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elementary statistics

Questions and Answers of Elementary Statistics

A Pew poll found that in a sample of 1002 adults, 621 had a social media account. The study was repeated a year later, and 631 out of 971 adults has social media accounts.a. Construct a 95%
The following TI-84 Plus calculator display presents a 99% confidence interval for the difference between two proportions.a. Compute the point estimate of p1 − p2.b. Fill in the blanks: We are 99%
The following MINITAB output presents a confidence interval for the difference between two proportions.a. Compute the point estimate of p1 − p2.b. Fill in the blanks: We are _____________ confident
The following MINITAB output presents a confidence interval for the difference between two proportions.a. Compute the point estimate of p1 − p2.b. Fill in the blanks: We are _____________ confident
Polls are to be conducted in two cities to determine the difference in the proportions of residents who believe that the economy will improve over the next year. A 95% confidence interval will be
A group of five individuals with high blood pressure were given a new drug that was designed to lower blood pressure. Systolic blood pressure was measured before and after treatment for each
The statistics department at a large university instituted a program in which students could get extra help with statistics in the evening. The following table presents scores for tests taken before
With ______________ samples, each value in one sample can be matched with a corresponding value from another sample.In Exercises 3 and 4, fill in each blank with the appropriate word or phrase.
The margin of error for the mean difference between matched pairs is usually ______________ than the margin of error for independent samples.In Exercises 3 and 4, fill in each blank with the
Paired data reduce a two-sample problem to a one-sample problem.In Exercises 5 and 6, determine whether the statement is true or false. If the statement is false, rewrite it as a true statement.
To construct a confidence interval using matched pairs, we must compute the standard deviation of each sample.In Exercises 5 and 6, determine whether the statement is true or false. If the statement
Two microprocessors are compared on a sample of 6 benchmark codes to determine whether there is a difference in speed. The times (in seconds) used by each processor on each code are as follows:a.
For a sample of 9 automobiles, the mileage (in 1000s of miles) at which the original front brake pads were worn to 10% of their original thickness was measured, as was the mileage at which the
The compressive strength, in kilopascals, was measured for concrete blocks from five different batches of concrete, both three and six days after pouring. The data are as follows:a. Construct a 95%
In an experiment to determine the effect of ambient temperature on the emissions of oxides of nitrogen(NOx) of diesel trucks, 10 trucks were run at temperatures of 40°F and 80°F. The emissions, in
A group of eight individuals with high cholesterol levels were given a new drug that was designed to lower cholesterol levels. Cholesterol levels, in milligrams per deciliter, were measured before
A tire manufacturer is interested in testing the fuel economy for two different tread patterns. Tires of each tread type were driven for 1000 miles on each of 9 different cars. The mileages, in miles
It is generally known that boys grow at an unusually fast rate between the ages of about 12 and 14.Following are heights, in inches of 40 boys, measured at age 12 and again at age 14.a. Construct a
A sample of 32 students took a class designed to improve their SAT math scores. Following are their scores before and after the class.a. Construct a 95% confidence interval for the mean increase in
The following TI-84 Plus calculator display presents a 95% confidence interval for the mean difference between matched pairs.a. What is the point estimate of μd?b. How many degrees of freedom are
The following TI-84 Plus calculator display presents a 99% confidence interval for the mean difference between matched pairs.a. What is the point estimate of μd?b. How many degrees of freedom are
The following output from MINITAB presents a confidence interval for the mean difference between matched pairs.a. What is the point estimate of μd?b. How many degrees of freedom are there?c. Fill in
The following output from MINITAB presents a confidence interval for the mean difference between matched pairs.a. What is the point estimate of μd?b. How many degrees of freedom are there?c. Fill in
Refer to Exercise 12.a. Assume that the measurements for tread A and for tread B come from independent samples, and construct a 95% confidence interval for the difference in mean tread wear using the
A sample of 15 weight lifters is tested to see how much weight they can bench press. They then follow a special training program for three weeks, after which they are tested again. The samples are
