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statistics
elementary statistics in social research
Elementary Statistics Picturing The World 7th Global Edition Betsy Farber, Ron Larson - Solutions
A laptop repair shop advertises that the mean cost of repairing a laptop is less than $125.Describe type I and type II errors for a hypothesis test of the indicated claim.
A glass manufacturer claims that the mean number of glasses that break is no more than 3 glasses per production run.State H0 and Ha in words and in symbols. Then determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed. Explain your reasoning. Sketch a normal sampling
An insurance agent claims that at least 65% of all businesses have a fire insurance policy.State H0 and Ha in words and in symbols. Then determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed. Explain your reasoning. Sketch a normal sampling distribution and shade the
An IT college claims that its mean placement rate is 95%.State H0 and Ha in words and in symbols. Then determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed. Explain your reasoning. Sketch a normal sampling distribution and shade the area for the P-value.
A derby analyst claims that the standard deviation of a jockey clearing the obstacles is less than 2 obstacles.State H0 and Ha in words and in symbols. Then determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed. Explain your reasoning. Sketch a normal sampling
A polling organization reports that the number of samples distributed to 5,000 households does not increase the mean sale by 5,000 units.State H0 and Ha in words and in symbols. Then determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed. Explain your reasoning. Sketch a
A researcher claims that standard deviation of the life span of a brand of air conditioner is at most 4.6 years.Determine whether the claim represents the null hypothesis or the alternative hypothesis. If a hypothesis test is performed, how should you interpret a decision that(a) rejects the null
A scientist claims that the mean number of migratory bird species is less than 3,800.Determine whether the claim represents the null hypothesis or the alternative hypothesis. If a hypothesis test is performed, how should you interpret a decision that(a) rejects the null hypothesis?(b) fails to
An automotive manufacturer claims that the standard deviation for the gas mileage of one of the vehicles it manufactures is 5.6 kilometers per liter.Determine whether the claim represents the null hypothesis or the alternative hypothesis. If a hypothesis test is performed, how should you interpret
A non-governmental organization claims that none of the children in a particular slum area get a balanced diet. Determine whether the claim represents the null hypothesis or the alternative hypothesis. If a hypothesis test is performed, how should you interpret a decision that(a) rejects the null
A fitness research team is investigating the mean cost of a 45-day weight loss course. A fitness center thinks that the mean cost is less than $75. You want to support this claim. How would you write the null and alternative hypotheses?
An internet service provider claims that the mean bandwidth drop time is about 7 minutes. You work for one of the ISP’s competitors and want to reject the claim. How would you write the null and alternative hypotheses?
A carbine manufacturer claims that the mean life span of its competitor’s carbines is less than 46 runs.You are asked to perform a hypothesis test to test this claim. How would you write the null and alternative hypotheses when(a) you represent the manufacturer and want to support the claim?(b)
The P-value for a hypothesis test is P = 0.0237. What is your decision when the level of significance is (1) α = 0.05 and (2) α = 0.01?
Find the P-value for a left-tailed hypothesis test with a standardized test statistic of z = –2.23. Decide whether to reject H0 when the level of significance is α = 0.01.
Find the P-value for a two-tailed hypothesis test with a standardized test statistic of z = 2.14. Decide whether to reject H0 when the level of significance is α = 0.05.
In auto racing, a pit stop is where a racing vehicle stops for new tires, fuel, repairs, and other mechanical adjustments. The efficiency of a pit crew that makes these adjustments can affect the outcome of a race. A pit crew claims that its mean pit stop time (for 4 new tires and fuel) is less
According to a study of U.S. homes that use heating equipment, the mean indoor temperature at night during winter is 68.3°F. You think this information is incorrect. You randomly select 25 U.S. homes that use heating equipment in the winter and find that the mean indoor temperature at night is
Use the TI-84 Plus displays to make a decision to reject or fail to reject the null hypothesis at a level of significance of α = 0.05. TI-84 PLUS Z-Test Inpt: Data Stats Ho:6.2 :.47 x:6.07 n:53 Po Ho Calculate Draw TI-84 PLUS 6.2 Z-Test z=-2.013647416 p=.0440464253 x=6.07 n=53
Find the critical value and rejection region for a left-tailed test with α = 0.01.
Find the critical values and rejection regions for a two-tailed test with α = 0.05.
