective drug, with the usual risks of side effects, against the consequences of not allowing an effective drug to be sol d.
Referring to Exercise 8.1: a. How is the distribution of the sample height data on p. 344 related to: (1) The distribution of the population? (2) The sampling distribution of sample means? b. Using the techniques of Chapter 7, find the limits that would bound the middle 90% of the sampling
A recruiter estimates that if you are hired to work for her company and you put in a full week at the commissioned sales representative position she is offer- ing, you will make “$525 plus or minus $250, 80% of the time.” She adds, “It all depends on you!” a. What does “$525 plus or
The drug manufacturer in Exercise 8.199 has a different viewpoint on the matter. It wants to market the new drug starting as soon as possible so that it can beat its competitors to the marketplace and make lots of money. Its position is,“Market the drug unless the drug is totally ineffective.”
This computer output shows a simulated sample of size 28 randomly generated from a normal population with µ = 18 and Ïƒ = 4. Computer commands were then used to complete a hypothesis test for µ = 18 against a two-tailed alternative.a. State the alternative hypothesis, the
Use a computer and generate 50 random samples, each of size n = 28 from a normal probability distribution with µ = 18 and s = 4 a. Calculate the z corresponding to each sample mean. b. In regard to the p-value approach, find the proportion of 50 z_ values that are “more extreme” than the z
Use a computer and generate 50 random samples, each of size n = 28, from a normal probability distribution with µ = 19 and σ = 4. a. Calculate the z corresponding to each sample mean that would result when testing the null hypothesis µ = 18 b. In regard to the p-value approach, find the
Determine the value of the confidence coefficient z(a/2) for each situation described:
Determine the value of the confidence coefficient z(a/2) for each situation described: a. 98% confidence b. 99% confidence
Determine the level of the confidence given the confidence coefficient z(a/2) for each situation:
a. Find the 0.95 confidence interval for m.b. Are the assumptions satisfied? Explain.
a. Find the 0.98 confidence interval for m.b. Are the assumptions satisfied? Explain.
a. Find the 0.90 confidence interval for m.b. Are the assumptions satisfied? Explain.
a. Find the 0.99 confidence interval for m.b. Are the assumptions satisfied? Explain.
Based on the confidence interval formed in Exercise 8.27, give the value for each of the following: a. Point estimate b. Confidence coefficient c. Standard error of the mean d. Maximum error of estimate, E e. Lower confidence limit f. Upper confidence limit
Based on the confidence interval formed in Exercise 8.26, give the value for each of the following: a. Point estimate b. Confidence coefficient c. Standard error of the mean d. Maximum error of estimate, E e. Lower confidence limit f. Upper confidence limit
“Mean Travel Time to Work” (Applied Example 8.5) provides commuting information for various cities and states in the United States. Considering the city of Chicago and the confidence interval information given: a. What confidence interval term is the 32.7? b. What confidence interval term is
a. Set the slider for level of confidence to 68%. Click €œsample!€ to construct one 68% confidence interval. Note the upper and lower confidence limits and calculate the width of the interval. Using €œanimate!€ construct many samples and note the percent of
Discuss the effect that each of the following has on the confidence interval: a. Point estimate b. Level of confidence c. Sample size d. Variability of the characteristic being measured
a. Find the point estimate for µ.b. Find the 98% confidence maximum error of estimate for µ.c. Find the 98% confidence interval for µ.
A sample of 60 night-school students' ages is obtained in order to estimate the mean age of night-school students years. The population variance is 16.a. Give a point estimate for .b. Find the 95% confidence interval for .c. Find the 99% confidence interval for .
Two hundred fish caught in Cayuga Lake had a mean length of 14.3 inches. The population standard deviation is 2.5 inches. a. Find the 90% confidence interval for the population mean length. b. Find the 98% confidence interval for the population mean length.
Based on a survey conducted by Greenfield Online, 25- to 34-year-olds spend the most each week on fast food. The average weekly amount of $44 (based on 115 respondents) was reported in a May 2009 USA Today Snapshot. Assuming that weekly fast food expenditures are normally distributed with a known
The Eurostar was Europe’s first international train, designed to take advantage of the Channel Tunnel that connects England with Continental Europe. It carries nearly 800 passengers and occasionally reaches a peak speed of more than 190 mph [www.o-keating.com/]. Assume the standard deviation of
Identify each numerical value by “name” (e.g., mean, variance) and by symbol (e.g., ): a. The mean height of 24 junior high school girls is 4 ft 11 in. b. The standard deviation for IQ scores is 16. c. The variance among the test scores on last week’s exam was 190. d. The mean height of
The Trends in International Mathematics and Science Study (TIMSS) in 2007 examined eighth-grade proficiency in math and science. The mean mathematics scale score for the sample of eighth-grade students in the United States was 508.5 with a standard error of 2.83. Construct a 95% confidence interval
A certain adjustment to a machine will change the length of the parts it makes but will not affect the standard deviation. The length of the parts is normally distributed, and the standard deviation is 0.5 mm. After an adjustment is made, a random sample is taken to determine the mean length of the
€œTweens or teens€ refers to the age group of students in seventh grade. Growth spurts are very common at this age. A sample of 12 randomly selected seventhgrade females in a New York City school resulted in the following heights:Assuming heights of females in the 12- to
The atomic weight of a reference sample of silver was measured at the National Institute of Standards and Technology (NIST) using two nearly identical mass spectrometers. This project was undertaken in conjunction with the redetermination of the Faraday constant. Following are 48
The force required to extract a cork from a wine bottle is an important property of the cork. If the force is too little, the cork probably is not a good protector of the wine inside. If the force is too great, it will be difficult to remove. Neither is desirable. The no. 9 corks in Applied Example
“College costs rise” (October 29, 2008), an article on the CNN Money website, gave the latest figures from the College Board on annual tuition, fees, and room and boar d. The average total figures are $34,132 for private colleges and $14,333 for public colleges. Source: money.cnn.com/ In an
Find the sample size needed to estimate m of a normal population with =3 to within 1 unit at the 98% level of confidence.
