An Introduction to Mathematical Statistics and Its Applications (6th Edition)
6th Edition
ISBN: 9780134114217
Author: Richard J. Larsen, Morris L. Marx
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Videos
Textbook Question
Chapter 6.2, Problem 3Q
(a) Suppose
(b) Suppose
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
An article in the San Jose Mercury News stated that students in the California state
university system take 4.5 years, on average, to finish their undergraduate degrees.
Dr. Lewis believes the mean time for students at Clayton State University is longer
than this average. A survey of 49 graduates from Clayton State had a mean time of
5.1 years to complete their Bachelor's degree, with a sample standard deviation of
1.2 years. Correctly identify the null and alternative hypotheses for this study:
A random sample of
n1 = 49
measurements from a population with population standard deviation
σ1 = 3
had a sample mean of
x1 = 14.
An independent random sample of
n2 = 64
measurements from a second population with population standard deviation
σ2 = 4
had a sample mean of
x2 = 16.
Test the claim that the population means are different. Use level of significance 0.01.
(c) Compute
x1 − x2.
x1 − x2 =
Compute the corresponding sample distribution value. (Test the difference μ1 − μ2. Round your answer to two decimal places.)(d) Find the P-value of the sample test statistic. (Round your answer to four decimal places.)
2) Suppose that we are testing Ho:µ = 4 vs Ha: µ > 4. A p-value of 0.023 was
determined. Which of the following is a correct interpretation of this p-value?
(a) The null hypothesis would be rejected at a 5% level but not a 1% level.
(b) The null hypothesis would be rejected at a 1% level but not a 5% level.
(c) The null hypothesis would be rejected at both 5% and 1% levels.
(d) The null hypothesis would not be rejected at either the 5% or 1% level.
Chapter 6 Solutions
An Introduction to Mathematical Statistics and Its Applications (6th Edition)
Ch. 6.2 - State the decision rule that would be used to test...Ch. 6.2 - An herbalist is experimenting with juices...Ch. 6.2 - (a) Suppose H0:=0 is rejected in favor of H1:0 at...Ch. 6.2 - Company records show that drivers get an average...Ch. 6.2 - If H0:=0 is rejected in favor of H1:0, will it...Ch. 6.2 - A random sample of size 16 is drawn from a normal...Ch. 6.2 - Recall the breath analyzers described in Example...Ch. 6.2 - Calculate the P-values for the hypothesis tests...Ch. 6.2 - Suppose H0:=120 is tested against H1:120. If =10...Ch. 6.2 - As a class research project, Rosaura wants to see...
Ch. 6.2 - As input for a new inflation model, economists...Ch. 6.3 - Commercial fishermen working certain parts of the...Ch. 6.3 - Efforts to find a genetic explanation for why...Ch. 6.3 - Defeated in his most recent attempt to win a...Ch. 6.3 - Suppose H0:p=0.45 is to be tested against H1:p0.45...Ch. 6.3 - Recall the median test described in Example 5.3.2....Ch. 6.3 - Among the early attempts to revisit the death...Ch. 6.3 - What levels are possible with a decision rule of...Ch. 6.3 - Suppose H0:p=0.75 is to be tested against H1:p0.75...Ch. 6.4 - Recall the Math for the Twenty-First Century...Ch. 6.4 - Carry out the details to verify the decision rule...Ch. 6.4 - For the decision rule found in Question 6.2.2 to...Ch. 6.4 - Construct a power curve for the =0.05 test of...Ch. 6.4 - If H0:=240 is tested against H1:240 at the =0.01...Ch. 6.4 - Suppose n=36 observations are taken from a normal...Ch. 6.4 - If H0:=200 is to be tested against H1:200 at the...Ch. 6.4 - Will n=45 be a sufficiently large sample to test...Ch. 6.4 - If H0:=30 is tested against H1:30 using n=16...Ch. 6.4 - Suppose a sample of size 1 is taken from the pdf...Ch. 6.4 - Polygraphs used in criminal investigations...Ch. 6.4 - Prob. 12QCh. 6.4 - Prob. 13QCh. 6.4 - A sample of size 1 is taken from the pdf...Ch. 6.4 - Prob. 15QCh. 6.4 - Prob. 16QCh. 6.4 - Prob. 17QCh. 6.4 - Prob. 18QCh. 6.4 - Prob. 19QCh. 6.4 - Suppose that one observation from the exponential...Ch. 6.4 - Prob. 21QCh. 6.4 - Prob. 22QCh. 6.4 - Prob. 23QCh. 6.4 - Given the pdf fY(y;)=2y2,0y. Take a sample of size...Ch. 6.5 - Let k1,k2,...,kn be a random sample from the...Ch. 6.5 - Let y1,y2,...,y10 be a random sample from an...Ch. 6.5 - Let y1,y2,...,yn be a random sample from a normal...Ch. 6.5 - Let k denote the number of successes observed in a...Ch. 6.5 - Suppose a sufficient statistic exists for the...