Employees at a construction and mining company claim that the mean salary of the company’s mechanical engineers is less than that of one of its competitors, which is \($88,200.\) A random sample of 20 of the company’s mechanical engineers has a mean salary of \($85,900.\) Assume the population
A researcher claims that the mean annual cost of raising a child (age 2 and under) by married-couple families in the U.S. is \($14,050.\) In a random sample of married-couple families in the U.S., the mean annual cost of raising a child (age 2 and under) is \($13,795.\) The sample consists of 500
Explain the difference between the z-test for μ using a P-value and the z-test for μ using rejection region(s).
A manufacturer of smoke detectors designed for fire protection claims that the average area that the smoke detector covers is at least 60 square meters. To test this claim, you randomly select a sample of 22 systems and find the mean coverage area to be 58 square meters. Assume the population
A cookie manufacturer claims that the mean sugar content in each of the cookies produced is no more than 18%. A random sample of 56 cookies has a mean sugar content of 19%. Assume the population standard deviation is 4%. At α = 0.02, do you have enough evidence to reject the manufacturer’s
An LED lamp manufacturer guarantees that the mean life of a certain type of LED lamp is at least 25,000 hours. A random sample of 49 LED lamps has a mean life of 24,800 hours. Assume the population is normally distributed and the population standard deviation is 500 hours. At α = 0.05, do you have
Find the critical value t0 for a left-tailed test with α = 0.05 and n = 21.
Find the critical value t0 for a right-tailed test with α = 0.01 and n = 17.
Find the critical values –t0 and t0 for a two-tailed test with α = 0.10 and n = 26.
A used car dealer says that the mean price of used cars sold in the last 12 months is at least \($21,000.\) You suspect this claim is incorrect and find that a random sample of 14 used cars sold in the last 12 months has a mean price of \($19,189\) and a standard deviation of \($2950.\) Is there
An industrial company claims that the mean pH level of the water in a nearby river is 6.8. You randomly select 39 water samples and measure the pH of each.The sample mean and standard deviation are 6.7 and 0.35, respectively. Is there enough evidence to reject the company’s claim at α = 0.05?
A department of motor vehicles office claims that the mean wait time is less than 14 minutes. A random sample of 10 people has a mean wait time of 13 minutes with a standard deviation of 3.5 minutes. At α = 0.10, test the office’s claim. Assume the population is normally distributed.
An estate agent says that the mean rental of a warehouse (with basic amenities) is \($2,500.\) You suspect this claim is incorrect and find that a random sample of 38 such warehouses has a mean rental of \($2,850\) and a standard deviation of \($700.\) Is there enough evidence to reject the claim
A call center claims that the mean wait time for a customer to connect with a customer care executive is at most 2.5 minutes. A random sample of 35 calls at the call center has a mean wait time of 2.75 minutes and a standard deviation of 1.25 minutes. Is there enough evidence to reject the claim at
Flash Drive Cycles A company claims that the mean number of usage cycles of their flash drives is at least 25,000 hours. You suspect this claim is incorrect and find that a random sample of 15 flash drives has a mean number of 24,500 usage cycles and a standard deviation of 750 usage cycles. Is
You receive a brochure from a courier company. The brochure indicates that the mean number of deliveries per deliveryman is more than 28 packets per day. You want to test this claim. You randomly select 18 deliverymen and determine the number of deliveries of each person per day. The results are
The director of a courier company estimates that the mean time spent by a deliveryman in dropping off packages per day is 6.0 hours. As a member of the labor union, you want to test this claim. A random sample of the number of hours for eight deliverymen for a day is shown in the table at the left.
In an article in the Journal of Statistics Education (vol. 4, no. 2), Allen Shoemaker describes a study that was reported in the Journal of the American Medical Association (JAMA).* It is generally accepted that the mean body temperature of an adult human is 98.6°F. In his article, Shoemaker uses
A researcher claims that less than 45% of U.S. adults use passwords that are less secure because complicated ones are too hard to remember. In a random sample of 100 adults, 41% say they use passwords that are less secure because complicated ones are too hard to remember. At α = 0.01, is there
A researcher claims that 51% of U.S. adults believe, incorrectly, that antibiotics are effective against viruses. In a random sample of 2202 adults, 1161 say antibiotics are effective against viruses. At α = 0.10, is there enough evidence to support the researcher’s claim?
Explain how to test a population proportion p.