A sample of 20 weight lifters is tested to see how much weight they can bench press. Ten of them are chosen at random as the treatment group. They participate in a special training program for three
In a survey of 300 randomly selected female and 240 male holiday shoppers, 87 of the females and 98 of the males stated that they will wait until the last week before Christmas to finish buying
Refer to Exercise 3.Find the critical value for a 95% confidence interval for the difference p1 − p2.Exercise 3In a survey of 300 randomly selected female and 240 male holiday shoppers, 87 of the
Refer to Exercise 3.Compute the margin of error for a 95% confidence interval for the difference p1 − p2.Exercise 3In a survey of 300 randomly selected female and 240 male holiday shoppers, 87 of
Refer to Exercise 3.Construct a 95% confidence interval for the difference p1 − p2.Exercise 3In a survey of 300 randomly selected female and 240 male holiday shoppers, 87 of the females and 98 of
Eight students in a particular college course are given a pre-test at the beginning of the semester and are then given the same exam at the end to test what they have learned. The exam scores at the
Refer to Exercise 7.Find the critical value for a 99% confidence interval for μd.Exercise 7Eight students in a particular college course are given a pre-test at the beginning of the semester and are
Refer to Exercise 7.Compute the margin of error for a 99% confidence interval for the difference μd.Exercise 7Eight students in a particular college course are given a pre-test at the beginning of
Refer to Exercise 7.Construct a 99% confidence interval for the difference μd.Exercise 7Eight students in a particular college course are given a pre-test at the beginning of the semester and are
A random sample of 76 residents in a small town had a mean annual income of \($34,214\), with a sample standard deviation of \($2171\). In a neighboring town, a random sample of 88 residents had a
Refer to Exercise 11.Find the critical value for a 90% confidence interval for the difference μ1 − μ2.Exercise 11A random sample of 76 residents in a small town had a mean annual income of
Refer to Exercise 11.Compute the margin of error for a 90% confidence interval for the differenceμ1 − μ2.Exercise 11A random sample of 76 residents in a small town had a mean annual income of
Refer to Exercise 11.Construct a 90% confidence interval for the difference μ1 − μ2.Exercise 11A random sample of 76 residents in a small town had a mean annual income of \($34,214\), with a
In a poll of 100 voters, 57 said they were planning to vote for the incumbent governor, and 48 said they were planning to vote for the incumbent mayor. Explain why these data should not be used to
An investor is trying to decide in which of two stocks to invest. He examines records for the past 365 days, and finds that the price of stock A increased on 197 of them and the price of stock B
Why is it necessary for all values in the confidence interval to be positive to conclude that μ1 > μ2? What would have to be true to conclude that μ1 < μ2?
Provide an example of two samples that are independent. Explain why these samples are independent.
Provide an example of two samples that are paired. Explain why these samples are paired.
A test was made of H0 : μ1 = μ2 versus H1: μ1 > μ2. Independent random samples were drawn from approximately normal populations. The sample means were x̄1 = 6.8 and x̄2 = 4.9. The sample
A test was made of H0 : μ1 = μ2 versus H1: μ1 ≠ μ2. Independent random samples were drawn from approximately normal populations. The sample means were x̄1 = 73.9 and x̄2 = 71.8. The sample
To use the methods of this section to test a hypothesis about the difference between two means when the samples are small, the samples must show no evidence of strong ________________ and must
If the sample sizes are n1 and n2, the simplest way to compute the degrees of freedom is to use the smaller of___________________ and ________________ .In Exercises 3 and 4, fill in each blank with
To use the methods of this section to test a hypothesis about the difference between two means, the population standard deviations must be known.In Exercises 5 and 6, determine whether the statement
In general, it is not recommended to use a pooled standard deviation when testing a hypothesis for the difference between means.In Exercises 5 and 6, determine whether the statement is true or false.
A test was made of H0: μ1 = μ2 versus H1: μ1 < μ2. The sample means were x̄1 = 6 and x̄2 = 11, the sample standard deviations were s1 = 3 and s2 = 5, and the sample sizes were n1 = 10 and n2 =
A test was made of H0: μ1 = μ2 versus H1: μ1 ≠ μ2. The sample means were x̄1 = 10 and x̄2 = 8, the sample standard deviations were s1 = 4 and s2 = 7, and the sample sizes were n1 = 15 and n2
The General Social Survey polled a sample of 1048 adults in the year 2010, asking them how many hours per week they spent on the Internet. The sample mean was 9.79 with a standard deviation of 13.41.
