Introductory Statistics (2nd Edition)
2nd Edition
ISBN: 9780321978271
Author: Robert Gould, Colleen N. Ryan
Publisher: PEARSON
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Chapter 7, Problem 77CRE
Sample Proportion A poll on a proposition showed that we are
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Set up a free RStudio account at posit.cloud. At the start of your R session, you should enter the following commands.
set.seed(1)
e<-rnorm(n = 100,mean = 0,sd = 80)
x<-seq(1,100,1)
y<-10+15*x + e
Follow the examples in the Panopto Videos to use R to obtain the values requested below. (As always, if you round your answers, make sure you do so correctly and keep at least
three decimal places.)
(a) The smallest value of y =
(b) The largest value of y =
(c) The standard deviation of y =
(d) The mean of y =
(e) The median of y =
(f) The correlation between x and y =
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(g) Using the variable e as data, the p-value for a test of Hoμ = 0 vs. HA μ0 is
Does Chi-squared(alpha) always represent the right tail of the the chi-square distribution and does Chi-squared(1-alpha) always represent the left tail of the the chi-square distribution. Also, for a standard normal distribution would Z(1-alpha) be equivalent to -Zalpha in represneting the left tail of the standard normal distribution curve because they both have the same z-score. Furthermore, is my understanding correct in the sense that if we have a critical value,say Zalpha, would the area to the right of it will be alpha and to the left of it would be 1-alpha
One bulb manufacturer claims an average bulb life of 1,600 hours. It is suspected that the actual average is significantly lower. To verify this, a sample of 49 bulbs is selected and the life of each bulb is measured. A sample mean of 1,500 hours and a standard deviation of 120 hours were obtained from them.
Can you be sure, at 5% significance, that the mean life is less than what the manufacturer claims?
Chapter 7 Solutions
Introductory Statistics (2nd Edition)
Ch. 7 - Parameter vs. Statistic (Example 1) Explain the...Ch. 7 - Sample vs. Census Explain the difference between a...Ch. 7 - x vs. Two symbols are used for the mean: and x....Ch. 7 - xvs. The mean GPA of all 5000 students at Uneeda...Ch. 7 - Ages of Presidents Suppose you knew the age at...Ch. 7 - Heights of Basketball Team Suppose you find all...Ch. 7 - Sample vs. Census You are receiving a large...Ch. 7 - Sampling GPAs Suppose you want to estimate the...Ch. 7 - Sampling with and without Replacement Explain the...Ch. 7 - Simple Random Sampling Is simple random sampling...
Ch. 7 - Finding a Random Sample (Example 5) You need to...Ch. 7 - Finding a Random Sample You need to select a...Ch. 7 - Random Sampling Assume your class has 30 students...Ch. 7 - Random Sampling with Coins Assume your class has...Ch. 7 - Questionnaire Response (Example 3) A teacher at a...Ch. 7 - Survey on Social Security A phone survey asked...Ch. 7 - Views on Capital Punishment In carrying out a...Ch. 7 - Views on Capital Punishment Use the data given in...Ch. 7 - Targets: Bias or Lack of Precision? a. If a...Ch. 7 - Targets: Bias or Lack of Precision, Again a. If a...Ch. 7 - Bias? Suppose that, when taking a random sample of...Ch. 7 - Unbiased Sample? Suppose you attend a school that...Ch. 7 - Proportion of Odd Digits A large collection of...Ch. 7 - Proportion of Odd Digits...Ch. 7 - Prob. 25SECh. 7 - Prob. 26SECh. 7 - ESP A Zener deck of cards has cards that show one...Ch. 7 - ESP Again In the graphs for Exercise 7.33, explain...Ch. 7 - Standard Error Which of the dotplots given in...Ch. 7 - Bias? Assuming that the true proportion of success...Ch. 7 - Fair Coin? One