Write each claim as a mathematical statement. State the null and alternative hypotheses, and identify which represents the claim.1. A school publicizes that the proportion of its students who are involved in at least one extracurricular activity is 61%.2. A car dealership announces that the mean
The USDA limit for salmonella contamination for ground beef is 7.5%. A meat inspector reports that the ground beef produced by a company exceeds the USDA limit. You perform a hypothesis test to determine whether the meat inspector’s claim is true. When will a type I or type II error occur? Which
For each claim, state H0 and Ha in words and in symbols. Then determine whether the hypothesis test is a left-tailed test, right-tailed test, or two-tailed test. Sketch a normal sampling distribution and shade the area for the P@value.1. A school publicizes that the proportion of its students who
You perform a hypothesis test for each claim. How should you interpret your decision if you reject H0? If you fail to reject H0?1. H0 (Claim): A school publicizes that the proportion of its students who are involved in at least one extracurricular activity is 61%.2. Ha (Claim): A car dealership
A medical research team is investigating the benefits of a new surgical treatment. One of the claims is that the mean recovery time for patients after the new treatment is less than 96 hours.1. How would you write the null and alternative hypotheses when you are on the research team and want to
Find the critical values x2R and x2L for a 95% confidence interval when the sample size is 18.
You randomly select and weigh 30 samples of an allergy medicine. The sample standard deviation is 1.20 milligrams. Assuming the weights are normally distributed, construct 99% confidence intervals for the population variance and standard deviation.
c = 0.99, n = 15 Find the critical values x2R and x2L for the level of confidence c and sample size n.
The heights (in centimeters) of 18 randomly selected bottles produced by a machine are listed. Use a 90% level of confidence Assume the sample is from a normally distributed population and construct the indicated confidence intervals for(a) the population variance σ2 (b) the population standard
The quantity (in thousand IUs) of Vitamin D in 15 randomly selected supplement tablets are listed. Use a 95% level of confidence.Assume the sample is from a normally distributed population and construct the indicated confidence intervals for(a) the population variance σ2(b) the population standard
The reserve capacities (in hours) of 18 randomly selected inverter batteries have a sample standard deviation of 0.40 hour. Use a 90% level of confidence.Assume the sample is from a normally distributed population and construct the indicated confidence intervals for(a) the population variance
The waiting times (in minutes) of a random sample of 26 people at a book-signing event have a sample standard deviation of 4.9 minutes. Use a 99% level of confidence.Assume the sample is from a normally distributed population and construct the indicated confidence intervals for(a) the population
The prices of a random sample of 23 new smartphones have a sample standard deviation of $1,200. Use an 80% level of confidence.Assume the sample is from a normally distributed population and construct the indicated confidence intervals for(a) the population variance σ2 (b) the population standard
You are analyzing the sample of bottles in Exercise 13. The population standard deviation of the bottles’ heights should be less than 0.35 centimeter. Does the confidence interval you constructed for σ suggest that the variation in the bottles’ heights is at an acceptable level? Explain your
You are analyzing the sample of Vitamin D Tablets in Exercise 14. The population standard deviation of the amount of Vitamin D in the tablets should be less than 0.50 thousand IUs. Does the confidence interval you constructed for σ suggest that the variation in the amounts of Vitamin D in the
You are analyzing the sample of inverter batteries in Exercise 21. The population standard deviation of the batteries’ reserve capacities should be less than 0.50 hour. Does the confidence interval you constructed for σ suggest that the variation in the batteries’ reserve capacities is at an
Waiting Times You are analyzing the sample of waiting times in Exercise 23.The population standard deviation of the waiting times should be less than 7.9 minutes. Does the confidence interval you constructed for σ suggest that the variation in the waiting times is at an acceptable level? Explain
The systolic blood pressures (in mmHg) of 40 persons are shown in the table. Assume the population standard deviation is 25 mmHg. Find(a) the point estimate of the population mean μ and(b) the margin of error for a 90% confidence interval. Systolic blood pressures (in mmHg) 125 80 118 130 80 118
The ages (in completed years) of 30 persons attending a course are shown below. Assume the population standard deviation is 10 years.Find(a) the point estimate of the population mean μ and(b) the margin of error for a 95% confidence interval. Ages (in completed years) 15 16 16 14 21 22 19 29 30 14
Construct a 90% confidence interval for the population mean in Exercise 1. Interpret the results.Data from Exercises 1The systolic blood pressures (in mmHg) of 40 persons are shown in the table. Assume the population standard deviation is 25 mmHg. Systolic blood pressures (in mmHg) 125 80 118 130
Construct a 95% confidence interval for the population mean in Exercise 2. Interpret the results.Data from Exercises 2The ages (in completed years) of 30 persons attending a course are shown below. Assume the population standard deviation is 10 years. Ages (in completed years) 15 16 16 14 21 22 19
(30.25, 42.50)Use the confidence interval to find the margin of error and the sample mean.
