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elementary statistics
Elementary Statistics 3rd Edition William Navidi, Barry Monk - Solutions
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 margin of error be larger or smaller?
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 margin of error be larger or smaller?
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 the margin of error be larger or smaller?
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 the margin of error be larger or smaller?
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 not approximately normal, would the confidence interval constructed in part (a) be valid?Explain.
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 not approximately normal, would the confidence interval constructed in part (a) be valid?Explain.
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 were 95%, would the necessary sample size be larger or smaller?
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 were 98%, would the necessary sample size be larger or smaller?
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 were 1.5, would the necessary sample size be larger or smaller?
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 were 1.4, would the necessary sample size be larger or smaller?
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. Construct a 99% confidence interval for the mean mathematics SAT score for the entering freshman
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 the mean number of personal computers.b. If the sample size were 100 rather than 150, would the margin
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 pounds.a. Construct a 95% confidence interval for the mean weight of all one-year-old baby boys in
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 liter. Assume the population standard deviation is σ = 0.18.a. Construct a 98% confidence interval for
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 population is approximately normal before constructing a confidence interval.b. Following is a
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 day.Assume the population standard deviation is σ = 50.a. Explain why it is necessary to check whether the
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 population is approximately normal before constructing a confidence interval.b. Following is a dotplot of
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 whether the population is approximately normal before constructing a confidence interval.b. Following
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 deviationσ = 20 hours.a. Construct a 98% confidence interval for the mean battery life.b. Find the
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 holes. In a sample of 75 clamps, the mean time to complete this step was 50.1 seconds. Assume that the
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 interval will have the larger margin of error? Or will they both be the same?b. 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 interval will have the larger margin of error? Or will they both be the same?b. 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 use a sample of size 100.The samples will be drawn from the same population.a. Which confidence
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 sample of size 75.The samples will be drawn from the same population.a. Which confidence interval
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 deviation σ = 1, and Bob’s comes from a population withσ = 2.Both sample sizes are the same.a.
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 standard deviation σ = 25, and Bianca’s comes from a population withσ = 18.Both sample sizes are the
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 < 13.4.Unfortunately, Sam has forgotten which confidence interval has which level. Match each
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 6.8 < μ < 11.9. Unfortunately, Matilda has forgotten which confidence interval has which level.
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 positive attitude. There were 30 students in the class, and their mean score was 78.Scores on this test are
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 standard deviation is ???? = $10,000. Explain why these data should not be used to construct a
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 < μ < 2.88. True or false, and explain:a. We are 95% confident that the mean GPA of all students in
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 for the mean number of people in the 100,000 households was 2.16 < μ < 2.44. True or false, and
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 speed.a. Fill in the blanks: We are _____________ confident that the population mean number of words per
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 time.a. Fill in the blanks: We are _______________ confident that the population mean flight time
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 population mean weight loss.a. Fill in the blanks: We are _________________ confident that the population
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. Fill in the blanks: We are _______________ confident that the population mean number of years employed
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 to assess their learning. The sample mean score was 78 points, and the population standard deviation
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 interval provides likely minimum and maximum values for a parameter.In some cases, we are interested
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. Level 90%, sample size 63d. Level 95%, sample size 2 4 0.271 0.741 1.533 2.132 5 0.267 0.727 1.476
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 sample of size 8 is drawn from a distribution that is approximately normal.b. A simple random sample
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 8.12 ounces with a sample standard deviation of 0.1 ounce. Assume the weights are approximately
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 deviation of 30 hours. Construct a 95% confidence interval for the population mean lifetime of all bulbs
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. Use the critical value along with the information in the display to construct a 99%confidence
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 critical value along with the information in the computer output to construct a 99% confidence
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, fill in each blank with the appropriate word or phrase.
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 statement.
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 false. If the statement is false, rewrite it as a true statement.
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 size 18d. Level 99%, sample size 29
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 size 32d. Level 99%, sample size 10
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 be smaller or larger?
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 be smaller or larger?