of the graphs shows the proportion...Ch. 7 - Far from Fair Which of the graphs in Exercise 7.37...Ch. 7 - What Is the Proportion of Seniors? (Example 5) A...Ch. 7 - Simulation From a very large (essentially...Ch. 7 - MMs (Example 5) Return to Exercise 7.25 and find...Ch. 7 - Random Letters Return to Exercise 7.26 and find...Ch. 7 - Jury Selection (Example 6) Juries should have the...Ch. 7 - Mercury in Freshwater Fish According to an article...Ch. 7 - The Oregon Bar Exam (Example 7) According to the...Ch. 7 - Feeding Vegans A survey of eating habits showed...Ch. 7 - Overweight Children The Ventura County Star (June...Ch. 7 - Living in Poverty The Ventura County Star article...Ch. 7 - Passing a Test by Guessing A true/false test has...Ch. 7 - Gender: Randomly Chosen? A large community college...Ch. 7 - Prob. 45SECh. 7 - Is Marriage Becoming Obsolete? When asked whether...Ch. 7 - East Germany According to a Gallup Poll taken in...Ch. 7 - View of Immigration In June 2012, a Gallup Poll...Ch. 7 - Voting A random sample of likely voters showed...Ch. 7 - Voting A random sample of likely voters showed...Ch. 7 - High School Diplomas (Example 8) In a simple...Ch. 7 - Diabetes In a simple random sample of 1200...Ch. 7 - Confidence in Public Schools A 2012 Gallup Poll...Ch. 7 - Confidence in the Military In June 2012, a Gallup...Ch. 7 - Thriving In June 2012, a Gallup Poll showed that...Ch. 7 - Benefits of Rich Class In May 2012, a Gallup Poll...Ch. 7 - Understanding the Meaning of Confidence Levels: 90...Ch. 7 - Understanding the Meaning of Confidence Levels: 80...Ch. 7 - Past Presidential Vote In the 1960 presidential...Ch. 7 - Human Cloning In a Gallup Poll, 441 of 507 adults...Ch. 7 - Do People Think Astrology Is Scientific? (Example...Ch. 7 - Do People Think the Sun Goes around the Earth? In...Ch. 7 - Good News on Jobs The Pew Research Center reports...Ch. 7 - Obesity In a 2013 Pew Poll, 36#37; of Republicans...Ch. 7 - Stressed Moms (Example 11, 12, 13, and 14) An...Ch. 7 - Gay Marriage According to the Pew Research Center,...Ch. 7 - Perry Preschool and Graduation from High School...Ch. 7 - Preschool: Just the Boys Refer to Exercise 7.77...Ch. 7 - Antibiotics for Malnutrition (Example 15) A study...Ch. 7 - Transfusions for Bleeding in the Stomach Should...Ch. 7 - Gender and Use of Turn Signals Statistics student...Ch. 7 - Diet Drug (Meridia) A randomized,...Ch. 7 - Drug for Nausea Ondansetron (Zofran) is a drug...Ch. 7 - Preschool: Just the Girls The Perry Preschool...Ch. 7 - Banning Super-Size Sugary Drinks A June 2012...Ch. 7 - Banning Smoking A July 2011 Roper Poll showed that...Ch. 7 - Sample Proportion A poll on a proposition showed...Ch. 7 - Sample Proportion A poll on a proposition showed...Ch. 7 - Margin of Error A poll on a proposition showed...Ch. 7 - Margin of Error A poll on a proposition showed...Ch. 7 - Prob. 81CRECh. 7 - Prob. 82CRECh. 7 - Dreaming in Color According to studies done in the...Ch. 7 - Hand Washing Ignaz Semmelweiss (1818-1865) was the...Ch. 7 - Romney vs. Santorum During the Republican primary...Ch. 7 - Sampling Error In March 2012, President Obama's...Ch. 7 - Young Women's Career Goals Are the career goals of...Ch. 7 - Young Men's Career Goals Are the career goals of...Ch. 7 - Voters Poll: Sample Size A polling agency wants to...Ch. 7 - Ratio of Sample Sizes Find the sample size...Ch. 7 - Criticize the Sampling Marco is interested in...Ch. 7 - Criticize the Sampling Maria opposes capital...Ch. 7 - Random Sampling? If you walked around your school...Ch. 7 - Biased Sample? You want to find the mean weight of...Ch. 7 - Bias? Suppose that, when taking a random sample of...Ch. 7 - Bias? Four women selected from a photo of 123 were...