Determine the minimum sample size required to be 95% confident that the sample mean systolic blood pressure is within 8 mmHg of the population mean systolic blood pressure. Use the population standard deviation from Exercise 1.Data from Exercises 1The systolic blood pressures (in mmHg) of 40
Determine the minimum sample size required to be 99% confident that the sample mean age is within 3 years of the population mean age. Use the population standard deviation from Exercise 2.Data from Exercises 2The ages (in completed years) of 30 persons attending a course are shown below. Assume the
c = 0.90, n = 12 Find the critical value tc for the level of confidence c and sample size n.
c = 0.80, n = 16 Find the critical value tc for the level of confidence c and sample size n.
c = 0.80, s = 27.4, n = 36, x̅ = 81.6(a) find the margin of error for the values of c, s, and n, and(b) construct the confidence interval for μ using the t-distribution. Assume the population is normally distributed.
c = 0.90, s = 3.6, n = 20, x̅ = 20.6(a) find the margin of error for the values of c, s, and n, and(b) construct the confidence interval for μ using the t-distribution. Assume the population is normally distributed.
c = 0.90, n = 15 Find the critical values x2R and x2L for the level of confidence c and sample size n.
c = 0.95, n = 20 Find the critical values x2R and x2L for the level of confidence c and sample size n.
The winning times (in hours) for a sample of 30 randomly selected Boston Marathon Women’s Open Division champions are shown in the table at the left.(a) Find the point estimate of the population mean.(b) Find the margin of error for a 95% confidence level.(c) Construct a 95% confidence interval
You wish to estimate the mean winning time for Boston Marathon Women’s Open Division champions. The estimate must be within 0.13 hour of the population mean. Determine the minimum sample size required to construct a 99% confidence interval for the population mean. Use the population standard
The data set represents the amounts of time (in minutes) spent checking email for a random sample of employees at a company.7.5 2.0 12.1 8.8 9.4 7.3 1.9 2.8 7.0 7.3(a) Find the sample mean and the sample standard deviation.(b) Construct a 90% confidence interval for the population mean. Interpret
In a random sample of 12 senior-level chemical engineers, the mean annual earnings was \($133,326\) and the standard deviation was \($36,729.\) Assume the annual earnings are normally distributed and construct a 95% confidence interval for the population mean annual earnings for senior-level
You research the salaries of senior-level chemical engineers and find that the population mean is \($131,935.\) In Exercise 4, does the t-value fall between -t0.95 and t0.95?Data from Exercises 4In a random sample of 12 senior-level chemical engineers, the mean annual earnings was \($133,326\) and
In a survey of 1018 U.S. adults, 753 say that the energy situation in the United States is very or fairly serious.(a) Find the point estimate for the population proportion.(b) Construct a 90% confidence interval for the population proportion.Interpret the results.(c) Does it seem possible that the
Refer to the data set in Exercise 3.Assume the population of times spent checking email is normally distributed. Construct a 95% confidence interval for(a) the population variance and(b) the population standard deviation.Interpret the results.Data from Exercises 3The data set represents the amounts
From a random sample of 48 business days from November 14, 2017 through January 23, 2018, London’s crude oil prices had a mean of \($59.23.\) Assume the population standard deviation is \($2.79.\) You are given the sample mean and the population standard deviation. Use this information to
From a random sample of 36 business days from January 12, 2017 through January 12, 2018, the mean closing price of Egyptian iron and steel stock was 5.62 Egyptian pound. Assume the population standard deviation is 1.91 EGP.You are given the sample mean and the population standard deviation. Use
From a random sample of 64 dates, the mean record of high daily rainfall in Changi (Singapore) area has a mean of 10.22 mm. Assume the population standard deviation is 15.77 mm.You are given the sample mean and the population standard deviation. Use this information to construct 90% and 95%
From a random sample of 24 years from 1923 through 2004, the mean number of fire accidents per year in Japan was about 43.202. Assume the population standard deviation is 20,469.You are given the sample mean and the population standard deviation. Use this information to construct 90% and 95%
In Exercise 35, does it seem possible that the population mean could equal the sample mean? Explain.Data from Exercises 35From a random sample of 48 business days from November 14, 2017 through January 23, 2018, London’s crude oil prices had a mean of \($59.23.\) Assume the population standard
In Exercise 36, does it seem possible that the population mean could be within 1% of the sample mean? Explain.Data from Exercises 36From a random sample of 36 business days from January 12, 2017 through January 12, 2018, the mean closing price of Egyptian iron and steel stock was 5.62 Egyptian
In Exercise 37, does it seem possible that the population mean could be greater than 14 millimeters? Explain.Data from Exercises 37From a random sample of 64 dates, the mean record of high daily rainfall in Changi (Singapore) area has a mean of 10.22 mm. Assume the population standard deviation is
In Exercise 38, does it seem possible that the population mean could be less than 35,000? Explain.Data from Exercises 38From a random sample of 24 years from 1923 through 2004, the mean number of fire accidents per year in Japan was about 43.202. Assume the population standard deviation is 20,469.
