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elementary statistics
Elementary Statistics 3rd Edition William Navidi, Barry Monk - Solutions
A simple random sample of size 18 has mean x̄ = 71.32 and standard deviation s = 15.78. The population is approximately normally distributed. Construct a 95% confidence interval for the population mean.In Exercises 5–12, state which type of parameter is to be estimated, then construct the
In a simple random sample of 400 voters, 220 said that they were planning to vote for the incumbent mayor in the next election. Construct a 99% confidence interval for the proportion of voters who plan to vote for the incumbent mayor in the next election.In Exercises 5–12, state which type of
A simple random sample of size 8 has mean x̄ = 3.21 and standard deviation s = 1.69. The population is normally distributed. Construct a 99% confidence interval for the population standard deviation.In Exercises 5–12, state which type of parameter is to be estimated, then construct the
A simple random sample of size 12 has mean x̄ = 3.37. The population standard deviation is σ = 1.62. The population is approximately normally distributed. Construct a 95%confidence interval for the population mean.In Exercises 5–12, state which type of parameter is to be estimated, then
In a survey of 250 employed adults, 185 said that they had missed one or more days of work in the past six months.Construct a 95% confidence interval for the proportion of employed adults who missed one or more days of work in the past six months.In Exercises 5–12, state which type of parameter
A simple random sample of size 17 has mean x̄ = 8.44 and standard deviation s = 5.38. The population is normally distributed. Construct a 95% confidence interval for the population standard deviation.In Exercises 5–12, state which type of parameter is to be estimated, then construct the
A simple random sample of size 120 has mean x̄ = 8.45. The population standard deviation is σ = 4.81. Construct a 99%confidence interval for the population mean.In Exercises 5–12, state which type of parameter is to be estimated, then construct the confidence interval.
A simple random sample of size 23 has mean x̄ = 1.48 and standard deviation s = 1.32. The population is approximately normally distributed. Construct a 99% confidence interval for the population mean.In Exercises 5–12, state which type of parameter is to be estimated, then construct the
The weights of 52 randomly selected NFL football players are presented below. The sample mean is x̄ = 248.38 and the sample standard deviation is s = 46.68.Construct a 95% confidence interval for the mean weight of NFL football players. 305 265 287 285 290 235 300 230 195 236 244 194 190 307 218
A simple random sample of 100 U.S.college students had a mean age of 22.68 years. Assume the population standard deviation is σ = 4.74 years. Construct a 99% confidence interval for the mean age of U.S. college students.
Following are the numbers of calories in a random sample of 10 slices of bread. Assume the population is normally distributed.Construct a 95% confidence interval for the standard deviation of the number of calories. 55 51 49 48 68 52 62 70 67 70 70
In a survey of 1118 U.S. adults conducted by the Financial Industry Regulatory Authority, 626 said they always pay their credit cards in full each month. Construct a 95% confidence interval for the proportion of U.S. adults who pay their credit cards in full each month.
Mt. Washington, New Hampshire, is one of the windiest places in the United States. Wind speed measurements on a simple random sample of 50 days had a sample mean of 45.01 mph. Assume the population standard deviation is σ = 25.6 mph. Construct a 95% confidence interval for the mean wind speed on
Following are the numbers of grams of sugar per 100 grams of apple in a random sample of six Red Delicious apples. Assume the population is normally distributed.Construct a 95% confidence interval for the standard deviation of the number of grams of sugar. 12.0 12.6 13.1 13.5 12.1 10.5
In a simple random sample of 1500 patients admitted to the hospital with pneumonia, 145 were under the age of 18.Construct a 99% confidence interval for the proportion of pneumonia patients who are under the age of 18.
A simple random sample of 35 colleges and universities in the United States had a mean tuition of \($18,702\) with a standard deviation of \($10,653\). Construct a 95%confidence interval for the mean tuition for all colleges and universities in the United States.
Define the following terms:a. Point estimateb. Confidence intervalc. Confidence level
Find the critical value tα∕2 needed to construct a 90% confidence interval for a population mean with sample size 27.
