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elementary statistics

Questions and Answers of Elementary Statistics

Pulse Rates of Men A simple random sample of 40 men results in a standard deviation of 10.3 beats per minute (based on Data Set 1 in Appendix: Data Sets). The normal range of pulse rates of adults is
Weights of Pennies The preceding exercise involved the claim that post-1983 pennies have weights with a standard deviation less than 0.0230 g. Data Set 21 in Appendix:Data Sets includes the weights
Weights of Pennies Data Set 21 in Appendix: Data Sets includes a simple random sample of 37 weights of post-1983 pennies. Those 37 weights have a mean of 2.49910 g and a standard deviation of 0.01648
Cans of Pepsi Repeat the preceding exercise using these statistics from a simple random sample of cans of regular Pepsi: n = 36, x = 12.29 oz, s = 0.09 oz.
Cans of Coke Data Set 19 in Appendix: Data Sets includes volumes (oz) of a simple random sample of 36 cans of regular Coke. Those volumes have a mean of 12.19 oz and a standard deviation of 0.11 oz,
Hypothesis Test For the sample data from Exercise 1, we have s = 0.5 and we want to use that sample to test the claim that the sample is from a population with a standard deviation less than 1.8 min
Confidence Interval Method of Hypothesis Testing Assume that we want to use the sample data from Exercise 1 to test the claim that the sample is from a population with a standard deviation less than
Requirements If we want to use the sample data from Exercise 1 to test the claim that the sample is from a population with a standard deviation less than 1.8 min, we must satisfy the requirements of
Waiting in Line The Jefferson Valley Bank once had a separate customer waiting line at each teller window, but it now has a single waiting line that feeds the teller windows as vacancies occur. The
Interpreting Power For Example 1 in this section, the hypothesis test has power of 0.4274 of supporting the claim that m 6 1.00 W/kg when the actual population mean is 0.80 W/kg.a. Interpret the
Using the Wrong Distribution When testing a claim about a population mean with a simple random sample selected from a normally distributed population with unknown s, the Student t distribution should
Finding Critical t Values When finding critical values, we sometimes need significance levels other than those available in Table 3 of Appendix: Tables. Some computer programs approximate critical t
Repeat Exercise 12 assuming that the population standard deviation s is known to be 1.065 lb.
Repeat Exercise 11 assuming that the population standard deviation s is known to be 11.1 years.
Repeat Exercise 10 assuming that the population standard deviation s is known to be 5.01 km.
Repeat Exercise 9 assuming that the population standard deviation s is known to be 3.8 chocolate chips.
Power Supply Data Set 18 in Appendix: Data Sets lists measured voltage amounts supplied directly to the author’s home. The Central Hudson power supply company states that it has a target power
College Weights Use the September weights of males in Data Set 4 from Appendix:Data Sets and test the claim that male college students have a mean weight that is less than the 83 kg mean weight of
Blood Pressure Use the systolic blood pressure measurements for females listed in Data Set 1 in Appendix: Data Sets and test the claim that the female population has a mean systolic blood pressure
Earthquake Magnitudes Use the earthquake magnitudes listed in Data Set 16 in Appendix: Data Sets and test the claim that the population of earthquakes has a mean magnitude greater than 1.00. Use a
Highway Speeds Listed below are speeds (mi/h) measured from southbound traffic on I-280 near Cupertino, California (based on data from SigAlert). This simple random sample was obtained at 3:30 p.m.
Heights of Supermodels Listed below are the heights (inches) for the simple random sample of supermodels Lima, Bundchen, Ambrosio, Ebanks, Iman, Rubik, Kurkova, Kerr, Kroes, and Swanepoel. Use a 0.01
Brain Volume Listed below are brain volumes (cm3) of unrelated subjects used in a study. (See Data Set 6 in Appendix: Data Sets.) Use a 0.01 significance level to test the claim that the population
Lead in Medicine Listed below are the lead concentrations (in mg/g) measured in different Ayurveda medicines. Ayurveda is a traditional medical system commonly used in India. The lead concentrations
Ages of Race Car Drivers Listed below are the ages (years) of randomly selected race car drivers (based on data reported in USA Today). Use a 0.05 significance level to test the claim that the mean
Years in College Listed below are the numbers of years it took for a random sample of college students to earn bachelor’s degrees (based on data from the National Center for Education Statistics).
