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mathematics
elementary statistics picturing

Questions and Answers of Elementary Statistics Picturing

Original claim: The percentage of Americans who believe in heaven is equal to 90%.Initial conclusion: Reject the null hypothesis.State the final conclusion in simple nontechnical terms. Be sure to
Original claim: The percentage of Americans who know their credit score is equal to 20%.Initial conclusion: Fail to reject the null hypothesis.State the final conclusion in simple nontechnical terms.
The percentage of nonsmokers exposed to secondhand smoke is equal to 41%.Identify the type I error and the type II error that correspond to the given hypothesis.
The percentage of Americans who believe that life exists only on earth is equal to 20%.Identify the type I error and the type II error that correspond to the given hypothesis.
The percentage of college students who consume alcohol is greater than 70%.Identify the type I error and the type II error that correspond to the given hypothesis.
The percentage of households with at least two cell phones is less than 60%.Identify the type I error and the type II error that correspond to the given hypothesis.
a. If a null hypothesis is rejected with a significance level of 0.05, is it also rejected with a significance level of 0.01? Why or why not?b. If a null hypothesis is rejected with a significance
Listed below are the numbers of words (in thousands) males and females in randomly selected couples spoke in a day (based on data from ?Are Women Really More Talkative Than Men?? by Mehl, Vazire,
If the pulse rates of men and women from Data Set 1 in Appendix B are used to construct a 95% confidence interval for the difference between the two population means, the result is -12.2 1 - ?2
Listed below are the time intervals (in minutes) before and after eruptions of the Old Faithful geyser. Find the values of d and sd. In general, what does ?d represent? Time interval before eruption
What does it mean when we say that some methods in this chapter are robust against departures from normality? Which method of this chapter is not robust against departures from normality?
In clinical trials of the drug Zocor, some subjects were treated with Zocor and others were given a placebo. The 95% confidence interval estimate of the difference between the proportions of subjects
The drug Dozenol is tested on 40 male subjects recruited from New York and 40 female subjects recruited from California. The researcher pairs the 40 male subjects and the 40 female subjects. Can the
The word ginormous was added to the Merriam-Webster Dictionary at the time this exercise was written. AOL conducted an online poll in which Internet users were asked “What do you think of the word
Researchers conducted a study to assess the effects that occur when children are exposed to cocaine before birth. Children were tested at age 4 for object assembly skill, which was described as “a
The author repeated the process of selecting two different random samples of heights of men (from data obtained through the National Health and Nutrition Examination Survey). In each case, the ratio
In clinical trials of the drug Zocor, 1583 subjects were treated with Zocor and 15 of them experienced headaches. A placebo is used for 157 other subjects, and 8 of them experienced headaches (based
Assume that you want to use a 0.01 significance level to test the claim that the mean pulse rate of men is less than the mean pulse rate of women. What confidence level should be used if you want to
Using Data Set 1 in Appendix B, a researcher pairs pulse rates and cholesterol levels for the 40 women. Can the methods of this section be used to construct a confidence interval? Why or why not?
A nutritionist selects a simple random sample of 50 cans of Coke and another simple random sample of 50 cans of Pepsi. The cans are arranged as 50 pairs, then the sugar content of each can is
In 1908, ?Student? (William Gosset) published the article ?The Probable Error of a Mean? (Biometrika, Vol. 6, No. 1). He included the data listed below for two different types of straw seed (regular
What does it mean when we say that the F test described in this section is not robust against departures from normality? Name two alternatives that are more robust against departures from normality.
