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statistics
elementary statistics in social research
Questions and Answers of
Elementary Statistics In Social Research
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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