Insomnia Treatment A clinical trial was conducted to test the effectiveness of the drug Zopiclone for treating insomnia in older subjects. Before treatment with Zopiclone, 16 subjects had a mean wake
Garlic for Reducing Cholesterol In a test of the effectiveness of garlic for lowering cholesterol, 49 subjects were treated with raw garlic. Cholesterol levels were measured before and after the
Is the Diet Practical? When 40 people used the Weight Watchers diet for one year, their mean weight loss was 3.0 lb and the standard deviation was 4.9 lb (based on data from“Comparison of the
Human Body Temperature Data Set 3 in Appendix: Data Sets includes a sample of 106 body temperatures with a mean of 98.20°F and a standard deviation of 0.62°F. Use a 0.05 significance level to test
M&M Weights A simple random sample of the weights of 19 green M&Ms has a mean of 0.8635 g and a standard deviation of 0.0570 g (as in Data Set 20 in Appendix:Data Sets). Use a 0.05 significance level
Discarded Plastic The weights (lb) of discarded plastic from a sample of households is listed in Data Set 23 in Appendix: Data Sets, and the summary statistics are n = 62, x = 1.911 lb, and s = 1.065
Oscar-Winning Actresses Data Set 11 in Appendix: Data Sets lists ages of actresses when they won Oscars, and the summary statistics are n = 82, x = 35.9 years, and s = 11.1 years. Use a 0.01
Earthquake Depths Data Set 16 in Appendix: Data Sets lists earthquake depths, and the summary statistics are n = 50, x = 9.81 km, and s = 5.01 km. Use a 0.01 significance level to test the claim of a
Chocolate Chip Cookies Suppose the sample mean of the numbers of chocolate chips in 40 Chips Ahoy reduced fat cookies is known. The sample mean is x =19.6 chocolate chips and the sample standard
Pulse Rates The claim is that for pulse rates of women, m = 73.The sample size is n = 40 and the test statistic is t = 2.463.
Car Crash Tests The claim is that for measurements of standard head injury criteria in car crash tests, m = 475 HIC. The sample size is n = 21 and the test statistic is t = -2.242.
Cigarette Tar The claim is that for the tar amounts in king-size cigarettes, m 7 20.0 mg.The sample size is n = 25 and the test statistic is t = 1.733.
Cigarette Nicotine The claim is that for the nicotine amounts in king-size cigarettes, m 7 1.10 mg. The sample size is n = 25 and the test statistic is t = 3.349.
Confidence Interval Assume that we will use the sample data from Exercise 1 with a 0.05 significance level in a test of the claim that the population mean is greater than 90 sec.If we want to
t Test Exercise 2 refers to a t test. What is a t test? Why are the t test methods of Part 1 in this section so much more likely to be used than the z test methods in Part 2?
df If we are using the sample data from Exercise 1 in a t test of the claim that the population mean is greater than 90 sec, what does df denote, and what is its value?
Requirements Twelve different video games showing alcohol use were observed. The duration times of alcohol use were recorded, with the times (seconds) listed below (based on data from “Content and
Power For a hypothesis test with a specified significance levela, the probability of a type I error isa, whereas the probability b of a type II error depends on the particular value of p that is used
Using Confidence Intervals to Test Hypotheses When analyzing the last digits of telephone numbers in Port Jefferson, it is found that among 1000 randomly selected digits, 119 are zeros. If the digits
Binomial Distribution We want to use a 0.05 significance level to test the claim that a coin favors heads, and sample data consist of 7 heads in 8 tosses. We can’t use the normal approximation
On-Time Flights Consider a flight to be on time if it arrives no later than 15 minutes after the scheduled arrival time. Refer to Data Set 15 in Appendix: Data Sets, and use the sample data to test
M&Ms Refer to Data Set 20 in Appendix: Data Sets and find the sample proportion of M&Ms that are green. Use that result to test the claim of Mars, Inc., that 16% of its plain M&M candies are green.