Given a simple random sample of men and a simple random sample of women, we want to use a 0.05 significance level to test the claim that the percentage of men who smoke is equal to the percentage of
Assume that you want to use a 0.01 significance level to test the claim that the mean pulse rate of women is greater than the mean pulse rate of men using the sample data from Data Set 1 in Appendix
Example 4 showed that the 67 dependent April and September weight measurements from Data Set 3 in Appendix B result in this 95% confidence interval: 0.2 kg d 1 - ?2 Data Set 3: Freshman 15 Data
An employee of the U.S. Department of Labor obtains the mean age of men and the mean age of women for each of the 50 states. She then uses those means to construct a confidence interval estimate of
Given that the F test is not robust against departures from normality, it becomes necessary to verify that the two samples are from populations having distributions that are quite close to normal
From an article in Journal of the American Medical Association: Among 8834 malfunctioning pacemakers, in 15.8% the malfunctions were due to batteries.Find the number of successes x suggested by the
Listed below are measured fuel consumption amounts (in miles gal) from a sample of cars (Acura RL, Acura TSX, Audi A6, BMW 525i) taken from Data Set 16 in Appendix B. City fuel consumption Highway
Express the confidence interval 0.200 < p < 0.500 in the form of p ± E.Express the confidence interval using the indicated format.
95% confidence; n = 30, x = 1533, s = 333Use the given confidence level and sample data to find a confidence interval for the population standard deviation σ. In each case, assume that a simple
a. Use the sample data from Exercise 9 to construct a 95% confidence interval estimate of the population standard deviation.b. Use the sample data from Exercise 9 to construct a 95% confidence
If you conduct a poll by surveying all of your friends that you see during the next week, which of the following terms best describes the type of sampling used: random, systematic, cluster,
The braking distances of a simple random sample of cars: 95% confidence; n = 32, x = 137 ft, and σ is known to be 7 ft.Find the margin of error and confidence interval if the necessary requirements
95%; n = 9; σ is unknown; population appears to be very skewed.Assume that we want to construct a confidence interval using the given confidence level. Do one of the following, as appropriate: (a)
Express the confidence interval 0.720 < p < 0.780 in the form of p ± E.Express the confidence interval using the indicated format.
95% confidence; n = 25, x = 81.0 mi/h, s = 2.3 mi/h.Use the given confidence level and sample data to find a confidence interval for the population standard deviation σ. In each case, assume that a
The amounts of rainfall for a simple random sample of Saturdays in Boston: 99% confidence; n = 12, x = 0.133 in., σ is known to be 0.212 in., and the population is known to have daily rainfall
99%; n = 12; σ is unknown; population appears to be normally distributed.Assume that we want to construct a confidence interval using the given confidence level. Do one of the following, as
Express the confidence interval (0.437, 0.529) in the form of p ± E.Express the confidence interval using the indicated format.
99% confidence; n = 7, x = 7.106, s = 2.019Use the given confidence level and sample data to find a confidence interval for the population standard deviation σ. In each case, assume that a simple
The times before failure of integrated circuits used in calculators: 99% confidence; n = 25 x = 112 hours σ is known to be 18.6 hours, and the distribution of all times before failure is far from
95%; n = 38; σ is unknown; population appears to be skewed.Assume that we want to construct a confidence interval using the given confidence level. Do one of the following, as appropriate: (a) Find
Express the confidence interval 0.222 ± 0.044 in the form of p - E < p < p + E.Express the confidence interval using the indicated format.
