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elementary statistics
Questions and Answers of
Elementary Statistics
The Bonferroni adjustment is made by multiplying the P-value by the number of___________________ .In Exercises 3 and 4, fill in each blank with the appropriate word or phrase.
The Bonferroni-adjusted P-value is always greater than the uncorrected P-value.In Exercises 5 and 6, determine whether the statement is true or false. If the statement is false, rewrite it as a true
When testing several hypotheses, it is reasonable to reject every hypothesis for which P < 0.05.In Exercises 5 and 6, determine whether the statement is true or false. If the statement is false,
Five null hypotheses were tested, and the P-values were:a. Which hypotheses, if any, can be rejected at the α = 0.05 level?b. Which hypotheses, if any, can be rejected at the α = 0.01 level?
Six null hypotheses were tested, and the P-values were:a. Which hypotheses, if any, can be rejected at the α = 0.05 level?b. Which hypotheses, if any, can be rejected at the α = 0.01 level?
A sociologist surveys a sample of college students to determine whether there are differences in the attitudes and behaviors of male and female students. The survey contains 20 questions. For one
Six different settings are tried on a machine to determine whether any of them will reduce the proportion of defective parts. For each setting, an appropriate null hypothesis is tested to determine
Refer to Exercise 9.For the result that was statistically significant, the P-value was 0.01. What P-value would be needed to conclude at the α = 0.05 level that the time spent studying differs
Refer to Exercise 10.The quality engineer suspects that the setting with a P-value of 0.03 may actually reduce the proportion of defective parts. What P-value would be needed to make this conclusion
Five hundred null hypotheses are tested at the α = 0.05 level, and 40 of them are rejected. Assume the tests are independent,a. Assuming that all 500 null hypotheses are true, what is the
A simple random sample of 75 people are given a new drug that is designed to relieve pain. A second sample of 50 people are given a standard drug. The question of interest is whether the proportion
Two machines are used to fill cans. The machines are supposed to fill each can with 12 ounces of liquid. The amounts actually filled follow a normal distribution. A simple random sample of 10 cans is
A fleet of 100 taxis is divided into two groups of 50 cars each to determine whether premium gasoline reduces maintenance costs. Premium unleaded fuel is used in group A, while regular unleaded fuel
A simple random sample of 75 people are given a new drug that is designed to relieve pain. After taking this drug for a month, they switch to a standard drug. The question of interest is whether the
In a test of H0: p1 = p2 versus H1: p1 ≠ p2, the value of the test statistic is z = −1.21. What do you conclude about the difference p1 − p2 at the ???? = 0.05 level of significance?
A sample of size 15 is drawn from a normal population. The sample standard deviation is s1 = 5.2. A sample of size 10 is drawn from another normal population. The sample standard deviation is s2 =
For a test of H0: μ1 = μ2 versus H1: μ1 ≠ μ2, the sample sizes were n1 = 15 and n2 = 25.How many degrees of freedom are there for the test statistic? Use the simple method.
In a set of 12 matched pairs, the mean difference was d̄ = 18 and the standard deviation of the differences was sd = 4.Find the value of the test statistic for testing H0: μd = 15 versus H1: μd >
Two suppliers of machine parts delivered large shipments. A simple random sample of 150 parts was chosen from each shipment.For supplier A, 12 of the 150 parts were defective. For supplier B, 28 of
Refer to Exercise 9.Compute the value of the test statistic.Exercise 9Two suppliers of machine parts delivered large shipments. A simple random sample of 150 parts was chosen from each shipment.For
Refer to Exercise 9.Can you reject H0 at the α = 0.01 level? State a conclusion.Exercise 9Two suppliers of machine parts delivered large shipments. A simple random sample of 150 parts was chosen
A simple random sample of 17 business majors from a certain university had a mean GPA of 2.81 with a standard deviation of 0.27. A simple random sample of 23 psychology majors was selected from the
Refer to Exercise 12.Compute the value of the test statistic.Exercise 12A simple random sample of 17 business majors from a certain university had a mean GPA of 2.81 with a standard deviation of
Refer to Exercise 12.Can you reject H0 at the α = 0.05 level? State a conclusion.Exercise 12A simple random sample of 17 business majors from a certain university had a mean GPA of 2.81 with a
Five null hypotheses were tested, and the P-values were 0.24, 0.17, 0.03, 0.002, and 0.02. How many of the hypotheses are rejected at the α = 0.05 level if the Bonferroni adjustment is made?