HDTV Penetration In a survey of 1500 households, it is found that 47% of them have a high-definition television (based on data from the Consumer Electronics Association). Use a 0.01 significance
Nielsen Ratings A recent Super Bowl football game between the New Orleans Saints and the Indianapolis Colts set a record for the number of television viewers. According to the Nielsen company, that
Finding a Job Through Networking In a survey of 703 randomly selected workers, 61% got their jobs through networking (based on data from Taylor Nelson Sofres Research).Use the sample data with a 0.05
Bias in Jury Selection In the case of Casteneda v. Partida, it was found that during a period of 11 years in Hidalgo County, Texas, 870 people were selected for grand jury duty and 39% of them were
Misleading Survey Responses Voting records show that 61% of eligible voters actually did vote in a recent presidential election. In a survey of 1002 people, 70% said that they voted in that election
Job Interviews In a Harris poll of 514 human resource professionals, 90% said that the appearance of a job applicant is most important for a good first impression. Use a 0.01 significance level to
Job Interviews In a Harris poll of 514 human resource professionals, 45.9% said that body piercings and tattoos were big grooming red flags. Use a 0.01 significance level to test the claim that less
Postponing Death An interesting and popular hypothesis is that individuals can temporarily postpone death to survive a major holiday or important event such as a birthday. In a study of this
Smartphone Users A RingCentral survey of 380 smartphone users showed that 152 of them said that their smartphone is the only thing they could not live without. Use a 0.01 significance level to test
Overtime Rule in Football In “The Overtime Rule in the National Football League:Fair or Unfair?” by Gorgievski et al., MathAMATYC Educator, Vol. 2, No. 1, the authors report that among 414
Twitter Poll The Pew Research Center conducted a survey of 1007 adults and found that 856 of them know what Twitter is. Use a 0.01 significance level to test the claim that more than 75% of adults
Cell Phones and Cancer In a study of 420,095 Danish cell phone users, 135 subjects developed cancer of the brain or nervous system (based on data from the Journal of the National Cancer Institute as
Perception and Reality In a presidential election, 308 out of 611 voters surveyed said that they voted for the candidate who won (based on data from ICR Survey Research Group).Use a 0.10 significance
Tennis Instant Replay The Hawk-Eye electronic system is used in tennis for displaying an instant replay that shows whether a ball is in bounds or out of bounds so players can challenge calls made by
Touch Therapy Repeat the preceding exercise using a 0.01 significance level. Does the conclusion change?
Touch Therapy When she was 9 years of age, Emily Rosa did a science fair experiment in which she tested professional touch therapists to see if they could sense her energy field.She flipped a coin to
Gender Selection The Genetics & IVF Institute conducted a clinical trial of the YSORT method designed to increase the probability of conceiving a boy. As of this writing, 291 babies were born to
Gender Selection The Genetics & IVF Institute conducted a clinical trial of the XSORT method designed to increase the probability of conceiving a girl. As of this writing, 945 babies were born to
Plane Seats In a 3M Privacy Filters poll, 806 adults were asked to identify their favorite seat when they fly, and 492 of them chose a window seat. Use a 0.01 significance level to test the claim
Identity Theft In a KRC Research poll, 1002 adults were asked if they felt vulnerable to identity theft, and 531 of them said “yes.” Use a 0.05 significance level to test the claim that the
M&Ms Data Set 20 in Appendix: Data Sets lists data from 100 M&Ms, and 8% of them are brown. Use a 0.05 significance level to test the claim of the Mars candy company that the percentage of brown M&Ms
Mendelian Genetics When Mendel conducted his famous genetics experiments with peas, one sample of offspring consisted of 428 green peas and 152 yellow peas. Use a 0.01 significance level to test
Public Speaking A TNS poll of 1000 randomly selected adults showed that 460 of them say that public speaking is an activity that they dread most. Shown next is the StatCrunch display resulting from a
Brand Recognition A PriceGrabber.com survey of 1631 randomly selected adults showed that 555 of them have heard of the Sony Reader. The following STATDISK display results from a test of the claim
Guns in the Home In a Gallup poll of 1003 randomly selected subjects, 373 said that they have a gun in their home. The accompanying display shows results from a test of the claim that 35% of homes
Adverse Reactions to Drug The drug Symbicort is used to treat asthma. In a clinical trial of Symbicort, 18 of 277 treated subjects experienced headaches (based on data from AstraZeneca). The
Notation and P-Valuea. Refer to Exercise 2 and distinguish between the value of p and the P-value.b. It was stated that we can easily remember how to interpret P-values with this: “If the P is low,
P-Value Using the sample data from Exercise 2, we can test the claim that p 6 0.5, where p denotes the proportion of “yes” responses for the population. Some technologies provide results that
Sample Proportion In a Wakefield Research survey, respondents were asked if they ever hesitated to give a handshake because of a fear of germs. Of the respondents, 411 answered“yes” and 592 said
Hypothesis Tests and Confidence Intervals We can test a claim about a population proportion using the P-value method of hypothesis testing or the critical value method of hypothesis testing, or we
Finding Sample Size to Achieve Power Researchers plan to conduct a test of a genderselection method. They plan to use the alternative hypothesis of H1: p 7 0.5 and a significance level of a = 0.05.
