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elementary statistics

Questions and Answers of Elementary Statistics

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
A sample of size n = 80 is drawn from a normal population whose standard deviation is σ = 6.8. The sample mean is x̄ = 40.41.a. Construct a 90% confidence interval for μ.b. If the population were
A population has standard deviation σ = 21.3.a. How large a sample must be drawn so that a 99% confidence interval for μ will have a margin of error equal to 2.5?b. If the required confidence level
A population has standard deviation σ = 17.3.a. How large a sample must be drawn so that a 95% confidence interval for μ will have a margin of error equal to 1.4?b. If the required confidence level
A population has standard deviation σ = 12.7.a. How large a sample must be drawn so that a 96% confidence interval for μ will have a margin of error equal to 2.5?b. If the required margin of error
A population has standard deviation σ = 9.2.a. How large a sample must be drawn so that a 92% confidence interval for μ will have a margin of error equal to 0.8?b. If the required margin of error
A college admissions officer takes a simple random sample of 100 entering freshmen and computes their mean mathematics SAT score to be 458.Assume the population standard deviation is σ = 116.a.
In a simple random sample of 150 households, the sample mean number of personal computers was 1.32. Assume the population standard deviation is σ = 0.41.a. Construct a 95% confidence interval for
According to the National Health Statistics Reports, a sample of 360 one-year-old baby boys in the United States had a mean weight of 25.5 pounds. Assume the population standard deviation is σ = 5.3
A sample of 314 patients between the ages of 38 and 82 were given a combination of the drugs ezetimibe and simvastatin. They achieved a mean reduction in total cholesterol of 0.94 millimole per
A random sample of 11 smartphones sold over the Internet had the following prices, in dollars:Assume the population standard deviation is σ = 85.a. Explain why it is necessary to check whether the
The Standard and Poor’s (S&P) 500 is a group of 500 large companies traded on the New York Stock Exchange.Following are prices, in dollars, for a random sample of ten stocks on a recent
A random sample of energy drinks had the following amounts of caffeine per fluid ounce.Assume the population standard deviation is σ = 24.a. Explain why it is necessary to check whether the
A random sample of 12-ounce milkshakes from 14 fast-food restaurants had the following number of calories.Assume the population standard deviation is σ = 90.a. Explain why it is necessary to check
In a simple random sample of 100 electronic components produced by a certain method, the mean lifetime was 125 hours. Assume that component lifetimes are normally distributed with population standard
Efficiency experts study the processes used to manufacture items in order to make them as efficient as possible. One of the steps used to manufacture a metal clamp involves the drilling of three
Joe and Sally are going to construct confidence intervals from the same simple random sample.Joe’s confidence interval will have level 90% and Sally’s will have level 95%.a. Which confidence
Bertha and Todd are going to construct confidence intervals from the same simple random sample.Bertha’s confidence interval will have level 98% and Todd’s will have level 95%.a. Which confidence
Javier and Rachel are going to construct confidence intervals from different simple random samples. Both confidence intervals will have level 95%. Javier will use a sample of size 50 and Rachel will
Emily and Fred are going to construct confidence intervals from different simple random samples.Both confidence intervals will have level 99%. Emily will use a sample of size 40 and Fred will use a
Maria and Bob are going to construct confidence intervals from different simple random samples. Both confidence intervals will have level 95%.Maria’s sample comes from a population with standard
Martin and Bianca are going to construct confidence intervals from different simple random samples. Both confidence intervals will have level 99%.Martin’s sample comes from a population with
Sam constructed three confidence intervals, all from the same random sample. The confidence levels are 90%, 95%, and 99%. The confidence intervals are 5.6 < μ < 14.4, 7.2 < μ < 12.8, and 6.6 < μ <
Matilda has constructed three confidence intervals, all from the same random sample. The confidence levels are 95%, 98%, and 99.9%. The confidence intervals are 6.4 < μ < 12.3, 5.1 < μ < 13.6, and
A psychology professor at a certain college gave a test to the students in her class. The test was designed to measure students’attitudes toward school, with higher scores indicating a more
A college alumni organization sent a survey to all recent graduates to ask their annual income. Twenty percent of the alumni responded, and their mean annual income was $40,000. Assume the population
A dean at a certain college looked up the GPA for a random sample of 85 students. The sample mean GPA was 2.82, and a 95% confidence interval for the mean GPA of all students in the college was 2.76
