- A polling organization reports that the proportion of U.S. adults who believe that Earth’s temperature has been increasing over the past 100 years is 81%.(a) state the null and alternative
- A researcher claims that the mean air concentration of nitrogen dioxide in U.S. cities is 9 parts per billion (ppb). In a random sample of 52 U.S. cities, the mean air concentration of nitrogen
- A travel analyst claims that the mean price of a round trip flight from New York City to Los Angeles is less than \($725\). In a random sample of 47 round trip flights from New York City to Los
- Right-tailed test, α = 0.01, n = 33 find the critical value(s) and rejection region(s) for the type of t-test with level of significance a and sample size n.
- Right-tailed test, α = 0.02, n = 63 find the critical value(s) and rejection region(s) for the type of t-test with level of significance a and sample size n.
- Left-tailed test, α = 0.05, n = 48 find the critical value(s) and rejection region(s) for the type of t-test with level of significance a and sample size n.
- Left-tailed test, α = 0.005, n = 15 find the critical value(s) and rejection region(s) for the type of t-test with level of significance a and sample size n.
- Two-tailed test, α = 0.02, n = 12 find the critical value(s) and rejection region(s) for the type of t-test with level of significance a and sample size n.
- Claim: μ ≠ 333; α = 0.05. Sample statistics: x̄ = 328, s = 13, n = 35 test the claim about the population mean μ at the level of significance α. Assume the population is normally distributed.
- Claim: p = 0.15; α = 0.05 Sample statistics: p̂ = 0.09, n = 40 determine whether a normal sampling distribution can be used to approximate the binomial distribution. If it can, test the claim.
- Claim: p = 0.65; α = 0.03 Sample statistics: p̂ = 0.76, n = 116 determine whether a normal sampling distribution can be used to approximate the binomial distribution. If it can, test the claim.
- Claim: p 6 0.70; α = 0.01 Sample statistics: p̂ = 0.50, n = 68 determine whether a normal sampling distribution can be used to approximate the binomial distribution. If it can, test the claim.
- Claim: p Ú 0.04; α = 0.10 Sample statistics: p̂ = 0.03, n = 30 determine whether a normal sampling distribution can be used to approximate the binomial distribution. If it can, test the claim.
- A reporter claims that over 56% of U.S. adults think it is likely that robots and computers will do most jobs 25 years from now. In a random sample of 1000 U.S. adults, 59% say it is likely that most
- A sports analyst claims that 40% of U.S. adults have a positive view of the sports industry. In a random sample of 550 U.S. adults, 165 say they have a positive view of the sports industry. At α =
- Explain how to test a population proportion p.
- In 2021, a reporter claims that at least 55% of U.S. adults feel that COVID-19 vaccinations should be required for high school students to attend school in the fall. In a random sample of 200 U.S.
- A tax analyst says that at least 60% of tax filers are expecting a tax refund. In a random sample of 2494 U.S. tax filers, 56% are expecting a tax refund. At α = 0.05, is there enough evidence to
- An education researcher claims that 65% of full-time college students work year-round. In a random sample of 105 college students, 66 say they work year-round. At α = 0.10, is there enough evidence
- A patient care manager claims that more than half of all nurses feel they became better professionals during the coronavirus pandemic. In a random sample of 300 nurses, 174 say they became better
- A researcher claims that 40% of U.S. adults would consider changing jobs. In a random sample of 50 U.S. adults, 25 say they would consider changing jobs. At α = 0.10, is there enough evidence to
- A research center claims that at most 35% of U.S. adults seek to buy naturally raised and fed meat and poultry. In a random sample of 1000 U.S. adults, 38% say they seek to buy naturally raised and
- A politician claims that more than 25% of U.S. adults believe moral values in the country are getting better. In a random sample of 50 U.S. adults, 17 say moral values in the country are getting
- An animal advocate claims that 25% of U.S. households have taken in a stray cat. In a random sample of 500 U.S. households, 105 say they have taken in a stray cat. At α = 0.05, is there enough
- How do the critical values for a two-tailed test change as α decreases?