Are low-fat diets or low-carb diets more effective for weight loss? A sample of 77 subjects went on a low-carbohydrate diet for six months. At the end of that time, the sample mean weight loss was
In a study of birth order and intelligence, IQ tests were given to 18- and 19-year-old men to estimate the size of the difference, if any, between the mean IQs of firstborn sons and secondborn
A new postsurgical treatment was compared with a standard treatment. Seven subjects received the new treatment, while seven others (the controls) received the standard treatment. The recovery times,
The concentration of benzene was measured in units of milligrams per liter for a simple random sample of five specimens of untreated wastewater produced at a gas field. The sample mean was 7.8 with a
Medical researchers conducted a study to determine whether treadmill exercise could improve the walking ability of patients suffering from claudication, which is pain caused by insufficient blood
King Tut was an ancient Egyptian ruler whose tomb was discovered and opened in 1923. Legend has it that the archaeologists who opened the tomb were subject to a ‘‘mummy’s curse,’’ which
Following are weights in pounds for random samples of 25 newborn baby boys and baby girls born in Denver in 2011. Boxplots indicate that the samples come from populations that are approximately
The Interpersonal Reactivity Index is a survey designed to assess four different types of empathy. One type of empathy, called Empathetic Concern, measures the tendency to feel sympathy and
The Pew Internet and American Life Project surveyed 2227 adults, asking them about their texting habits. Among men, the mean number of text messages sent per day was 40.9, and among women it was
Do you prefer taking tests on paper or online?A college instructor gave identical tests to two randomly sampled groups of 35 students. One group took the test on paper and the other took it online.
How often does the average driver have an accident? The Allstate Insurance Company determined the average number of years between accidents for drivers in a large number of U.S. cities. Following are
The following TI-84 Plus calculator display presents the results of a hypothesis test for the difference between two means. The sample sizes are n1 = 12 and n2 = 15.a. Is this a left-tailed test, a
The following TI-84 Plus calculator display presents the results of a hypothesis test for the difference between two means. The sample sizes are n1 = 25 and n2 = 28.a. Is this a left-tailed test, a
The following computer output(from MINITAB) presents the results of a hypothesis test for the difference μ1 − μ2 between two population means:a. What is the alternate hypothesis?b. Can H0 be
The following computer output(from MINITAB) presents the results of a hypothesis test for the difference μ1 − μ2 between two population means:a. What is the alternate hypothesis?b. Can H0 be
A test will be made of H0: μ1 = μ2 versus H1: μ1 > μ2. The sample sizes were n1 = 10 and n2 = 20.The sample standard deviations were s1 = 3 and s2 = 8.a. Compute the critical value for a level α
A sample of students is enrolled in a speed-reading class. Each takes a reading test before and again after the class. The two samples of scores are compared to determine how large an improvement in
A sample of students is enrolled in an online statistics class, and another sample is enrolled in a traditional statistics class. At the end of the semester, the students are given a test. The scores
A sample of 87 one-year-old spotted flounder had a mean length of 126.31 millimeters with a sample standard deviation of 18.10 millimeters, and a sample of 132 two-year-old spotted flounder had a
The mean speed for a sample of 39 cars at a certain intersection was 26.50 kilometers per hour with a standard deviation of 2.37 kilometers per hour, and the mean speed for a sample of 142
If observations in one sample do not influence the observations in another sample, the samples are said to be _______________ .In Exercises 5 and 6, fill in each blank with the appropriate word or
When determining the number of degrees of freedom by hand with sample sizes n1 and n2, we choose the smaller of ___________________ and __________________ .In Exercises 5 and 6, fill in each blank
The point estimate for μ1 − μ2 is x̄1 + x̄2.In Exercises 7 and 8, determine whether the statement is true or false. If the statement is false, rewrite it as a true statement.