An owner of a fleet of taxis wants to estimate the mean gas mileage, in miles per gallon, of the cars in the fleet. A random sample of 40 cars is followed for one month, and the sample mean gas mileage is 23.2 with a standard deviation of 5.8.Construct a 90% confidence interval for the mean gas
Construct a 95% confidence interval for the population standard deviation σ if a sample of size 20 has standard deviation s = 10.
A cookie manufacturer wants to estimate the length of time that her boxes of cookies spend in the store before they are bought. She visits a sample of 15 supermarkets and determines the number of days since manufacture of the oldest box of cookies in the store. The mean is 54.8 days with a standard
A person selects a random sample of 15 credit cards and determines the annual interest rate, in percent, of each. The sample mean is 12.42 with a sample standard deviation of 1.3. Construct a 95% confidence interval for the mean credit card annual interest rate, assuming that the rates are
Construct a 90% confidence interval for the population standard deviation σ if a sample of size 6 has standard deviation s = 22.
Find the critical value zα∕2 needed to construct a confidence interval for a population proportion with confidence level 92%.
Find the critical values for a 98% confidence interval using the chi-square distribution with 18 degrees of freedom.
The amount of time that a certain cell phone will keep a charge is known to be normally distributed with standard deviationσ = 16 hours. A sample of 40 cell phones had a mean time of 141 hours. Let μ represent the population mean time that a cell phone will keep a charge.a. What is the point
Refer to Exercise 10.Suppose that a 95% confidence interval is to be constructed for the mean time.a. What is the critical value?b. What is the margin of error?c. Construct the 95% confidence interval.Exercise 10The amount of time that a certain cell phone will keep a charge is known to be normally
Refer to Exercise 10.What sample size is necessary so that a 95% confidence interval will have a margin of error of 1 hour?Exercise 10The amount of time that a certain cell phone will keep a charge is known to be normally distributed with standard deviationσ = 16 hours. A sample of 40 cell phones
In a survey of 802 U.S. adult drivers, 265 state that traffic is getting worse in their community. Construct a 99%confidence interval for the proportion of adult drivers who think that traffic is getting worse.
Refer to Exercise 13.How large a sample is needed so that a 99% confidence interval will have margin of error of 0.08, using the sample proportion for p̂ ?Exercise 13 In a survey of 802 U.S. adult drivers, 265 state that traffic is getting worse in their community. Construct a 99%confidence
Refer to Exercise 13.How large a sample is needed so that a 99% confidence interval will have margin of error of 0.08, assuming no estimate of p̂ is available?Exercise 13 In a survey of 802 U.S. adult drivers, 265 state that traffic is getting worse in their community. Construct a 99%confidence
A meteorology student examines precipitation records for a certain city and discovers that of the last 365 days, it rained on 46 of them. Explain why these data cannot be used to construct a confidence interval for the proportion of days in this city that are rainy.
When constructing a confidence interval for μ when σ is known, we assume that we have a simple random sample, that σis known, and that either the sample size is large or the population is approximately normal. Why is it necessary for these assumptions to be met?
What factors can you think of that may affect the width of a confidence interval? In what way does each factor affect the width?
Explain the difference between confidence and probability.
According to a survey of 1000 American adults, 55% of Americans do not have a will specifying the handling of their estate. The survey’s margin of error was plus or minus 3%.In Exercises 4 and 5, express the following survey results in terms of confidence intervals for p:
In a survey of 5050 U.S. adults, 29% would consider traveling abroad for medical care because of medical costs. The survey’s margin of error was plus or minus 2%.In Exercises 4 and 5, express the following survey results in terms of confidence intervals for p:
When constructing a confidence interval for μ, how do you decide whether to use the t distribution or the normal distribution? Are there any circumstances when it is acceptable to use either distribution?In Exercises 4 and 5, express the following survey results in terms of confidence intervals
It is stated in the text that there are many different t distributions. Explain how this is so.In Exercises 4 and 5, express the following survey results in terms of confidence intervals for p:
The town of Libby, Montana, has experienced high levels of air pollution in the winter because many of the houses in Libby are heated by wood stoves that produce a lot of pollution. In an attempt to reduce the level of air pollution in Libby, a program was undertaken in which almost every wood
Last year, the mean amount spent by customers at a certain restaurant was $35. The restaurant owner believes that the mean may be higher this year. State the appropriate null and alternate hypotheses.