The General Social Survey reported that in a sample of 68 men aged 18–25, the mean number of hours of television watched per day was 2.76 with a standard deviation of 2.21. In a sample of 72 women
A sample of five third graders took a reading test. They then participated in a reading improvement program, and took the test again to determine whether their reading ability had improved. Following
Following are the annual amounts of rainfall, in inches, in six randomly chosen cities for two consecutive years. Can you conclude that the mean rainfall was greater in year 2 than in year 1?a. Let
If the sample size is small, the differences between the items in the matched pairs must show no evidence of strong and must contain no ______________ .In Exercises 3 and 4, fill in each blank with
With matched pairs, the test for the difference between population means is the same as the test for a single population _________________ .In Exercises 3 and 4, fill in each blank with the
Paired data are data for which each value in one sample can be matched with a corresponding value in another sample.In Exercises 5 and 6, determine whether the statement is true or false. If the
To compute the test statistic for a test with matched pairs, we must compute the standard deviations of the samples.In Exercises 5 and 6, determine whether the statement is true or false. If the
Following is a sample of five matched pairs.Let μ1 and μ2 represent the population means and let μd = μ1 − μ2. A test will be made of the hypotheses H0: μd = 0 versus H1: μd > 0.a.
Following is a sample of 10 matched pairs.Let μ1 and μ2 represent the population means and let μd = μ1 − μ2. A test will be made of the hypotheses H0: μd = 0 versus H1: μd ≠ 0.a. Compute
A crossover trial is a type of experiment used to compare two drugs. Subjects take one drug for a period of time, then switch to the other. The responses of the subjects are then compared using
In an experiment to determine whether there is a systematic difference between the weights obtained with two different scales, 10 rock specimens were weighed, in grams, on each scale. The following
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:Can you conclude
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
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.Can you conclude
A sample of 32 students took a class designed to improve their SAT math scores. Following are their scores before and after the class.Can you conclude that the mean increase in score is less than 15
The following MINITAB output presents the results of a hypothesis test for a mean difference.a. Is this a left-tailed test, a right-tailed test, or a two-tailed test?b. Can H0 be rejected at the 0.05
The following MINITAB output presents the results of a hypothesis test for a mean difference.a. Is this a left-tailed test, a right-tailed test, or a two-tailed test?b. Can H0 be rejected at the 0.05
Refer to Exercise 12.Assume you did not know that the two samples were paired, so you used the methods of Section 11.1 to perform the test.a. What is the P-value?b. Explain why the P-value is greater
Find f0.05 for F8,18.
Find f0.01 for F12,8.
For testing H0 : σ1 = σ2 versus H1: σ1 < σ2, we observe s1 = 0.9, s2 = 1.5, n1 = 16, and n2 = 11.Test at the significance level α = 0.01.a. Find the critical value.b. Do you reject H0?
For testing H0 : σ1 = σ2 versus H1: σ1 ≠ σ2, we observe s1 = 9.3, s2 = 2.1, n1 = 6, and n2 = 13.Test at the significance level α = 0.05.a. Find the critical value.b. Do you reject H0?
To use an F-test, both populations must have a _______________ distribution.In Exercises 5 and 6, fill in each blank with the appropriate word or phrase.
The F statistic is the quotient of the sample ____________ .In Exercises 5 and 6, fill in each blank with the appropriate word or phrase.
The test statistic F is never greater than 1.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 F-test for two standard deviations is very sensitive to the normality assumption.In Exercises 7 and 8, determine whether the statement is true or false. If the statement is false, rewrite it as a
Find the critical value f0.05 for F7,20.
