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mathematics
elementary statistics picturing

Elementary Statistics Picturing The World 7th Edition Ron Larson, Betsy Farber - Solutions

Find the critical value tc for the level of confidence c and sample size n.c = 0.98, n = 15
Find the critical value tc for the level of confidence c and sample size n.c = 0.95, n = 24
Find the critical value tc for the level of confidence c and sample size n.c = 0.80, n = 10
Determine the minimum sample size required to be 99% confident that the sample mean driving distance to work is within 2 miles of the population mean driving distance to work. Use the population standard deviation from Exercise 2.Data from Exercise 2;The driving distances (in miles) to work of 30
Determine the minimum sample size required to be 95% confident that the sample mean waking time is within 10 minutes of the population mean waking time. Use the population standard deviation from Exercise 1.Data from Exercise 1:The waking times (in minutes past 5:00 a.m.) of 40 people who start
Use the confidence interval to find the margin of error and the sample mean.(7.428, 7.562)
Use the confidence interval to find the margin of error and the sample mean.(20.75, 24.10)
(a) Construct a 90% confidence interval for the population mean in Exercise 1. Interpret the results. (b) Does it seem possible that the population mean could be within 10% of the sample mean? Explain.Data from Exercise 1:The waking times (in minutes past 5:00 a.m.) of 40 people who start work
In your own words, explain how finding a confidence interval for a population variance is different from finding a confidence interval for a population mean or proportion.
You are analyzing the sample of waiting times in Exercise 23. The population standard deviation of the waiting times should be less than 2.5 minutes. Does the confidence interval you constructed for s suggest that the variation in the waiting times is at an acceptable level? Explain your
You are analyzing the sample of car batteries in Exercise 21. The population standard deviation of the batteries’ reserve capacities should be less than 0.25 hour. Does the confidence interval you constructed for σ suggest that the variation in the batteries’ reserve capacities is at an
You are analyzing the sample of cough syrup bottles in Exercise 14. The population standard deviation of the volumes of the bottles’ contents should be less than 0.025 fluid ounce. Does the confidence interval you constructed for σ suggest that the variation in the volumes of the bottles’
You are analyzing the sample of bolts in Exercise 13. The population standard deviation of the bolts’ diameters should be less than 0.5 inch. Does the confidence interval you constructed for σ suggest that the variation in the bolts’ diameters is at an acceptable level? Explain your
The record high daily temperatures (in degrees Fahrenheit) of a random sample of 64 days of the year in Grand Junction, Colorado, have a sample standard deviation of 16.8°F. Use a 98% level of confidence.Assume the sample is from a normally distributed population and construct the indicated
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.Assume the sample is from a normally distributed population and construct the indicated confidence intervals for (a) The population
As part of a survey, you ask a random sample of business owners how much they would be willing to pay for a website for their company. The results are shown in the figure at the left. Use a 90% level of confidence.Assume the sample is from a normally distributed population and construct the
As part of a water quality survey, you test the water hardness in several randomly selected streams. The results are shown in the figure at the left. Use a 95% level of confidence.Assume the sample is from a normally distributed population and construct the indicated confidence intervals
The numbers of touchdowns scored by 11 randomly selected NCAA Division I Subdivision teams in a recent season have a sample standard deviation of 9.35. Use an 80% level of confidence.Assume the sample is from a normally distributed population and construct the indicated confidence intervals
The durations (in days) of 14 randomly selected space shuttle flights have a sample standard deviation of 3.54 days. 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 variance σ2
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.Assume the sample is from a normally distributed population and construct the indicated confidence intervals for (a) The population variance σ2
The annual earnings (in thousands of dollars) of 21 randomly selected clinical pharmacists are listed. 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 variance σ2 and (b) the
The diameters (in inches) of 18 randomly selected bolts produced by a machine 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 and (b) the population
Construct the indicated confidence intervals for (a) The population variance σ2 and (b) The population standard deviation σ. Assume the sample is from a normally distributed population.c = 0.98, s = 278.1, n = 41
Construct the indicated confidence intervals for (a) The population variance σ2 and (b) The population standard deviation σ. Assume the sample is from a normally distributed population.c = 0.90, s = 35, n = 18
Construct the indicated confidence intervals for (a) The population variance σ2 and (b) The population standard deviation σ. Assume the sample is from a normally distributed population.c = 0.99, s2 = 0.64, n = 7
Construct the indicated confidence intervals for (a) The population variance σ2 and (b) The population standard deviation σ. Assume the sample is from a normally distributed population.c = 0.95, s2 = 11.56, n = 30
Find the critical values X2R and X2L for the level of confidence c and sample size n.c = 0.80, n = 51
Find the critical values X2R and X2L for the level of confidence c and sample size n.c = 0.99, n = 30
Find the critical values X2R and X2L for the level of confidence c and sample size n.c = 0.98, n = 26
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.c = 0.90, n = 8
Does a population have to be normally distributed in order to use the chi-square distribution?