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- The specification calls for the dimension of a certain mechanical part to be 0.55 inches. A random sample of 35 parts taken from a large batch showed a mean 0.54 in. with a deviation of 0.05 in. Can it be concluded, at 1% significance, that the batch of parts meets the required specification?arrow_forwardA manufacturer produces a wire rope of a certain type, which has a breaking strength of not more than 300 kg. A new and cheaper process is discovered which is desired to be employed, provided that the wire rope thus produced has an average breaking strength greater than 300 kg. If a random sample of 26 wires produced with the new process has given a mean of 304.5 kg and a standard deviation of 15 kg, should the manufacturer adopt the new process?arrow_forwardWe are interested in whether the proportions of female suicide victims for ages 15 to 24 are the same between the white and the black races in the United States. We randomly pick one year to compare the races. The number of suicides estimated in the United States in that year for white females is 4,930. Five hundred eighty-three were aged 15 to 24. The estimate for black females is 330. Forty-one were aged 15 to 24. We will let female suicide victims be our population. (Use α = 0.05.) NOTE: If you are using a Student's t-distribution for the problem, including for paired data, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) Part (a) State the null hypothesis. ○ Ho: PW> PB O Ho: PW + PB Ho: Pw≤ PB Ho: PW-PB ○ Ho: Pw PB Part (c) In words, state what your random variable P'w-P'B represents. P'w-P'B represents the average difference of white and black female suicide victims, aged 15 to 24. ○ P'w-P'B…arrow_forward
- please solve this problem step by step and make it quick pleasearrow_forwardplease solve this problem step by step and make it quick pleasearrow_forward8.67 Free recall memory strategy. Psychologists who study ①memory often use a measure of "free recall" (e.g., the RECALL number of correctly recalled items in a list of to-be- remembered items). The strategy used to memorize the list-for example, category clustering-is often just as important. Researchers at Central Michigan University developed an algorithm for computing measures of cat- egory clustering in Advances in Cognitive Psychology (Oct. 2012). One measure, called ratio of repetition, was recorded for a sample of 8 participants in a memory study. These ratios are listed in the table. Test the theory that the average ratio of repetition for all participants in a similar memory study differs from .5. Select an appropriate Type I error rate for your test. .25 .43 .57 .38 .38 .60 .47 .30 Source: Senkova, O., & Otani, H. "Category clustering calculator for free recall." Advances in Cognitive Psychology, Vol. 8, No. 4, Oct. 2012 (Table 3).arrow_forward
- 8.64 Radon exposure in Egyptian tombs. Refer to the D Radiation Protection Dosimetry (Dec. 2010) study TOMBS of radon exposure in Egyptian tombs, Exercise 7.39 (p. 334). The radon levels-measured in becquerels per cubic meter (Bq/m³)-in the inner chambers of a sam- ple of 12 tombs are listed in the table. For the safety of the guards and visitors, the Egypt Tourism Authority (ETA) will temporarily close the tombs if the true mean level of radon exposure in the tombs rises to 6,000 Bq/m³. Consequently, the ETA wants to conduct a test to deter- mine if the true mean level of radon exposure in the tombs is less than 6,000 Bq/m³, using a Type I error probabil- ity of .10. A SAS analysis of the data is shown on p. 399. Specify all the elements of the test: Ho, Ha, test statistic, p-value, a, and your conclusion. 50 390 910 12100 180 580 7800 4000 3400 1300 11900 1100 N Mean Std Dev Std Err Minimum Maximum 12 3642.5 4486.9 1295.3 50.0000 12100.0arrow_forwardHow does probability help businesses make informed decisions under uncertainty? Provide an example of how businesses use probability in marketing to predict customer behavior. Why is probability considered essential in financial decision-making, particularly in portfolio management? Discuss how the use of probability in inventory management can improve customer satisfaction. Compare the role of probability in marketing and financial decision-making. How do the applications differ in their objectives?arrow_forward55 5.5 A glass bottle manufacturing company has recorded data on the average number of defects per 10,000 bottles due to stones (small pieces of rock embedded in the bottle wall) and the number of weeks since the last furnace overhaul. The data are shown below. Defects per 10,000 Weeks 13.0 4 16.1 5 14.5 6 17.8 7 22.0 8 27.4 9 16.8 10 65.6 ☐☐ Defects per 10,000 Weeks 34.2 11 12 49.2 13 66.2 81.2 87.4 14 15 16 114.5 17 a. Fit a straight-line regression model to the data and perform the standard tests for model adequacy. b. Suggest an appropriate transformation to eliminate the problems encoun- tered in part a. Fit the transformed model and check for adequacy.arrow_forward
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