Find the critical value f0.01 for F2,5.
An F-test with 12 degrees of freedom in the numerator and 6 degrees of freedom in the denominator produced a test statistic whose value was 3.42. The null and alternate hypotheses were H0: σ1 = σ2
An F-test with 5 degrees of freedom in the numerator and 7 degrees of freedom in the denominator produced a test statistic whose value was 5.31. The null and alternate hypotheses were H0: σ1 = σ2
A broth used to manufacture a pharmaceutical product has its sugar content, in milligrams per milliliter, measured several times on each of three successive days.a. Can you conclude that the
The breaking strength of hockey stick shafts made of two different graphite-kevlar composites yields the following results (in newtons).Can you conclude that the standard deviation of the breaking
A computer system administrator notices that computers running a particular operating system seem to freeze up 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 secondborn
It is desired to find the value f0.99 for an F10,5 distribution. Use Table A.5 and the F5,10 distribution to find this value. Table A.5 Critical Values for the F Distribution Area Denominator Degrees
In a clinical trial to compare the effectiveness of two pain relievers, a sample of 100 patients was given drug 1 and an independent sample of 200 patients was given drug 2.Of the patients on drug 1,
A sample of 200 voters over the age of 60 were asked whether they thought Social Security benefits should be increased for people over the age of 65.A total of 95 of them answered yes. A sample of
To use the method of this section to test a hypothesis about the difference between two proportions, each population must be at least _______________ times as large as the sample drawn from it.In
To use the method of this section to test a hypothesis about the difference between two proportions, each sample must contain at least _________________ individuals in each category.In Exercises 3
The individuals in each sample are divided into three or more categories.In Exercises 5 and 6, determine whether the statement is true or false. If the statement is false, rewrite it as a true
To compute the test statistic, it is necessary to compute the pooled proportion.In Exercises 5 and 6, determine whether the statement is true or false. If the statement is false, rewrite it as a true
In a test for the difference between two proportions, the sample sizes were n1 = 120 and n2 = 85, and the numbers of events were x1 = 55 and x2 = 45.A test is made of the hypotheses H0: p1 = p2
In a test for the difference between two proportions, the sample sizes were n1 = 68 and n2 = 76, and the numbers of events were x1 = 41 and x2 = 25.A test is made of the hypotheses H0: p1 = p2 versus
The National Health and Nutrition Examination Survey (NHANES) weighed a sample of 546 boys aged 6–11 and found that 87 of them were overweight. They weighed a sample of 508 girls aged 6–11 and
In a random sample of 340 cars driven at low altitudes, 46 of them exceeded a standard of 10 grams of particulate pollution per gallon of fuel consumed. In an independent random sample of 85 cars
Medical researchers performed a comparison of two drugs, clopidogrel and ticagrelor, which are designed to reduce the risk of heart attack or stroke in coronary patients. A total of 6676 patients
An article in the Archives of Internal Medicine reported that in a sample of 244 men, 73 had elevated total cholesterol levels (more than 200 milligrams per deciliter). In a sample of 232 women, 44
Angioplasty is a medical procedure in which an obstructed blood vessel is widened. In some cases, a wire mesh tube, called a stent, is placed in the vessel to help it remain open. A study was
In August and September 2005, Hurricanes Katrina and Rita caused extraordinary flooding in New Orleans, Louisiana. Many homes were severely damaged or destroyed, and of those that survived, many
In a certain year, there was measurable snowfall on 80 out of 365 days in Denver, and 63 out of 365 days in Chicago. A meteorologist proposes to perform a test of the hypothesis that the proportions
A new reading program is being tested. Parents are asked whether they would like to enroll their children, and 50 children are enrolled in the program. There are 45 children whose parents do not
The following TI-84 Plus calculator display presents the results of a hypothesis test for the difference between two proportions. The sample sizes are n1 = 165 and n2 = 152.a. Is this a left-tailed
The following TI-84 Plus calculator display presents the results of a hypothesis test for the difference between two proportions. The sample sizes are n1 = 71 and n2 = 62.a. Is this a left-tailed
The following computer output(from MINITAB) presents the results of a hypothesis test on the difference between two proportions.a. Is this a left-tailed test, a right-tailed test, or a two-tailed
The following computer output(from MINITAB) presents the results of a hypothesis test on the difference between two proportions.a. Is this a left-tailed test, a right-tailed test, or a two-tailed
A computer manufacturer has a choice of two machines, a less expensive one and a more expensive one, to manufacture a particular computer chip. Out of 500 chips manufactured on the less expensive
A class of 30 computer science students were taught introductory computer programming class with an innovative teaching method that used a graphical interface and drag-and-drop methods of creating
In a test of the effect of dampness on electrical connections, 80 electrical connections were tested under damp conditions and 130 were tested under dry conditions. Twenty of the damp connections
3. To construct a confidence interval for p1 − p2, we must have two ______________ samples.In Exercises 3 and 4, fill in each blank with the appropriate word or phrase.