Why is it necessary to check that np̂ ≥ 5 and nq̂ ≥ 5?
In a survey of 1052 parents of children ages 8–14, 68% say they are willing to get a second or part-time job to pay for their children’s college education, and 42% say they lose sleep worrying about college costs. The survey’s margin of error is ± 3%.Translate the statement into a confidence
In a survey of 3539 U.S. adults, 47% believe the economy is getting better. Three weeks prior to this survey, 53% believed the economy was getting better. The survey’s margin of error is ± 2%.Translate the statement into a confidence interval. Approximate the level of confidence.
In a survey of 1035 U.S. adults, 37% say the U.S. spends too little on defense. The survey’s margin of error is ±4%.Translate the statement into a confidence interval. Approximate the level of confidence.
In a survey of 1000 U.S. adults, 71% think teaching is one of the most important jobs in our country today. The survey’s margin of error is ± 3%.Translate the statement into a confidence interval. Approximate the level of confidence.
In a survey of 1503 U.S. adults, 79% say people have the right to nonviolent protest. The survey’s margin of error is ± 2.9%.Translate the statement into a confidence interval. Approximate the level of confidence.
In a survey of 1003 U.S. adults, 70% said being able to speak English is at the core of national identity. The survey’s margin of error is ± 3.4%.Translate the statement into a confidence interval. Approximate the level of confidence.
In Exercise 27, does it seem possible that any of the population proportions could be equal? Explain.Use the figure, which shows the results of a survey in which 2000 U.S. college graduates from the year 2016 were asked questions about employment.Data from Exercise 27:Construct (a) a 95% confidence
Construct (a) a 95% confidence interval and (b) a 99% confidence interval for the population proportion of college students who gave each response.Use the figure, which shows the results of a survey in which 2000 U.S. college graduates from the year 2016 were asked questions about employment.
In Exercise 25, does it seem possible that any of the population proportions could be equal? Explain.Use the figure, which shows the results of a survey in which 1003 adults from the United States, 1020 adults from Canada, 999 adults from France, 1000 adults from Japan, and 1000 adults from
Construct a 99% confidence interval for the population proportion of adults who say national identity is strongly tied to birthplace for each country listed.Use the figure, which shows the results of a survey in which 1003 adults from the United States, 1020 adults from Canada, 999 adults from
In Exercise 20(b), would a sample size of 600 be acceptable? Explain.Data from Exercise 20:You wish to estimate, with 95% confidence, the population proportion of motor vehicle fatalities that were caused by alcohol-impaired driving. Your estimate must be accurate within 5% of the population
In Exercise 17(b), would a sample size of 200 be acceptable? Explain.Data from Exercise 17:You wish to estimate, with 95% confidence, the population proportion of U.S. adults who think Congress is doing a good or excellent job. Your estimate must be accurate within 4% of the population proportion.
In Exercise 14, does it seem possible that the population proportion could be within 1% of the point estimate? Explain.Data from Exercise 14:In a survey of 600 United Kingdom teachers, 226 say they would wear a body camera in school.
In Exercise 11, does it seem possible that the population proportion could equal 0.59? Explain.Data from exercise 11:In a survey of 2241 U.S. adults in a recent year, 1322 say they have made a New Year’s resolution.