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 the population to be approximately normal?
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 for the confidence interval to be valid?
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 confidence interval be narrower or wider?
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 confidence interval be narrower or wider?
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 the confidence interval be narrower or wider?
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 the confidence interval be narrower or wider?
A sample of 263 students who were taking online courses were asked to describe their overall impression of online learning on a scale of 1–7, with 7 representing the most favorable impression. The average score was 5.53, and the standard deviation was 0.92.a. Construct a 95% confidence interval
The General Social Survey asked 1972 adults how many years of education they had. The sample mean was 13.37 years with a standard deviation of 3.13 years.a. Construct a 98% confidence interval for the mean number of years of education.b. Data collected in an earlier study suggests that the mean ten
Many celebrities and public figures have Twitter accounts with large numbers of followers.However, some of these followers are fake, resulting from accounts generated by spamming computers. In a sample of 46 twitter audits, the mean percentage of fake followers was 14.1 with a standard deviation of
A random sample of 35 Hollywood movies made in the last 10 years had a mean length of 125.2 minutes, with a standard deviation of 20.4 minutes.a. Construct a 95% confidence interval for the true mean length of all Hollywood movies made in the last 10 years.b. As of January 2017 there have been five
In a sample of 123 hip surgeries of a certain type, the average surgery time was 136.9 minutes with a standard deviation of 22.6 minutes.a. Construct a 95% confidence interval for the mean surgery time for this procedure.b. If a 99% confidence interval were constructed with these data, would it be
Phonics is an instructional method in which children are taught to connect sounds with letters or groups of letters. A sample of 134 first graders who were learning English were asked to identify as many letter sounds as possible in a period of one minute. The average number of letter sounds
A hybrid course is one that contains both online and classroom instruction. In a study performed at Middle Georgia State University, a software package was used as the main source of instruction in a hybrid college algebra course. The software tracked the number of hours it took for each student to
In a sample of 77 children, the mean age at which they first began to combine words was 16.51 months, with a standard deviation of 9.59 months.a. Construct a 95% confidence interval for the mean age at which children first begin to combine words.b. If a sample of 50 children had been studied, would
Following are weights, in pounds, of 12 two-month-old baby girls. It is reasonable to assume that the population is approximately normal.a. Construct a 98% confidence interval for the mean weight of two-month-old baby girls.b. According to the National Health Statistics Reports, the mean weight of
Boxes of cereal are labeled as containing 14 ounces. Following are the weights, in ounces, of a sample of 12 boxes: It is reasonable to assume that the population is approximately normal.a. Construct a 98% confidence interval for the mean weight.b. The quality control manager is concerned that the
Six measurements were made of the mineral content (in percent) of spinach, with the following results. It is reasonable to assume that the population is approximately normal.a. Construct a 95% confidence interval for the mean mineral content.b. Based on the confidence interval, is it reasonable to
Following are interest rates (annual percentage rates) for a 30-year fixed rate mortgage from a sample of lenders in Macon, Georgia on a recent day. It is reasonable to assume that the population is approximately normal.a. Construct a 99% confidence interval for the mean rate.b. One week earlier,
Following are prices of a random sample of 18 smart TVs sold on shopper.cnet.com in 2013 with screen sizes between 46’’ and 50’’, along with a dotplot of the data.a. Is it reasonable to assume that the conditions for constructing a confidence interval for the mean price are
Following is the total compensation, in millions of dollars, for Chief Executive Officers at 20 large U.S.corporations, along with a boxplot of the data.a. Is it reasonable to assume that the conditions for constructing a confidence interval for the mean compensation are satisfied? Explain.b. If
One of the ways in which doctors try to determine how long a single dose of pain reliever will provide relief is to measure the drug’s half-life, which is the length of time it takes for one-half of the dose to be eliminated from the body.Following are half-lives (in hours) of the pain reliever
Gas mileage, in miles per gallon, was measured for five Ford Explorer SUVs. Following are the results, along with a dotplot of the data.a. Is it reasonable to assume that the conditions for constructing a confidence interval for the mean gas mileage are satisfied?Explain.b. If appropriate,
Kale is a type of cabbage commonly found in salad and used in cooking in many parts of the world. Six measurements were made of the mineral content (in percent) of kale, with the following results.It turns out that the value 26.1 came from a specimen that the investigator forgot to wash before
A simple random sample of eight college freshmen were asked how many hours of sleep they typically got per night. The results wereNotice that one joker said that he sleeps 24 hours a day.a. The data contain an outlier that is clearly a mistake.Eliminate the outlier, then construct a 95% confidence
In a survey of 200 adult women in a certain city, the mean number of children they had was 2.3 with a standard deviation of 1.2. A sociologist states that the mean number of children per woman in this city is between 2.13 and 2.47. With what level of confidence can this claim be made?