When constructing a confidence interval for p1 − p2, we assume that items in each sample are divided into ________________ categories and that there are at least ________________ items in each
The point estimate for p1 − p2 is p̂1 − p̂2, where p̂1 = x1∕n1 and p̂2 = x2∕n2.In Exercises 5 and 6, determine whether the statement is true or false. If the statement is false, rewrite
The margin of error for p̂1 − p̂2 isIn Exercises 5 and 6, determine whether the statement is true or false. If the statement is false, rewrite it as a true statement. P1(1-1), 2(1-2) + 112
Level 95%: x1 = 42, n1 = 80, x2 = 18, n2 = 60 In Exercises 7–12, construct the confidence interval for the difference p1 − p2 for the given level and values of x1, n1, x2, and n2.
Level 90%: x1 = 14, n1 = 25, x2 = 12, n2 = 40 In Exercises 7–12, construct the confidence interval for the difference p1 − p2 for the given level and values of x1, n1, x2, and n2.
Level 99%: x1 = 57, n1 = 147, x2 = 86, n2 = 118 In Exercises 7–12, construct the confidence interval for the difference p1 − p2 for the given level and values of x1, n1, x2, and n2.
Level 95%: x1 = 63, n1 = 106, x2 = 70, n2 = 126 In Exercises 7–12, construct the confidence interval for the difference p1 − p2 for the given level and values of x1, n1, x2, and n2.
Level 98%: x1 = 49, n1 = 74, x2 = 62, n2 = 153 In Exercises 7–12, construct the confidence interval for the difference p1 − p2 for the given level and values of x1, n1, x2, and n2.
Level 99%: x1 = 24, n1 = 53, x2 = 17, n2 = 41 In Exercises 7–12, construct the confidence interval for the difference p1 − p2 for the given level and values of x1, n1, x2, and n2.
Traffic engineers compared rates of traffic accidents at intersections with raised medians with rates at intersections with two-way left-turn lanes. They found that out of 4644 accidents at
In a new experimental teaching method, when students have questions in class, they send them to the instructor via a laptop computer. From time to time, the instructor pauses to read the questions
In a random sample of 50 patients undergoing a standard surgical procedure, 15 required medication for postoperative pain. In a random sample of 90 patients undergoing a new procedure, only 16
In order to judge the effectiveness of an advertising campaign for a certain brand of pretzel, a company obtained a simple random sample of 90 convenience store receipts the week before the ad
A team of designers was given the task of reducing the defect rate in the manufacture of a certain printed circuit board. The team decided to reconfigure the cooling system. A total of 973 boards
A poll taken by the General Social Survey in 2010 asked people in the United States whether they were satisfied with their financial situation. A total of 478 out of 2038 people said they were
Colonoscopy is a medical procedure that is designed to find and remove precancerous lesions in the colon before they become cancerous. In a sample of 51,460 people without colorectal cancer, 5043 had
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