Calculating Power Consider a hypothesis test of the claim that the MicroSort method of gender selection is effective in increasing the likelihood of having a baby girl, so that the claim is p 7 0.5.
Interpreting Power Chantix tablets are used as an aid to help people stop smoking.In a clinical trial, 129 subjects were treated with Chantix twice a day for 12 weeks, and 16 subjects experienced
The proportion of husbands taller than their wives is less than 0.9.Type I and Type II Errors. In Exercises 31–34, identify expressions that identify the type I error and the type II error that
The proportion of female statistics students is greater than 0.5.Type I and Type II Errors. In Exercises 31–34, identify expressions that identify the type I error and the type II error that
The proportion of gamblers who consistently win in casinos is equal to 0.001.Type I and Type II Errors. In Exercises 31–34, identify expressions that identify the type I error and the type II error
The proportion of people who write with their left hand is equal to 0.1.Type I and Type II Errors. In Exercises 31–34, identify expressions that identify the type I error and the type II error that
Gender Selection A 0.05 significance level is used for a hypothesis test of the claim that when parents use the XSORT method of gender selection, the proportion of baby girls is different from 0.5.
Gender Selection A 0.01 significance level is used for a hypothesis test of the claim that when parents use the XSORT method of gender selection, the proportion of baby girls is greater than 0.5.
Original claim: Women have heights with a standard deviation equal to 5.00 cm. The hypothesis test results in a P-value of 0.0055.Stating Conclusions. In Exercises 25–28, assume a significance
Original claim: Women have heights with a mean equal to 160.00 cm. The hypothesis test results in a P-value of 0.0614.Stating Conclusions. In Exercises 25–28, assume a significance level of A =
Original claim: Fewer than 20% of M&M candies are green. The hypothesis test results in a P-value of 0.0721.Stating Conclusions. In Exercises 25–28, assume a significance level of A = 0.05 and use
Original claim: The percentage of blue M&Ms is greater than 5%. The hypothesis test results in a P-value of 0.0010.Stating Conclusions. In Exercises 25–28, assume a significance level of A = 0.05
With H1: p 7 7>8, the test statistic is z = 2.88.
With H1: p 6 0.6, the test statistic is z = -3.00.
With H1: p ≠ 0.25, the test statistic is z = -1.23.
The test statistic of z = 1.50 is obtained when testing the claim that p ≠ 0.25.
The test statistic of z = -1.75 is obtained when testing the claim that p = 1>3.
The test statistic of z = -2.00 is obtained when testing the claim that p 6 0.5.
The test statistic of z = 2.00 is obtained when testing the claim that p 7 0.5.
White Blood Cell Count Claim: For adult females, the standard deviation of their white blood cell counts is equal to 5.00. The random sample of 40 adult females in Data Set 1 from Appendix: Data Sets
Tax Returns Claim: Among those who file tax returns, less than one-half file them through an accountant or other tax professional. A Fellowes survey of 1002 people who file tax returns showed that

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