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.Similar questions
- You wish to test the following claim (H1H1) at a significance level of α=0.05α=0.05. For the context of this problem, d=x2−x1d=x2-x1 where the first data set represents a pre-test and the second data set represents a post-test. Ho:μd=0Ho:μd=0 H1:μd<0H1:μd<0 You believe the population of difference scores is normally distributed, but you do not know the standard deviation. You obtain the following sample of data: pre-test post-test 47.2 -2.7 45.4 34.9 27.6 15.1 43.3 92.7 41.3 -21.2 15.5 8.4 32.4 28.7 55.3 53.8 45.7 54.7 33.2 56.4 27.6 17.1 30.8 5.9 46.8 14.6 45.4 8.6 43 25.8 50 17 32 36.6 33.6 -22.7 What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value = The p-value is... less than (or equal to) αα greater than αα This test statistic leads to a decision to... reject…arrow_forward#6.3 (p.344). Conduct a test of H0: μ1>= μ2-2.3 versus Ha: μ1< μ2-2.3 for the sample data summarized here. Use α=0.01 in reaching your conclusions.arrow_forward1. You are performing a two-tailed test with a sample size of 44.If α=.02α=.02, find the positive critical value, to four decimal places.tα/2= ? 2. You are performing a two-tailed test with a sample size of 88.If α=.01α=.01, find the positive critical value, to four decimal places.tα/2= ?arrow_forward
- If Ho: µ = 50 and the computed value of the test statistic Z = (x - μ0)/(σ/√n) is 1.75, compute for the p-value when: Ha: µ > 50. Should Ho be rejected at 0.05 level of significance? Ha: µ < 50. Should Ho be rejected at 0.05 level of significance? Ha: µ ≠ 50. Should Ho be rejected at 0.05 level of significance?arrow_forwardOn average, a sample of n = 36 scores from a normal population with σ= 10 will provide a better estimate of the population mean than a researcher would get with a sample of n = 9 scores from a normal population with σ= 10.arrow_forwardA random sample of n1 = 49 measurements from a population with population standard deviation σ1 = 5 had a sample mean of x1 = 15. An independent random sample of n2 = 64 measurements from a second population with population standard deviation σ2 = 6 had a sample mean of x2 = 18. Test the claim that the population means are different. Use level of significance 0.01. (b) Compute x1 − x2. x1 − x2 = Compute the corresponding sample distribution value. (Test the difference μ1 − μ2. Round your answer to two decimal places.)(c) Find the P-value of the sample test statistic. (Round your answer to four decimal places.)arrow_forward
- A. 2. Tesla Motors claims that its Model S electric car can travel more than 300 miles at 55 mph when the larger 85 kWh battery offered in the cars is utilized. Use , the population mean miles of range for electric cars, to identify the null and alternative hypotheses. Η : μ 300 B. H₁ : μ = 300 C. H : μ 300arrow_forwardA dietitian wishes to see if a person’s cholesterol level will be changed if the diet is supplemented by a certain mineral. Four subjects were pre-tested, and they took the mineral supplement for a 6-week period. The results are shown in the table. Is there sufficient evidence to conclude that the population mean of cholesterol levels has been changed after six weeks at α=0.2α=0.2? Assume that the differences are from an approximately normally distributed population. Subject Cholestrol Level (mg/dl) Cholestrol Level after 6 Weeks (mg/dl) dd ¯dd¯ (d−¯d)2(d-d¯)2 1 206 217 11 2 219 184 -35 3 202 204 2 4 213 205 -8 Total -30 a) Calculate the mean, the sum of the squared deviation from the mean, and the standard deviation of differences. Do not include the unit for each answer: ¯d=d¯= (do not round) ∑(d−¯d)2=∑(d-d¯)2= (do not round) sd=sd= (rounded to one decimal place) b) Perform the hypothesis test in the following steps: Step 1.