In a recent year, the mean weight of newborn boys in a certain country was 6.6 pounds. A doctor wants to know whether the mean weight of newborn girls differs from this. State the appropriate null and alternate hypotheses.
A certain model of car can be ordered with either a large or small engine. The mean number of miles per gallon for cars with a small engine is 25.5. An automotive engineer thinks that the mean for cars with the larger engine will be less than this.State the appropriate null and alternate hypotheses.
A test is made of H0 : μ = 100 versus H1: μ ≠ 100.The true value of μ is 150, and H0 is rejected. Is this a Type I error, a Type II error, or a correct decision?
A test is made of H0 : μ = 18 versus H1: μ > 18.The true value of μ is 20, and H0 is not rejected. Is this a Type I error, a Type II error, or a correct decision?
A test is made of H0 : μ = 3 versus H1: μ < 3.The true value of μ is 3, and H0 is rejected. Is this a Type I error, a Type II error, or a correct decision?
The _______________ hypothesis states that a parameter is equal to a certain value while the __________________ hypothesis states that the parameter differs from this value.In Exercises 7 and 8, fill in each blank with the appropriate word or phrase.
Rejecting H0 when it is true is called a __________________ error, and failing to reject H0 when it is false is called a _______________ error.In Exercises 7 and 8, fill in each blank with the appropriate word or phrase.
H1: μ > 50 is an example of a left-tailed alternate hypothesis.In Exercises 9–12, determine whether the statement is true or false. If the statement is false, rewrite it as a true statement.
If we reject H0, we conclude that H0 is false.In Exercises 9–12, determine whether the statement is true or false. If the statement is false, rewrite it as a true statement.
If we do not reject H0, then we conclude that H1 is false.In Exercises 9–12, determine whether the statement is true or false. If the statement is false, rewrite it as a true statement.
If we do not reject H0, we conclude that H0 is true.In Exercises 9–12, determine whether the statement is true or false. If the statement is false, rewrite it as a true statement.
H0: μ = 5 H1: μ < 5 In Exercises 13–16, determine whether the alternate hypothesis is left-tailed, right-tailed, or two-tailed.
H0: μ = 10 H1: μ > 10 In Exercises 13–16, determine whether the alternate hypothesis is left-tailed, right-tailed, or two-tailed.
H0: μ = 1 H1: μ ≠ 1 In Exercises 13–16, determine whether the alternate hypothesis is left-tailed, right-tailed, or two-tailed.
H0: μ = 26 H1: μ ≠ 26 In Exercises 13–16, determine whether the alternate hypothesis is left-tailed, right-tailed, or two-tailed.
A test is made of H0: μ = 20 versus H1: μ ≠ 20.The true value of μ is 25, and H0 is rejected.In Exercises 17–20, determine whether the outcome is a Type I error, a Type II error, or a correct decision.
A test is made of H0: μ = 5 versus H1: μ < 5.The true value of???? is 5, and H0 is rejected.In Exercises 17–20, determine whether the outcome is a Type I error, a Type II error, or a correct decision.
A test is made of H0: μ = 63 versus H1: μ > 63.The true value of μ is 75, and H0 is not rejected.In Exercises 17–20, determine whether the outcome is a Type I error, a Type II error, or a correct decision.
A test is made of H0: μ = 45 versus H1: μ < 45.The true value of μ is 40, and H0 is rejected.In Exercises 17–20, determine whether the outcome is a Type I error, a Type II error, or a correct decision.