You wish to estimate, with 95% confidence, the population proportion of motor vehicle fatalities that were caused by alcohol-impaired driving. Your estimate must be accurate within 5% of the population proportion.(a) No preliminary estimate is available. Find the minimum sample size needed.(b) Find
You wish to estimate, with 90% confidence, the population proportion of U.S. adults who eat fast food four to six times per week. Your estimate must be accurate within 3% of the population proportion.(a) No preliminary estimate is available. Find the minimum sample size needed.(b) Find the minimum
You wish to estimate, with 99% confidence, the population proportion of U.S. adults who support labeling legislation for genetically modified organisms (GMOs). Your estimate must be accurate within 2% of the population proportion.(a) No preliminary estimate is available. Find the minimum sample
You wish to estimate, with 95% confidence, the population proportion of U.S. adults who think Congress is doing a good or excellent job. Your estimate must be accurate within 4% of the population proportion.(a) No preliminary estimate is available. Find the minimum sample size needed.(b) Find the
In a survey of 1000 U.S. adults, 490 oppose allowing transgender students to use the bathrooms of the opposite biological sex. Construct a 90% confidence interval for the population proportion of U.S. adults who oppose allowing transgender students to use the bathrooms of the opposite biological
In a survey of 1,626,773 U.S. adults, 49,311 personally identify as lesbian, gay, bisexual, or transgender. Construct a 95% confidence interval for the population proportion of U.S. adults who personally identify as lesbian, gay, bisexual, or transgender.
In a survey of 600 United Kingdom teachers, 226 say they would wear a body camera in school.Construct a 99% confidence interval for the population proportion. Interpret the results.
In a survey of 1000 U.S. adults, 700 think police officers should be required to wear body cameras while on duty.Construct a 99% confidence interval for the population proportion. Interpret the results.
In a survey of 2241 U.S. adults in a recent year, 650 made a New Year’s resolution to eat healthier.Construct 90% and 95% confidence intervals for the population proportion. Interpret the results and compare the widths of the confidence intervals.
New Year’s Resolutions In a survey of 2241 U.S. adults in a recent year, 1322 say they have made a New Year’s resolution.Construct 90% and 95% confidence intervals for the population proportion. Interpret the results and compare the widths of the confidence intervals.
In a survey of 2016 U.S. adults, 665 believe America should stop terrorism at all costs.Let p be the population proportion for the situation. Find point estimates of p and q.
In a survey of 2016 U.S. adults, 1310 think mainstream media is more interested in making money than in telling the truth.Let p be the population proportion for the situation. Find point estimates of p and q.
In a survey of 1040 U.S. adults, 478 believe the government should be able to access encrypted communications when investigating crimes.Let p be the population proportion for the situation. Find point estimates of p and q.
In a survey of 1040 U.S. adults, 62 have had someone impersonate them to try to claim tax refunds.Let p be the population proportion for the situation. Find point estimates of p and q.
The point estimate for the population proportion of failures is 1 - p̂.Determine whether the statement is true or false. If it is false, rewrite it as a true statement.
To estimate the value of p, the population proportion of successes, use the point estimate x.Determine whether the statement is true or false. If it is false, rewrite it as a true statement.
In Exercise 38, does it seem possible that the population mean could be within 10% of the sample mean? Explain.Data from Exercise 38:In a recent season, the population standard deviation of the yards per carry for all running backs was 1.80. The yards per carry of 13 randomly selected running backs
In Exercise 36, does it seem possible that the population mean could equal half the sample mean? Explain.Data from Exercise 36:In a random sample of 18 months from June 2008 through September 2016, the mean interest rate for 30-year fixed rate conventional home mortgages was 4.36% and the standard
In a recent season, the population standard deviation of the yards per carry for all running backs was 1.80. The yards per carry of 13 randomly selected running backs are listed. Assume the yards per carry are normally distributed.Use the standard normal distribution or the t-distribution to
The gas mileages (in miles per gallon) of 28 randomly selected sports cars are listed. Assume the mileages are not normally distributed.Use the standard normal distribution or the t-distribution to construct a 95% confidence interval for the population mean. Justify your decision. If neither
In a random sample of 18 months from June 2008 through September 2016, the mean interest rate for 30-year fixed rate conventional home mortgages was 4.36% and the standard deviation was 0.75%. Assume the interest rates are normally distributed.Use the standard normal distribution or the