99% confidence; n = 8, x = 1.24 sec, s = 0.12 secUse the given confidence level and sample data to find a confidence interval for the population standard deviation σ. In each case, assume that a
How many adults must be randomly selected to estimate the mean FICO (credit rating) score of working adults in the United States. We want 95% confidence that the sample mean is within 3 points of the
95% confidence; n = 20, x = $9004, s = $569 (based on data from hospital costs for car crash victims who wore seat belts, from the U.S. Department of Transportation)Use the given confidence level and
Find the minimum sample size needed to be 95% confident that the sample standard deviation s is within 1% of σ. Is this sample size practical in most applications?Assume that each sample is a simple
Use the given confidence interval limits to find the point estimate and the margin of error E.(0.320, 0.420)
How many cars must be randomly selected and tested in order to estimate the mean braking distance of registered cars in the United States. We want 99% confidence that the sample mean is within 2 ft
99% confidence; n = 7, x = 0.12, s = 0.04 (original values are nitrogenoxide emissions in grams mile, from the Environmental Protection Agency)Use the given confidence level and sample data to find
A researcher wants to estimate the mean grade point average of all current college students in the United States. She has developed a procedure to standardize scores from colleges using something
Use the given confidence interval limits to find the point estimate and the margin of error E.0.772 < p < 0.776
Find the minimum sample size needed to be 95% confident that the sample standard deviation s is within 30% of σ. Is this sample size practical in most applications?Assume that each sample is a
How many daily rainfall amounts in Boston must be randomly selected to estimate the mean daily rainfall amount? We want 99% confidence that the sample mean is within 0.010 in. of the population mean,
95% confidence; n = 20, x = 8.0710 g, s = 0.0411g (based on measurements made by the author). See the following SPSS display. Use the given data and the corresponding display to express the
Use the given confidence interval limits to find the point estimate and the margin of error E.0.433 < p < 0.527
Find the minimum sample size needed to be 99% confident that the sample variance is within 40% of the population variance. Is such a sample size practical in most cases?Assume that each sample is a
How many integrated circuits must be randomly selected and tested for time to failure in order to estimate the mean time to failure? We want 95% confidence that the sample mean is within 2 hr of the
99% confidence; n = 62, x = 1.911 lb, s = 1.065 lb (based on data from the Garbage Project, University of Arizona). See the TI-83/84 Plus calculator display in the margin.Use the given data and the
Use the given confidence interval limits to find the point estimate and the margin of error E.0.102 < p < 0.236
Find the minimum sample size needed to be 95% confident that the sample variance is within 20% of the population variance.Assume that each sample is a simple random sample obtained from a normally
Identify the value of the point estimate of the population mean μ.Refer to the accompanying TI-83 84 Plus calculator display of a 95% confidence interval. The sample display results from using a
In a test of the effectiveness of garlic for lowering cholesterol, 47 subjects were treated with Garlicin, which is garlic in a processed tablet form. Cholesterol levels were measured before and
n = 1000, x = 400, 95% confidenceAssume that a sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the given statistics and confidence level.
Express the confidence interval in the format of x - E < μ < x + E.Refer to the accompanying TI-83 84 Plus calculator display of a 95% confidence interval. The sample display results from
A random sample of the birth weights of 186 babies has a mean of 3103 g and a standard deviation of 696 g (based on data from “Cognitive Outcomes of Preschool Children with Prenatal Cocaine
n = 500, x = 220, 99% confidenceAssume that a sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the given statistics and confidence level.
Data Set 18 in Appendix B lists 100 weights (in grams) of M&M candies. The minimum weight is 0.696 g and the maximum weight is 1.015 g. a. Use the range rule of thumb to estimate ?, the standard
Express the confidence interval in the format of x ± E.Refer to the accompanying TI-83 84 Plus calculator display of a 95% confidence interval. The sample display results from using a simple random
Data Set 2 in Appendix B includes 106 body temperatures for which x= 98.20?F and s = 0.62?F. a. What is the best point estimate of the mean body temperature of all healthy humans? b. Using the sample
Using the simple random sample of weights of women from Data Set 1 in Appendix B, we obtain these sample statistics: n = 40 and x = 146.22. Research from other sources suggests that the population of
98% confidence; the sample size is 1230, of which 40% are successes.Assume that a sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the given
Data Set 9 in Appendix B includes 23 movies with ratings of PG or PG-13, and those movies have lengths (in minutes) with a mean of 120.8 min and a standard deviation of 22.9 min. That same data set
Write a statement that interprets the 95% confidence interval.Refer to the accompanying TI-83 84 Plus calculator display of a 95% confidence interval. The sample display results from using a simple
In a test of the Atkins weight loss program, 40 individuals participated in a randomized trial with overweight adults. After 12 months, the mean weight loss was found to be 2.1 lb, with a standard
90% confidence; the sample size is 1780, of which 35% are successes.Assume that a sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the given
Data Set 1 in Appendix B includes 40 pulse rates of men, and those pulse rates have a mean of 69.4 beats per minute and a standard deviation of 11.3 beats per minute. That data set also includes 40
In a study designed to test the effectiveness of echinacea for treating upper respiratory tract infections in children, 337 children were treated with echinacea and 370 other children were given a
Use the sample data and confidence level to construct the confidence interval estimate of the population proportion p.n = 200, x = 40, 95% confidence
Twelve different video games showing substance use were observed and the duration times of game play (in seconds) are listed below (based on data from “Content and Ratings of Teen-Rated Video
A simple random sample of 40 salaries of NCAA football coaches has a mean of $415,953. Assume that σ = $463,364.a. Find the best point estimate of the mean salary of all NCAA football coaches.b.
