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elementary statistics

Questions and Answers of Elementary Statistics

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
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
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
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
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
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
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
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
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
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%
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
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
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
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
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
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.
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
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
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,
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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 =
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
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
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
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
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
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
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
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,
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
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
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
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
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
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
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
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
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
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 =
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
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
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
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
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
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
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.
2.326 In Exercises 29–32, find the levels of the confidence intervals that have the given critical values.
2.576 In Exercises 29–32, find the levels of the confidence intervals that have the given critical values.
2.81 In Exercises 29–32, find the levels of the confidence intervals that have the given critical values.
1.04 In Exercises 29–32, find the levels of the confidence intervals that have the given critical values.
A sample of size n = 49 is drawn from a population whose standard deviation is σ = 4.8.a. Find the margin of error for a 95% confidence interval for μ.b. If the sample size were n = 60, would the
A sample of size n = 50 is drawn from a population whose standard deviation is σ = 26.a. Find the margin of error for a 90% confidence interval for μ.b. If the sample size were n = 40, would the
A sample of size n = 32 is drawn from a population whose standard deviation is σ = 12.1.a. Find the margin of error for a 99% confidence interval for μ.b. If the confidence level were 90%, would
A sample of size n = 64 is drawn from a population whose standard deviation is σ = 24.18.a. Find the margin of error for a 95% confidence interval for μ.b. If the confidence level were 98%, would
A sample of size n = 10 is drawn from a normal population whose standard deviation is σ = 2.5. The sample mean is x̄ = 7.92.a. Construct a 95% confidence interval for μ.b. If the population were

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