The number of degrees of freedom calculated with technology is generally different from the number calculated by hand.In Exercises 7 and 8, determine whether the statement is true or false. If the
Level 90%: x̄1 = 104.6, ̄x2 = 92.9, s1 = 4.8, s2 = 6.9, n1 = 26, n2 = 19 In Exercises 9–14, construct the confidence interval for the difference μ1 − μ2 for the given level and values of x̄1
Level 95%: x̄ 1 = 478.81, ̄x2 = 322.49, s1 = 42.84, s2 = 25.17, n1 = 14, n2 = 16 In Exercises 9–14, construct the confidence interval for the difference μ1 − μ2 for the given level and values
Level 99%: x̄1 = 603.55, ̄x2 = 516.63, s1 = 54.7, s2 = 45.2, n1 = 15, n2 = 24 In Exercises 9–14, construct the confidence interval for the difference μ1 − μ2 for the given level and values of
Level 98%: x̄1 = 77.3, ̄x2 = 72.6, s1 = 9.1, s2 = 8.8, n1 = 12, n2 = 16 In Exercises 9–14, construct the confidence interval for the difference μ1 − μ2 for the given level and values of x̄1
Level 95%: x̄1 = 47.7, ̄x2 = 42.6, s1 = 33.9, s2 = 17.6, n1 = 13, n2 = 19 In Exercises 9–14, construct the confidence interval for the difference μ1 − μ2 for the given level and values of
Level 99.5%: x̄1 = 82.9, ̄x2 = 64.1, s1 = 9.8, s2 = 6.2, n1 = 19, n2 = 10 In Exercises 9–14, construct the confidence interval for the difference μ1 − μ2 for the given level and values of
A group of 78 people enrolled in a weight-loss program that involved adhering to a special diet and to a daily exercise program. After six months, their mean weight loss was 25 pounds, with a sample
The concentration of benzene was measured in units of milligrams per liter for a simple random sample of five specimens of untreated wastewater produced at a gas field. The sample mean was 7.8 with a
In an agricultural experiment, the effects of two fertilizers on the production of oranges were measured. Sixteen randomly selected plots of land were treated with fertilizer A, and 12 randomly
A computer system administrator notices that computers running a particular operating system seem to crash more often as the installation of the operating system ages. She measures the time (in
In a study of birth order and intelligence, IQ tests were given to 18- and 19-year-old men to estimate the size of the difference, if any, between the mean IQs of firstborn sons and of secondborn
study was done to compare the effectiveness of distance learning with traditional classroom instruction. Twelve students took a business administration course online, while 14 students took it in a
The National Health Statistics Reports stated that a sample of 318 one-year-old boys had a mean weight of 25.0 pounds with a standard deviation of 3.6 pounds. In addition, a sample of 297
In a survey of adults with diabetes, the average body mass index (BMI) in a sample of 1924 women was 31.1 with a standard deviation of 0.2. The BMI in a sample of 1559 men was 30.4, with a standard
A survey of college students reported that in a sample of 413 male college students, the average number of energy drinks consumed per month was 2.49 with a standard deviation of 4.87, and in a sample
Are low-fat diets or low-carb diets more effective for weight loss? A sample of 77 subjects went on a low-carbohydrate diet for six months. At the end of that time, the sample mean weight loss was
Do you prefer taking tests on paper or online?A college instructor gave identical tests to two randomly sampled groups of 35 students. One group took the test on paper and the other took it online.
How often does the average driver have an accident? The Allstate Insurance Company determined the average number of years between accidents for drivers in a large number of U.S. cities. Following are
The following TI-84 Plus calculator display presents a 95% confidence interval for the difference between two means. The sample sizes are n1 = 7 and n2 = 10.a. Compute the point estimate of μ1 −
The following TI-84 Plus calculator display presents a 99% confidence interval for the difference between two means. The sample sizes are n1 = 50 and n2 = 42.a. Compute the point estimate of μ1 −
The following MINITAB output display presents a 98% confidence interval for the difference between two means.a. Compute the point estimate of μ1 − μ2.b. How many degrees of freedom did the
The following MINITAB output display presents a 95% confidence interval for the difference between two means.a. Compute the point estimate of μ1 − μ2.b. How many degrees of freedom did the
The following TI-84 Plus display presents a 95% confidence interval, using the more accurate formula for the degrees of freedom. The sample sizes are n1 = 12 and n2 = 10.a. Use the simpler method to
What does the P-value represent?

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