An Introduction to Mathematical Statistics and Its Applications (6th Edition)
6th Edition
ISBN: 9780134114217
Author: Richard J. Larsen, Morris L. Marx
Publisher: PEARSON
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Chapter 7.4, Problem 17Q
Recall the Bacillus subtilis data in Question 5.3.2. Test the null hypothesis that exposure to the enzyme does not affect a worker’s respiratory capacity (as measured by the
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The article in the ASCE Journal of Energy Engineering (1999, Vol. 125, pp.59-75) describes a study of the thermal inertia properties of autoclaved aerated concrete used as a building material. Five samples of the material were tested in a structure, and the average interior temperatures (°C) reported were as follows: 23.01, 22.22, 22.04, 22.62, and 22.59. Test that the average interior temperature is equal to 22.5°C using alpha (a) = 0.05.
This problem is a test on what population parameter?
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What standardized test statistic will be used?
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What is the statistical decision in the statement form?
Q1. An anthropologist wants to collect data to determine whether the two different cultural groups that occupy an isolated Pacific Island grow to be different heights. The results of his samples of the heights of adult females are as follows Do these samples constitute enough evidence to reject the null hypothesis that the heights of the two groups the same? Set alpha to .05.
An article includes the accompanying data on compression strength (lb) for a sample of 12-oz aluminum cans filled with strawberry drink and another sample filled with cola.
Beverage
Sample Size
Sample Mean
Sample SD
Strawberry Drink
10
535
24
Cola
10
559
15
Does the data suggest that the extra carbonation of cola results in a higher average compression strength? Base your answer on a P-value. (Use
? = 0.05.)
State the relevant hypotheses. (Use ?1 for the strawberry drink and ?2 for the cola.)
H0: ?1 − ?2 = 0Ha: ?1 − ?2 ≥ 0H0: ?1 − ?2 = 0Ha: ?1 − ?2 ≠ 0 H0: ?1 − ?2 = 0Ha: ?1 − ?2 < 0H0: ?1 − ?2 = 0Ha: ?1 − ?2 > 0
Calculate the test statistic and determine the P-value. (Round your test statistic to one decimal place and your P-value to three decimal places.)
t
=
P-value
=
State the conclusion in the problem context.
Reject H0. The data suggests that cola has a higher average compression strength than the strawberry drink.Reject H0. The…
Chapter 7 Solutions
An Introduction to Mathematical Statistics and Its Applications (6th Edition)
Ch. 7.3 - Show directlywithout appealing to the fact that n2...Ch. 7.3 - Find the moment-generating function for a chi...Ch. 7.3 - Prob. 3QCh. 7.3 - Use the fact that (n1)S2/2 is a chi square random...Ch. 7.3 - Let Y1,Y2,...,Yn be a random sample from a normal...Ch. 7.3 - If Y is a chi square random variable with n...Ch. 7.3 - Use Appendix Table A.4 to find (a) F.50,6,7 (b)...Ch. 7.3 - Let V and U be independent chi square random...Ch. 7.3 - Use Appendix Table A.4 to find the values of x...Ch. 7.3 - Suppose that two independent samples of size n are...
Ch. 7.3 - If the random variable F has an F distribution...Ch. 7.3 - Prob. 12QCh. 7.3 - Show that as n, the pdf of a Student t random...Ch. 7.3 - Prob. 14QCh. 7.3 - Prob. 15QCh. 7.4 - Use Appendix Table A.2 to find the following...Ch. 7.4 - What values of x satisfy the following equations?...Ch. 7.4 - Which of the following differences is larger?...Ch. 7.4 - A random sample of size n=9 is drawn from a normal...Ch. 7.4 - Suppose a random sample of size n=11 is drawn from...Ch. 7.4 - Let Y and S denote the sample mean and sample...Ch. 7.4 - Cell phones emit radio frequency energy that is...Ch. 7.4 - The following table lists the typical cost of...Ch. 7.4 - Creativity, as any number of studies have shown,...Ch. 7.4 - How long does it take to fly from Atlanta to New...Ch. 7.4 - In a nongeriatric population, platelet counts...Ch. 7.4 - If a normally distributed sample of size n=16...Ch. 7.4 - Prob. 13QCh. 7.4 - Revenues reported last week from nine boutiques...Ch. 7.4 - What confidence is associated with each of the...Ch. 7.4 - The weather station at Dismal Swamp, California,...Ch. 7.4 - Recall the Bacillus subtilis data in Question...Ch. 7.4 - Recall Case Study 5.3.1. Assess the credibility of...Ch. 7.4 - MBAs R Us advertises that its program increases a...Ch. 7.4 - In addition to the Shoshoni data of Case Study...Ch. 7.4 - A manufacturer of pipe for laying underground...Ch. 7.4 - In athletic contests, a wide-spread conviction...Ch. 7.4 - Prob. 23QCh. 7.4 - Prob. 24QCh. 7.4 - Prob. 25QCh. 7.4 - Suppose that random samples of size n are drawn...Ch. 7.4 - On which of the following sets of data would you...Ch. 7.5 - Use Appendix Table A.3 to find the following...Ch. 7.5 - Evaluate the following probabilities: (a)...Ch. 7.5 - Find the value y that satisfies each of the...Ch. 7.5 - For what value of n is each of the following...Ch. 7.5 - For df values beyond the range of Appendix Table...Ch. 7.5 - Let Y1,Y2,...,Yn be a random sample of size n from...Ch. 7.5 - Start with the fact that (n1)S2/2 has a chi square...Ch. 7.5 - A random sample of size n=19 is drawn from a...Ch. 7.5 - How long sporting events last is quite variable....Ch. 7.5 - How much interest certificates of deposit (CDs)...Ch. 7.5 - Prob. 11QCh. 7.5 - (a) Use the asymptotic normality of chi square...Ch. 7.5 - If a 90% confidence interval for 2 is reported to...Ch. 7.5 - Prob. 14QCh. 7.5 - Prob. 15QCh. 7.5 - When working properly, the amounts of cement that...Ch. 7.5 - A stock analyst claims to have devised a...
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- Given the Data:Test the hypothesis that p(rho)xy is not equal to 0 at the 0.05 level of significance.arrow_forwardIf the value of Cronbach’s alpha is 0.07, it means ___________; a. Research instrument is not reliable b. Research instrument is internally consistent c. Data is reliable d. Data is internally consistentarrow_forwardSOLVE QUESTIONS D & E ONLY!!!! Consider the accompanying data on flexural strength (MPa) for concrete beams of a certain type. 8.3 7.4 7.0 6.8 7.8 9.7 5.0 6.3 6.8 9.0 7.7 7.3 7.4 11.8 6.3 7.7 11.6 7.2 11.3 9.7 10.7 7.0 7.9 8.7 7.9 8.1 6.5 (a) Calculate a point estimate of the mean value of strength for the conceptual population of all beams manufactured in this fashion. [Hint: Σxi = 218.9.] (Round your answer to three decimal places.) MPa(b) Calculate a point estimate of the strength value that separates the weakest 50% of all such beams from the strongest 50%. MPa(c) Calculate a point estimate of the population standard deviation ?. [Hint: Σxi2 = 1851.35.] (Round your answer to three decimal places.) MPa(d) Calculate a point estimate of the proportion of all such beams whose flexural strength exceeds 10 MPa. [Hint: Think of an observation as a "success" if it exceeds 10.] (Round your answer to three decimal places.)(e) Calculate a point estimate of the population…arrow_forward
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