A new type of fertilizer is being tested on a plot of land in an orange grove, to see whether it increases the amount of fruit produced. The mean number of pounds of fruit on this plot of land with the old fertilizer was 400 pounds.Agriculture scientists believe that the new fertilizer may increase
A sample of 100 flounder of a certain species have sample mean weight 21.5 grams. Scientists want to perform a hypothesis test to determine how strong the evidence is that the mean weight differs from 20 grams. State the appropriate null and alternate hypotheses.
A restaurant owner claims that the mean amount spent by diners at his restaurant is more than $30. A test is made of H0: μ = 30 versus H1: μ > 30.The null hypothesis is rejected. State an appropriate conclusion.
The mean caffeine content per cup of regular coffee served at a certain coffee shop is supposed to be 100 milligrams.A test is made of H0: μ = 100 versus H1: μ ≠ 100.The null hypothesis is rejected. State an appropriate conclusion.
A veterinarian claims that the mean weight of adult German shepherd dogs is 75 pounds. A test is made of H0: μ = 75 versus H1: μ ≠ 75.The null hypothesis is not rejected. State an appropriate conclusion.
A sales manager believes that the mean number of days per year her company’s sales representatives spend traveling is less than 50.A test is made of H0: μ = 50 versus H1: μ < 50.The null hypothesis is not rejected. State an appropriate conclusion.
A company that manufactures steel wires guarantees that the mean breaking strength (in kilonewtons) of the wires is greater than 50.They measure the strengths for a sample of wires and test H0: μ = 50 versus H1: μ > 50.a. If a Type I error is made, what conclusion will be drawn regarding the mean
Washers used in a certain application are supposed to have a thickness of 2 millimeters. A quality control engineer measures the thicknesses for a sample of washers and tests H0: μ = 2 versus H1: μ ≠ 2.a. If a Type I error is made, what conclusion will be drawn regarding the mean washer
It is desired to check the calibration of a scale by weighing a standard 10-gram weight 100 times. Let μ be the population mean reading on the scale, so that the scale is in calibration if μ = 10 and out of calibration if μ ≠ 10.A test is made of the hypotheses H0: μ = 10 versus H1: μ ≠
Scores on a certain IQ test are known to have a mean of 100.A random sample of 60 students attend a series of coaching classes before taking the test. Let μ be the population mean IQ score that would occur if every student took the coaching classes. The classes are successful if μ > 100.A test is
A coin has probability p of landing heads when tossed. A test will be made of the hypotheses H0: p = 0.1 versus H1: p > 0.1, as follows. The coin will be tossed once. If it comes up heads, H0 will be rejected. If it comes up tails, H0 will not be rejected.a. If the true value of p is 0.1, what is
An article in Journal of Nutrition (Vol. 130, No. 8) noted that chocolate is rich in flavonoids. The article notes “regular consumption of foods rich in flavonoids may reduce the risk of coronary heart disease.” The study received funding from Mars, Inc., the candy company, and the Chocolate
In a study conducted by the Society for Human Resource Management, 347 human resource professionals were surveyed. Of those surveyed, 73% said that their companies conduct criminal background checks on all job applicants.a. What is the exact value that is 73% of the 347 survey subjects?b. Could the
Which of the following describe discrete data?a. The numbers of people surveyed in each of the next several years for the National Health and Nutrition Examination Surveysb. The exact foot lengths (measured in cm) of a random sample of statistics studentsc. The exact times that randomly selected
Find the margin of error given the standard error and the confidence level.a. Standard error = 1.2, confidence level 95%b. Standard error = 0.4, confidence level 99%c. Standard error = 3.5, confidence level 90%d. Standard error = 2.75, confidence level 98%
An IQ test was given to a simple random sample of 75 students at a certain college.The sample mean score was 105.2. Scores on this test are known to have a standard deviation of σ = 10.It is desired to construct a 90% confidence interval for the mean IQ score of students at this college.a. What is
The lifetime of a certain type of battery is known to be normally distributed with standard deviation σ = 20 hours. A sample of 50 batteries had a mean lifetime of 120.1 hours. It is desired to construct a 95% confidence interval for the mean lifetime for this type of battery.a. What is the point
In a survey of a simple random sample of students at a certain college, the sample mean time per week spent watching television was 18.3 hours and the margin of error for a 95% confidence interval was 1.2 hours. True or false:a. A 95% confidence interval for the mean number of hours per week spent