- Describe the difference between calculating the standardized test statistic, x2, for a chi-square test for variance and a chi-square test for standard deviation.
- Claim: σ ≤ 0.92; α = 0.01. Sample statistics: s = 0.67, n = 41 test the claim about the population variance σ2 or standard deviation σ at the level of significance α. Assume the population is
- Claim: σ2 ≠ 32.8; α = 0.1. Sample statistics: s2 = 40.9, n = 101 test the claim about the population variance σ2 or standard deviation σ at the level of significance α. Assume the population
- A tire manufacturer claims that the variance of the diameters in a tire model is 8.6. A random sample of 10 tires has a variance of 4.3. At α = 0.01, is there enough evidence to reject the claim?
- An auto manufacturer claims that the variance of the gas mileages in a model of hybrid vehicle is 0.16. A random sample of 30 vehicles has a variance of 0.26. At α = 0.05, is there enough evidence
- A school administrator claims that the standard deviation for grade 12 students on a mathematics assessment test is less than 37 points. A random sample of 28 grade 12 test scores has a standard
- A school administrator claims that the standard deviation for grade 12 students on a reading assessment test is greater than 41 points. A random sample of 25 grade 12 test scores has a standard
- A hospital claims that the standard deviation of the waiting times for patients in its emergency department is no more than 0.5 minute.A random sample of 25 waiting times has a standard deviation of
- A travel analyst claims that the standard deviation of the room rates for two adults at three-star hotels in Denver is at least $68.A random sample of 18 three-star hotels has a standard deviation of
- (a) t = 2.091(b) t = 0(c) t = -2.096state whether each standardized test statistic t allows you to reject the null hypothesis. Explain. -4-3 -1 0 1 2 3 4 to = -2.086
- (a) t = 1.4(b) t = 1.42(c) t = -1.402state whether each standardized test statistic t allows you to reject the null hypothesis. Explain. -4-3-2-1 0 1 2 3 4 to=1.402
- (a) t = -1.755(b) t = -1.585(c) t = 1.745state whether each standardized test statistic t allows you to reject the null hypothesis. Explain. -4-3-2-1 -to = -1.725 0 1 12 2 3 4 0 = 1.725
- (a) t = -1.1(b) t = 1.01(c) t = 1.7state whether each standardized test statistic t allows you to reject the null hypothesis. Explain. -4-3-2-10 1 2 3 4 -to=-1.071 to = 1.071
- An employment information service claims the mean annual salary for senior level statisticians is more than \($124,000\). The annual salaries (in dollars) for a random sample of 12 senior level
- A consumer group claims that the mean minimum time it takes for a sedan to travel a quarter mile is greater than 15.3 seconds.A random sample of 22 sedans has a mean minimum time to travel a quarter
- The mean of a random sample of 18 test scores is \(\bar{x}=85\). The standard deviation of the population of all test scores is \(\sigma=6\). Under what condition can you use a \(z\)-test to decide
- P = 0.0688match the P-value or z-statistic with the graph that represents the corresponding area. Explain your reasoning. (a) -3-2-1 0 2 z = = 1.08 2 (b) -3-2 -1 1/2 z = 1.82 2.
- P = 0.2802match the P-value or z-statistic with the graph that represents the corresponding area. Explain your reasoning. (a) -3-2-1 0 2 z = = 1.08 2 (b) -3-2 -1 1/2 z = 1.82 2.