How large a sample should be taken if the population mean is to be estimated with 99% confidence to within $75? The population has a standard deviation of $900.
A high-tech company wants to estimate the mean number of years of college education its employees have completed. A good estimate of the standard deviation for the number of years of college is 1.0. How large a sample needs to be taken to estimate to within 0.5 of a year with 99% confidence?
A random sample of the amount paid (in dollars) for taxi fare from downtown to the airport was obtained:Use the data to find a point estimate for each of the following parameters. a. Mean b. Variance c. Standard deviation
By measuring the amount of time it takes a component of a product to move from one workstation to the next, an engineer has estimated that the standard deviation is 5 seconds. a. How many measurements should be made to be 95% certain that the maximum error of estimation will not exceed 1 second?
a. The new mini-laptop computers can deliver as much computing power as machines several times their size, but they weigh in at less than 3 l b. How large a sample would be needed to estimate the population mean weight if the maximum error of estimate is to be 0.4 of 1 standard deviation with 95%
According to the USA Today (March 11, 2009) article “College freshmen study booze more than book,” freshmen spend an average of 8.4 hours studying per week. A large upstate college is interested in estimating this statistic with respect to its freshmen. How large will the sample need to be to
“Positively the Most Effective Sciatica & Back Pain Relief System on the Planet . . . ,” according to Dr. Craig Mueller. This claim appeared on www.EraseYourBackPain .com. a. How would you attempt to show that the above statement is true? What evidence would you need to collect? b. How would
You have heard that the average American male is 69.7 inches tall. Yet almost all of the adult males in your personal world seem to be between 5 and 6 feet tall, with a few just over 6 feet. So how does the average get to be almost 6 feet? In fact, you are quite convinced that the average height
State the null and alternative hypotheses for each of the following: a. You are investigating a complaint that “special delivery mail takes too much time” to be delivered. b. You want to show that people find the new design for a recliner chair more comfortable than the old design. c. You
State the null and alternative hypotheses for each of the following: a. You want to show an increase in buying and selling of single-family homes this year when compared with last year’s rate. b. You are testing a new recipe for “low-fat” cheesecake and expect to find that its taste is not
Using the example of your friend’s party (pp. 361 and 366) with Ho: “Party will be a dud” versus Ha: “The party will be a great time,” describe the four possible decisions and the resulting actions as described in Example
The number of engines owned per fire department was obtained from a random sample taken from the profiles of fire departments from across the United States (Firehouse/June 2003).Use the data to find a point estimate for each of the following parameters. a. Mean b. Variance c. Standard deviation
When a parachute is inspected, the inspector is looking for anything that might indicate the parachute might not open. a. State the null and alternative hypotheses. b. Describe the four possible outcomes that can result depending on the truth of the null hypothesis and the decision reached. c.
When a medic at the scene of a serious accident inspects each victim, she administers the appropriate medical assistance to all victims, unless she is certain the victim is dead. a. State the null and alternative hypotheses. b. Describe the four possible outcomes that can result depending on the
A supplier of highway construction materials claims he can supply an asphalt mixture that will make roads that are paved with his materials less slippery when wet. A general contractor who builds roads wishes to test the supplier’s claim. The null hypothesis is “Roads paved with this asphalt
Describe the actions that would result in a type I error and a type II error if each of the following null hypotheses were tested. (Remember, the alternative hypothesis is the negation of the null hypothesis.) a. Ho:The majority of Americans favor laws against assault weapons. b. Ho:The choices
Describe the action that would result in a correct decision type A and a correct decision type B if each of the null hypotheses in Exercise 8.64 were tested. In Exercise 8.64 a. Ho:The majority of Americans favor laws against assault weapons. b. Ho:The choices on the fast food menu are not low in
Describe the action that would result in a correct decision type A and a correct decision type B if the hypotheses for the new detonating system for explosives of Exercise 8.55 were tested.
Consider the null hypothesis in Applied Example 8.11, “Ho: Teaching techniques have no significant effect on students’ exam scores.” Describe the actions that would result in a type I and a type II error if Ho were tested.

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