In a study designed to test the effectiveness of acupuncture for treating migraine, 142 subjects were treated with acupuncture and 80 subjects were given a sham treatment. The numbers of migraine
Use the sample data and confidence level to construct the confidence interval estimate of the population proportion p.n = 2000, x = 400, 95% confidence
In the course of designing theater seats, the sitting heights (in mm) of a simple random sample of adult women is obtained, and the results are listed below (based on anthropometric survey data from
Randomly selected statistics students of the author participated in an experiment to test their ability to determine when 1 min (or 60 seconds) has passed. Forty students yielded a sample mean of
In a study designed to test the effectiveness of magnets for treating back pain, 20 patients were given a treatment with magnets and also a sham treatment without magnets. Pain was measured using a
Use the sample data and confidence level to construct the confidence interval estimate of the population proportion p.n = 1236, x = 109, 99% confidence
The ages of the 79 actresses at the time that they won Oscars for the Best Actress category have a mean of 35.8 years and a standard deviation of 11.3 years. The ages of the 79 actors at the time
Use the sample data and confidence level to construct the confidence interval estimate of the population proportion p.n = 5200, x = 4821, 99% confidence
a. The listed values are waiting times (in minutes) of customers at the Jefferson Valley Bank, where customers enter a single waiting line that feeds three teller windows. Construct a 95% confidence
A simple random sample of 125 SAT scores has a mean of 1522. Assume that SAT scores have a standard deviation of 333.a. Construct a 95% confidence interval estimate of the mean SAT score.b. Construct
Listed below are measured amounts of lead (in micrograms per cubic meter, or μg/m3) in the air. The Environmental Protection Agency (EPA) has established an air quality standard for lead of
Refer to Data Set 24 in Appendix B and use the credit rating scores to construct a 95% confidence interval estimate of the standard deviation of all credit rating scores. Data Set 24: FICO Credit
A simple random sample of birth weights in the United States has a mean of 3433 g. The standard deviation of all birth weights is 495 g.a. Using a sample size of 75, construct a 95% confidence
Margin of error: 0.005; confidence level: 99%; p and q unknownUse the given data to find the minimum sample size required to estimate a population proportion or percentage.
Refer to Data Set 12 in Appendix B and use the sample amounts of home energy consumption (in kWh) to construct a 99% confidence interval estimate of the standard deviation of all energy consumption
When 14 different second-year medical students at Bellevue Hospital measured the blood pressure of the same person, they obtained the results listed below. Assuming that the population standard
Listed below are the top 10 salaries (in millions of dollars) of television personalities in a recent year (listed in order for Letterman, Cowell, Sheindlin, Leno, Couric, Lauer, Sawyer, Viera,
Margin of error: two percentage points; confidence level: 99%; from a prior study, p is estimated by the decimal equivalent of 14%.Use the given data to find the minimum sample size required to

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