There have been 44 presidents of the United States. Their mean height is 70.8 inches, with a standard deviation of 2.7 inches. Explain why these data should not be used to construct a confidence interval for the mean height of the presidents.
As of July 1, 2012, the mean population of the 50 states of the United States was 6.3 million, with a standard deviation of 7.0 million. Explain why these data should not be used to construct a confidence interval for the mean population of the states.
Weights, in pounds, of a sample of male college soccer players were measured. The following display from a TI-84 Plus calculator presents a 98% confidence interval for the population mean weight.a. Fill in the blanks: We are ___________________ confident that the population mean weight is between
A sample of college students was asked how many hours per week they spent reading. The following display from a TI-84 Plus calculator presents a 95% confidence interval for the population mean time spent reading.a. Fill in the blanks: We are _________________ confident that the population mean
A sample of used cars on a lot was taken, and the age of each car was recorded. The following MINITAB output presents a confidence interval for the population mean age.a. How many degrees of freedom are there?b. If the population were not approximately normal, would this confidence interval be
A sample of college students was taken, and their ages were recorded. The following MINITAB output presents a confidence interval for the population mean age.a. How many degrees of freedom are there?b. If the population were not approximately normal, would this confidence interval be valid?
The concentration of carbon monoxide in parts per million is believed to be normally distributed with a standard deviation σ = 8.A single measurement of the concentration is made, and its value is 85.a. Use the methods of Section 8.1 to construct a 95%confidence interval for the mean
A normal distribution has mean μ = 15 and standard deviation σ = 4.Find and interpret the z-score for x = 11.
A normal distribution has mean μ = 60 and standard deviation σ = 20.Find and interpret the z-score for x = 75.
Compact fluorescent bulbs are more energy efficient than incandescent bulbs, but they take longer to reach full brightness. The time that it takes for a compact fluorescent bulb to reach full brightness is normally distributed with mean 29.8 seconds and standard deviation 4.5 seconds. A randomly
A normal population has mean μ = 3 and standard deviation σ = 1.Find the proportion of the population that is less than 1.
A normal population has mean μ = 40 and standard deviation σ = 10.Find the probability that a randomly sampled value is greater than 53.
A normal population has mean μ = 7 and standard deviation σ = 5.Find the proportion of the population that is between −2 and 10.
A population has mean μ = 6.9 and standard deviation σ = 2.6. Find the value that has 80% of the population below it (in other words, the 80th percentile).
A population has mean μ = 53 and standard deviation σ = 34.Find the value that has 35% of the population above it.
The process of converting a value x from a normal distribution to a z-score is known as __________________ .In Exercises 9–10, fill in each blank with the appropriate word or phrase.
A value that is two standard deviations below the mean will have a z-score of ___________________ .In Exercises 9–10, fill in each blank with the appropriate word or phrase.
z-scores follow a standard normal distribution.In Exercises 11–16, determine whether the statement is true or false. If the statement is false, rewrite it as a true statement.
A z-score indicates how many standard deviations a value is above or below the mean.In Exercises 11–16, determine whether the statement is true or false. If the statement is false, rewrite it as a true statement.
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