Use the data in Exercise 4 to construct a 95% confidence interval for the mean IQ score.Exercise 4An IQ test was given to a simple random sample of 75 students at a certain college.The sample mean score was 105.2. Scores on this test are known to have a standard deviation of σ = 10.It is desired
Use the data in Exercise 5 to construct a 98% confidence interval for the mean lifetime for this type of battery.Exercise 5The lifetime of a certain type of battery is known to be normally distributed with standard deviation σ = 20 hours. A sample of 50 batteries had a mean lifetime of 120.1
To estimate the accuracy of a laboratory scale, a weight known to have a mass of 100 grams is weighed 32 times. The reading of the scale is recorded each time. The following MINITAB output presents a 95% confidence interval for the mean reading of the scale.A scientist claims that the mean reading
Using the output in Exercise 9:a. Find the critical value zα∕2 for a 99% confidence interval.b. Use the critical value along with the information in the output to construct a 99%confidence interval for the mean reading of the scale.Exercise 9To estimate the accuracy of a laboratory scale, a
To determine how well a new method of teaching vocabulary is working in a certain elementary school, education researchers plan to give a vocabulary test to a sample of 100 sixth graders. It is known that scores on this test have a standard deviation of 8.The researchers plan to compute the sample
The researchers now plan to construct a 99% confidence interval for the test scores described in Exercise 11.a. What is the critical value zα∕2 for this confidence interval?b. Find the margin of error for this confidence interval.c. Let m represent the margin of error for this confidence
A machine used to fill beverage cans is supposed to put exactly 12 ounces of beverage in each can, but the actual amount varies randomly from can to can. The population standard deviation is σ = 0.05 ounce. A simple random sample of filled cans will have their volumes measured, and a 95%
An IQ test is designed to have scores that have a standard deviation of σ = 15.A simple random sample of students at a large university will be given the test in order to construct a 98% confidence interval for the mean IQ of all students at the university. How many students must be tested so that
A scientist plans to construct a 95% confidence interval for the mean length of steel rods that are manufactured by a certain process. She will draw a simple random sample of rods and compute the confidence interval using the methods described in this section. She says, ‘‘The probability is 95%
The scientist in Exercise 15 constructs the 95% confidence interval for the mean length in centimeters, and it turns out to be 25.1 < μ < 27.2. She says, ‘‘The probability is 95% that the population mean length is between 25.1 and 27.2 centimeters.’’ Is she right? Explain.
A single number that estimates the value of an unknown parameter is called a ________________ estimate.
The margin of error is the product of the standard error and the_________________ .
In the confidence interval 24.3 ± 1.2, the quantity 1.2 is called the ____________________ .
If we increase the confidence level and keep the sample size the same, we _________________ the margin of error.
The confidence level is the proportion of all possible samples for which the confidence interval will cover the true value.
To construct a confidence interval for a population mean, we add and subtract the critical value from the point estimate.In Exercises 21–24, determine whether the statement is true or false. If the statement is false, rewrite it as a true statement.
Increasing the sample size while keeping the confidence level the same will result in a narrower confidence interval.In Exercises 21–24, determine whether the statement is true or false. If the statement is false, rewrite it as a true statement.
If a 95% confidence interval for a population mean is 1.7 < μ < 2.3, then the probability is 0.95 that the mean is between 1.7 and 2.3.In Exercises 21–24, determine whether the statement is true or false. If the statement is false, rewrite it as a true statement.
Level 95%In Exercises 25–28, find the critical value zα∕2 needed to construct a confidence interval with the given level.
Level 85%In Exercises 25–28, find the critical value zα∕2 needed to construct a confidence interval with the given level.
Level 96%In Exercises 25–28, find the critical value zα∕2 needed to construct a confidence interval with the given level.
Level 99.7%In Exercises 25–28, find the critical value zα∕2 needed to construct a confidence interval with the given level.
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