…arrow_forwardFor a value of population parameter 0 equal to 2, which one of the following cases corresponds to an unbiased estimator with higher precision? E(Ô ) = 2 and Var(Ô) = 2 E(ô – 0) = 0 and Var( ô ) = 2 E(ô – 0 ) = 2 and Var(ô ) = 1 E(Ô) = 2 and Var( Ô ) = 1 ||arrow_forward
- The desired percentage of SiO₂ in a certain type of aluminous cement is 5.5. To test whether the true average percentage is 5.5 for a particular production facility, 16 independently obtained samples are analyzed. Suppose that the percentage of SiO₂ in a sample is normally distributed with o = 0.32 and that x = 5.23. (Use α = 0.05.) (a) Does this indicate conclusively that the true average percentage differs from 5.5? State the appropriate null and alternative hypotheses. O Ho: μ = 5.5 Ha: μ 5.5 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) Z = P-value = State the conclusion in the problem context. O Reject the null hypothesis. There is not sufficient evidence to conclude that the true average percentage differs from the desired percentage. O Do not reject the null hypothesis. There is sufficient evidence to conclude that the true average percentage differs from the desired percentage.…arrow_forwardThe difference in the observed neurological disease rate, xbar, for a sample of veterans who served in Iraq is not “statistically significantly different” (alpha = .05), from the overall population disease rate for all U.S. veterans, mu0. This means: a. xbar = mu0b. The disease rates xbar and mu0 are not equal, but the size of the difference is not practically important, not big enough to matter. c. H0: mu for Iraq vets = mu0 was not rejected d. None of the abovearrow_forwardSuppose you will perform a test to determine whether there is sufficient evidence to support a claim of a linear correlation between two variables. Find the critical value(s) of r given that n = 20 and α = 0.05. Group of answer choices r = ±0.632 r = ±0.456 r = ±0.811 r = ±0.444arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
MATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
Probability and Statistics for Engineering and th...StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage Learning
Statistics for The Behavioral Sciences (MindTap C...StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage Learning
Elementary Statistics: Picturing the World (7th E...StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSON
The Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. Freeman
Introduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman
MATLAB: An Introduction with Applications
Statistics
ISBN:9781119256830
Author:Amos Gilat
Publisher:John Wiley & Sons Inc
Probability and Statistics for Engineering and th...
Statistics
ISBN:9781305251809
Author:Jay L. Devore
Publisher:Cengage Learning
Statistics for The Behavioral Sciences (MindTap C...
Statistics
ISBN:9781305504912
Author:Frederick J Gravetter, Larry B. Wallnau
Publisher:Cengage Learning
Elementary Statistics: Picturing the World (7th E...
Statistics
ISBN:9780134683416
Author:Ron Larson, Betsy Farber
Publisher:PEARSON
The Basic Practice of Statistics
Statistics
ISBN:9781319042578
Author:David S. Moore, William I. Notz, Michael A. Fligner
Publisher:W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:9781319013387
Author:David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:W. H. Freeman
Introduction to experimental design and analysis of variance (ANOVA); Author: Dr. Bharatendra Rai;https://www.youtube.com/watch?v=vSFo1MwLoxU;License: Standard YouTube License, CC-BY