- z = -2.37match the P-value or z-statistic with the graph that represents the corresponding area. Explain your reasoning. (a) Z (b) 2
- z = -0.51match the P-value or z-statistic with the graph that represents the corresponding area. Explain your reasoning. (a) Z (b) 2
- Claim: \(\mu=40 ; \alpha=0.05 ; \sigma=1.97\)Sample statistics: \(\bar{x}=39.2, n=25\)test the claim about the population mean \(\mu\) at the level of significance \(\alpha\). Assume the population
- Claim: \(\mu \geq 1475 ; \alpha=0.07 ; \sigma=29\)Sample statistics: \(\bar{x}=1468, n=26\)test the claim about the population mean \(\mu\) at the level of significance \(\alpha\). Assume the
- Claim: \(\mu eq\) 5880; \(\alpha=0.03 ; \sigma=413\)Sample statistics: \(\bar{x}=5771, n=67\)test the claim about the population mean \(\mu\) at the level of significance \(\alpha\). Assume the
- Claim: \(\mu \leq 22,500 ; \alpha=0.01 ; \sigma=1200\)Sample statistics: \(\bar{x}=23,500, n=45\)test the claim about the population mean \(\mu\) at the level of significance \(\alpha\). Assume the
- sports statistician claims that the mean winning times for Boston Marathon women’s open division champions is at least 2.6 hours. The mean winning time of a sample of 30 randomly selected Boston
- A consumer group claims that the mean acceleration time from 0 to 60 miles per hour for all 3-cylinder vehicles is 9.4 seconds. A random sample of 33 3-cylinder vehicles has a mean acceleration time
- A consumer research organization states that the mean caffeine content per 12-ounce bottle of a population of caffeinated soft drinks is 37.7 milligrams. You want to test this claim. During your
- An education researcher claims that the mean high school 4-year graduation rate per state in the United States is 83%.You want to test this claim. You find that a random sample of 30 states has a
- A fast food restaurant estimates that the mean sodium content in one of its breakfast sandwiches is less than 920 milligrams. A random sample of 40 breakfast sandwiches has a mean sodium content of
- A light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at least 750 hours. A random sample of 25 light bulbs has a mean life of 745 hours. Assume the population is
- A compact fluorescent lamp (CFL) bulb manufacturer guarantees that the mean life of a CFL bulb is at least 10,000 hours. You want to test this guarantee. To do so, you record the lives of a random
- A politician estimates that the mean gross domestic product (GDP) per country in a recent year is greater than$400 billion. You want to test this estimate. To do so, you determine the GDPs of 42
- What are the two types of hypotheses used in a hypothesis test? How are they related?determine whether the statement is true or false. If it is false, rewrite it as a true statement.
- Describe the two types of errors possible in a hypothesis test decision.determine whether the statement is true or false. If it is false, rewrite it as a true statement.
- What are the two decisions that you can make from performing a hypothesis test?determine whether the statement is true or false. If it is false, rewrite it as a true statement.
- \(H_{0}: \sigma \geq 5.2\)\(H_{a}: \sigma
- \(H_{0}: p=0.25\)\(H_{a}: p eq 0.25\)determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed.
- According to a recent survey, 54% of today’s college students used student loans to pay for college.write the claim as a mathematical statement. State the null and alternative hypotheses, and
- According to a recent survey, 14% of adults currently carry student loan debt.write the claim as a mathematical statement. State the null and alternative hypotheses, and identify which represents the
- A researcher claims that the percentage of U.S.gamers that are women is not 50%.describe type I and type II errors for a hypothesis test of the indicated claim.
- A cell phone repair shop advertises that the mean cost of repairing a phone screen is less than $120.describe type I and type II errors for a hypothesis test of the indicated claim.
- A report claims that more than 30% of households in a Wisconsin county struggle to afford basic necessities.determine whether the claim represents the null hypothesis or the alternative hypothesis.
- A fitness equipment company claims that its competitor’s home gym does not have a customer satisfaction rate of 99%.determine whether the claim represents the null hypothesis or the alternative
- A recent study claims that at least 20% of renters are behind on rent payments in New Jersey.determine whether the claim represents the null hypothesis or the alternative hypothesis. If a hypothesis
- The diameters (in inches) of 18 randomly selected bolts produced by a machine are listed. Use a 95% level of confidence. 4.477 4.425 4.034 4.317 4.003 3.760 3.818 3.749 4.240 3.941 4.131 4.545 3.958
- The times (in minutes) for the drug concentration to peak when the drug epinephrine is injected into 15 randomly selected patients are listed. Use a 90% level of confidence. 4.87 9.67 3.43 8.19 2.92
- The annual earnings (in thousands of dollars) of 21 randomly selected level 1 computer hardware engineers are listed. Use a 99%level of confidence. 59.4 85.2 86.5 80.2 67.4 79.8 67.4 79.8 70.8 52.4
- The final exam scores of 24 randomly selected students in a statistics class are shown in the table at the left. Use a 95%level of confidence.