A survey organization drew a simple random sample of 625 households from a city of 100,000 households. The sample mean number of people in the 625 households was 2.30, and a 95% confidence interval
The number of words typed per minute was measured for a sample of typists. The following display from a TI-84 Plus calculator presents a 95% confidence interval for the population mean typing
Flight times, in minutes, were measured for a sample of drones delivering packages. The following display from a TI-84 Plus calculator presents a 99%confidence interval for the population mean flight
A sample of patients was put on a special diet. After six months, the number of pounds lost was measured for each of them. The following MINITAB output presents a confidence interval for the
The number of years employed was determined for a sample of employees at a large company.The following MINITAB output presents a confidence interval for the population mean length of employment.a.
A simple random sample of 50 middle-school children participated in an experimental class designed to introduce them to computer programming. At the end of the class, the students took a final exam
A random sample of 75 charges on a credit card had a mean of $56.85, and the population standard deviation is$21.08. Compute an upper 95% confidence bound for the mean amount charged.A confidence
Use Table A.3 to find the critical value tα∕2 needed to construct a confidence interval of the given level with the given sample size:a. Level 95%, sample size 15b. Level 99%, sample size 22c.
In each of the following situations, state whether the methods of this section should be used to construct a confidence interval for the population mean. Assume that σ is unknown.a. A simple random
A potato chip company wants to evaluate the accuracy of its potato chip bag-filling machine. Bags are labeled as containing 8 ounces of potato chips.A simple random sample of 12 bags had mean weight
A company has developed a new type of lightbulb, and wants to estimate its mean lifetime. A simple random sample of 100 bulbs had a sample mean lifetime of 750.2 hours with a sample standard
The following TI-84 Plus display presents a 95% confidence interval for a population mean.a. How many degrees of freedom are there?b. Find the critical value tα∕2 for a 99% confidence interval.c.
The following MINITAB output presents a confidence interval for a population mean.a. How many degrees of freedom are there?b. Find the critical value tα∕2 for a 99% confidence interval.c. Use the
When constructing a confidence interval for a population meanμ from a sample of size 12, the number of degrees of freedom for the critical value tα∕2 is ___________________ .In Exercises 7 and 8,
When the number of degrees of freedom is large, the Student’s t distribution is close to the ______________ distribution.In Exercises 7 and 8, fill in each blank with the appropriate word or phrase.
The Student’s t curve is less spread out than the standard normal curve.In Exercises 9 and 10, determine whether the statement is true or false. If the statement is false, rewrite it as a true
The Student’s t distribution should not be used to find a confidence interval for μ if outliers are present in a small sample.In Exercises 9 and 10, determine whether the statement is true or
Find the critical value tα∕2 needed to construct a confidence interval of the given level with the given sample size.a. Level 95%, sample size 23b. Level 90%, sample size 3c. Level 98%, sample
Find the critical value tα∕2 needed to construct a confidence interval of the given level with the given sample size.a. Level 90%, sample size 6b. Level 98%, sample size 12c. Level 95%, sample
A sample of size n = 18 is drawn from a normal population.a. Find the critical value tα∕2 needed to construct a 95%confidence interval.b. If the sample size were n = 25, would the critical value
A sample of size n = 22 is drawn from a normal population.a. Find the critical value tα∕2 needed to construct a 90%confidence interval.b. If the sample size were n = 15, would the critical value
A sample of size n = 12 is drawn from a normal population.a. Find the critical value tα∕2 needed to construct a 98%confidence interval.b. If the sample size were n = 50, would it be necessary for
A sample of size n = 61 is drawn.a. Find the critical value tα∕2 needed to construct a 95%confidence interval.b. If the sample size were n = 15, what additional assumption would need to be made
A sample of size n = 15 has sample mean ̄x = 2.1 and sample standard deviation s = 1.7.a. Construct a 95% confidence interval for the population mean σ.b. If the sample size were n = 25, would the
A sample of size n = 44 has sample mean ̄x = 56.9 and sample standard deviation s = 9.1.a. Construct a 98% confidence interval for the population mean σ.b. If the sample size were n = 30, would the
A sample of size n = 89 has sample mean ̄x = 87.2 and sample standard deviation s = 5.3.a. Construct a 95% confidence interval for the population mean σ.b. If the confidence level were 99%, would
A sample of size n = 35 has sample mean ̄x = 34.85 and sample standard deviation s = 17.9.a. Construct a 98% confidence interval for the population mean σ.b. If the confidence level were 95%, would

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