In Exercise 32, the population mean salary is $61,000. Does the t-value fall between -t0.98 and t0.98?Data from Exercise 32:The annual earnings (in dollars) of 40 randomly selected intermediate level life insurance underwriters. 31,530 79,749 53,851 92,386 45,186 64,852 72,372 61,498 92,630 62,000
In Exercise 31, the population mean salary is $72,000. Does the t-value fall between -t0.98 and t0.98?Data from Exercise 31:The annual earnings (in dollars) of 32 randomly selected magnetic resonance imaging technologists. 90,198 65,357 62,108 78,201 80,882 74,759 46,382 75,196 56,412 74,610 65,460
The annual earnings (in dollars) of 40 randomly selected intermediate level life insurance underwriters.Use 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. 31,530 79,749 53,851
The annual earnings (in dollars) of 32 randomly selected magnetic resonance imaging technologists.Use 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. 90,198 65,357 62,108 78,201
In Exercise 28, the population mean weekly time spent on homework by students is 7.8 hours. Does the t-value fall between -t0.99 and t0.99?Data from Exercise 28:The weekly time spent (in hours) on homework for 18 randomly selected high school students 12.0 11.3 13.5 11.7 12.0 13.0 15.5 10.8 12.5
In Exercise 25, the population mean SAT score is 1020. Does the t-value fall between -t0.99 and t0.99?Data from exercise 25:The SAT scores of 12 randomly selected high school seniors 1130 1290 1010 1320 |1340 1100 1260 1180 1470 950 1250 920
Use the data set to(a) Find the sample mean, (b) Find the sample standard deviation, and (c) Construct a 99% confidence interval for the population mean. Assume the population is normally distributed.The SAT scores of 12 randomly selected high school seniors 1130 1290 1010 1320 |1340 1100
You research repair costs of mobile devices and find that the population mean is $89.56. In Exercise 20, does the t-value fall between -t0.95 and t0.95?Data from exercise 20:In a random sample of 12 mobile devices, the mean repair cost was $90.42 and the standard deviation was $33.6.
You research prices of cell phones and find that the population mean is $431.61. In Exercise 19, does the t-value fall between -t0.95 and t0.95?Data from Exercise 19:In a random sample of eight cell phones, the mean full retail price was $526.50 and the standard deviation was $184.00.
In a random sample of 12 mobile devices, the mean repair cost was $90.42 and the standard deviation was $33.61.You are given the sample mean and the sample standard deviation. Assume the population is normally distributed and use the t-distribution to find the margin of error and construct a 95%
In a random sample of eight cell phones, the mean full retail price was $526.50 and the standard deviation was $184.00.You are given the sample mean and the sample standard deviation. Assume the population is normally distributed and use the t-distribution to find the margin of error and construct
Use the confidence interval to find the margin of error and the sample mean.(16.2, 29.8)
Use the confidence interval to find the margin of error and the sample mean.(64.6, 83.6)
Use the confidence interval to find the margin of error and the sample mean.(6.17, 8.53)
Construct the indicated confidence interval for the population mean μ using the t-distribution. Assume the population is normally distributed.c = 0.98, x̅ = 4.3, s = 0.34, n = 14
Construct the indicated confidence interval for the population mean μ using the t-distribution. Assume the population is normally distributed.c = 0.95, x̅ = 13.4, s = 0.85, n = 8
Construct the indicated confidence interval for the population mean μ using the t-distribution. Assume the population is normally distributed.c = 0.90, x̅ = 12.5, s = 2.0, n = 6
Find the margin of error for the values of c, s, and n.c = 0.98, s = 4.7, n = 9
Find the margin of error for the values of c, s, and n.c = 0.90, s = 2.4, n = 35
Find the margin of error for the values of c, s, and n.c = 0.99, s = 3, n = 6
Find the margin of error for the values of c, s, and n.c = 0.95, s = 5, n = 16
Find the critical value tc for the level of confidence c and sample size n.c = 0.98, n = 40
Find the critical value tc for the level of confidence c and sample size n.c = 0.99, n = 16
Find the critical value tc for the level of confidence c and sample size n.c = 0.95, n = 12
Find the critical value tc for the level of confidence c and sample size n.c = 0.90, n = 10
In a hypothesis test, you assume the alternative hypothesis is true.Determine whether the statement is true or false. If it is false, rewrite it as a true statement.
Does failing to reject the null hypothesis mean that the null hypothesis is true? Explain.
What are the two decisions that you can make from performing a hypothesis test?
Describe the two types of errors possible in a hypothesis test decision.
What are the two types of hypotheses used in a hypothesis test? How are they related?
Use the standard normal distribution or the t-distribution to construct the indicated confidence interval for the population mean of each data set. Justify your decision. If neither distribution can be used, explain why. Interpret the results.(a) In a random sample of 40 patients, the mean waiting
The data set represents the scores of 12 randomly selected students on the SAT Physics Subject Test. Assume the population test scores are normally distributed and the population standard deviation is 104. 590 450 490 680 380 500 570 620

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