A group of researchers calculates the mean quantity of sodium (in milligrams) in selected branded cereals consumed by people in each serving. To do so, the group takes a random sample of 30 branded cereals and obtain the quantity (in milligrams) below.From past studies, the research council assumes
Find the critical value tc for a 95% confidence level when the sample size is 15.
You randomly select 16 coffee shops and measure the temperature of the coffee sold at each. The sample mean temperature is 162.0°F with a sample standard deviation of 10.0 F. Construct a 95% confidence interval for the population mean temperature of coffee sold. Assume the temperatures are
You randomly select 36 cars of the same model that were sold at a car dealership and determine the number of days each car sat on the dealership’s lot before it was sold. The sample mean is 9.75 days, with a sample standard deviation of 2.39 days. Construct a 99% confidence interval for the
You randomly select 25 newly constructed houses. The sample mean construction cost is \($181,000\) and the population standard deviation is \($28,000.\)Assuming construction costs are normally distributed, should you use the standard normal distribution, the t-distribution, or neither to construct
c = 0.99, x̅ = 24.7, s = 4.6, n = 50 Construct the indicated confidence interval for the population mean m using the t-distribution. Assume the population is normally distributed.
The monthly earnings (in Yens) of 32 randomly selected teachers in JapanUse the data set to(a) find the sample mean,(b) find the sample standard deviation, and(c) construct a 98% confidence interval for the population mean. 240,833 308,333 380,456 296,364 199,980 332,325 269,654 212,294 236,245
The annual earnings (in thousand Yens) of 40 randomly selected editors in JapanUse the data set to(a) find the sample mean,(b) find the sample standard deviation, and(c) construct a 98% confidence interval for the population mean. 3,614 4,284 3,548 3,694 4,182 5,142 4,568 3,954 4,215 4,169 3,941
In Exercise 31, the population mean salary is 305,046 Yen. Does the t-value fall between t0.98 and t0.98?Data from Exercises 31The monthly earnings (in Yens) of 32 randomly selected teachers in Japan 240,833 308,333 380,456 296,364 199,980 332,325 269,654 212,294 236,245 222,301 362,321 254,269
In Exercise 32, the population mean salary is 3,750 Yen. Does the t-value fall between -t0.98 and t0.98?Data from Exercises 32The annual earnings (in thousand Yens) of 40 randomly selected editors in Japan 3,614 4,284 3,548 3,694 4,182 5,142 4,568 3,954 4,215 4,169 3,941 5,052 4,941 4,313 4,654
In a recent Indian Premier League season, the population standard deviation of the deliveries faced to score fifty runs for all batsmen was 6.37. The deliveries per fifty of 10 randomly selected batsmen are listed. Assume the deliveries per fifty are normally distributed.Use the standard normal
In Exercise 38, does it seem possible that the population mean could be within 10% of the sample mean? Explain.Data from Exercises 38In a recent Indian Premier League season, the population standard deviation of the deliveries faced to score fifty runs for all batsmen was 6.37. The deliveries per
In a survey of 1550 U.S. adults, 1054 said that they use the social media website Facebook. Find a point estimate for the population proportion of U.S. adults who use Facebook.
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