- The reserve capacities (in hours) of 18 randomly selected automotive batteries have a sample standard deviation of 0.25 hour. Use an 80% level of confidence.
- The annual precipitation amounts (in inches) of a random sample of 61 years for Chicago, Illinois, have a sample standard deviation of 6.46. Use a 98% level of confidence.
- The times (in seconds) spent by a random sample of 28 customers in the drive-thru of a fast-food restaurant have a sample standard deviation of 56.1. Use a 98% level of confidence.
- The times (in seconds) to accelerate from 0 to 60 miles per hour for a random sample of 20 motorcycles have a sample standard deviation of 0.91. Use a 90% level of confidence.
- In a survey of 912 U.S. adults in Generation Z (born after 1996), 383 said they are at least somewhat likely to consider an electric vehicle for their next vehicle purchase.
- In a survey of 13,749 U.S. adults, 5362 said they are at least somewhat likely to consider an electric vehicle for their next vehicle purchase.
- In a survey of 73,901 college graduates, 23,991 obtained a postgraduate degree.
- In a survey of 2223 U.S. adults, 1334 say an occupation as an athlete is prestigious.
- In Exercise 19, would it be unusual for the population proportion to be 38%?Explain.Exercise 19In a survey of 912 U.S. adults in Generation Z (born after 1996), 383 said they are at least somewhat
- In Exercise 22, would it be unusual for the population proportion to be 58%?Explain.Exercise 22In a survey of 2223 U.S. adults, 1334 say an occupation as an athlete is prestigious.
- The number of field goals attempted by LeBron James in 13 randomly selected games of a recent NBA basketball season are listed. Use a 95% level of confidence.assume the sample is from a normally
- The average weekly hours worked by service employees in the leisure and hospitality industry during a recent period of 31 months are listed.Use a 98% level of confidence.assume the sample is from a
- To find the minimum sample size required for a confidence interval, solve for n in the formula for margin of error and round to the nearest whole number.determine whether the statement is true or
- In a survey of 1040 U.S. adults, 62 have had someone impersonate them to try to claim tax refunds.
- In a survey of 351 retired Americans, 200 said that they rely on Social Security as major source of income.
- In a survey of 661 non-retired Americans, 218 said that they expect to rely on Social Security as major source of income when they retire.
- In a survey of 4272 U.S. adults, 1025 knew that private browsing mode only prevents someone using the same computer from seeing one’s online activities.
- In a survey of 1790 U.S. adults in a recent year, 1325 say they have a New Year’s resolution.
- In a survey of 1790 U.S. adults in a recent year, 816 have a New Year’s resolution related to their health.
- In a survey of 1010 U.S. adults, 364 said that they worry a great deal about the possibility of a future terrorist attack.
- In a survey of 1010 U.S. adults, 556 said that they worry a great deal about hunger and homelessness.
- In a survey of 15,349 U.S. adults, 860 identify as lesbian, gay, bisexual, or transgender. Construct a 95% confidence interval for the population proportion of U.S. adults who identify as lesbian,
- In a survey of 692 lesbian, gay, bisexual, or transgender U.S adults, 378 said that they consider themselves bisexual.Construct a 90% confidence interval for the population proportion of lesbian,
- You wish to estimate, with 95% confidence, the population proportion of likely U.S. voters who think Congress is doing a good or excellent job. Your estimate must be accurate within 4% of the
- In Exercise 11, would it be unusual for the population proportion to be 72.5%? Explain.Exercise 11In a survey of 1790 U.S. adults in a recent year, 1325 say they have a New Year’s resolution.
- In Exercise 12, would it be unusual for the population proportion to be 48%?Explain.Exercise 12In a survey of 1790 U.S. adults in a recent year, 816 have a New Year’s resolution related to their
- In Exercise 17(b), would a sample size of 400 be acceptable? Explain.Exercise 17(b)You wish to estimate, with 95% confidence, the population proportion of likely U.S. voters who think Congress is

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