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 14.3, Problem 5Q
To determine
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The test statistic of
z=−1.68
is obtained when testing the claim that
p<0.88.
a. Using a significance level of
a=0.01,
find the critical value(s).
b. Should we reject
H 0
or should we fail to reject
H 0?
Solve
An 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.
1.)This problem is a test on what population parameter?
a.Variance/ Standard Deviation
b.Mean
c.Population Proportion
d.None of the above
2.)What is the null and alternative 3 points hypothesis?
a.Ho / (theta = 22.5) , Ha: (0 # 22.5)
b.Ho / (theta > 22.5) , Ha: (0 # 22.5)
c.Ho / (theta < 22.5) , Ha: (theta >= 22.5)
d.None of the above
3.)What are the Significance level 3 points and type of test?
alpha = 0.05 two-tailed
alpha = 0.95 two-tailed
alpha = 0.95 one-tailed
None of the above
4.)What standardized test statistic will…
You are conducting quality control for a company that manufactures LED displays. The factory you are assessing is supposed to have a manufacturing defect rate of 1 in 100 LED displays.
As part of your assessment, you want to verify this defect rate by analyzing a random sample of LED displays. You are planning to randomly sample 1500 displays from this factory and observe how many of them contain manufacturing defects. Let Zi be equal to 1 if the i’th display has a defect and 0 otherwise, for i = 1,...,1500.
(a) What is the statistic that you will use to estimate the defect rate for this factory? How do you compute it using Z1, Z2, . . . , Z1500?
(b) Assuming that the true defect rate for this factory is in fact 1 in 100 displays, can we approximate the sampling distribution of the statistic that you selected in part (a) using a normal distribution? Please state and check the requirements for applying the approximation, and identify the mean and standard deviation of the normal…
Chapter 14 Solutions
An Introduction to Mathematical Statistics and Its Applications (6th Edition)
Ch. 14.2 - Recall the data in Question 8.2.9 giving the sizes...Ch. 14.2 - Test H0==0.12 versus H1=0.12 for the release chirp...Ch. 14.2 - Below are n=50 computer-generated observations...Ch. 14.2 - Let Y1,Y2,...,Y22 be a random sample of normally...Ch. 14.2 - Suppose that n=7 paired observations, (Xi,Yi), are...Ch. 14.2 - Analyze the Shoshoni rectangle data (Case Study...Ch. 14.2 - Recall the FEV1/VC data described in Question...Ch. 14.2 - Do a sign test on the ESP data in Question 13.2.2....Ch. 14.2 - In a marketing research test, twenty-eight adult...Ch. 14.2 - Suppose that a random sample of size...
Ch. 14.2 - Prob. 11QCh. 14.3 - The average energy expenditures for eight elderly...Ch. 14.3 - Prob. 2QCh. 14.3 - Prob. 3QCh. 14.3 - Prob. 4QCh. 14.3 - Prob. 5QCh. 14.3 - DoaWilcoxon signed rank test on the hemoglobin...Ch. 14.3 - Prob. 7QCh. 14.3 - Prob. 8QCh. 14.3 - Prob. 9QCh. 14.3 - Prob. 10QCh. 14.4 - Prob. 1QCh. 14.4 - Prob. 2QCh. 14.4 - Prob. 3QCh. 14.4 - Prob. 4QCh. 14.4 - Prob. 5QCh. 14.4 - A sample of ten 40-W light bulbs was taken from...Ch. 14.4 - Prob. 7QCh. 14.4 - Prob. 8QCh. 14.5 - The following data come from a field trial set up...Ch. 14.5 - Prob. 2QCh. 14.5 - Prob. 3QCh. 14.5 - Prob. 4QCh. 14.5 - Prob. 5QCh. 14.5 - Prob. 6QCh. 14.6 - Prob. 1QCh. 14.6 - Listed below for two consecutive fiscal years are...Ch. 14.6 - Prob. 3QCh. 14.6 - Prob. 4QCh. 14.6 - Prob. 5QCh. 14.6 - Prob. 6Q
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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
- 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? What is the null and alternative hypothesis? What are the Significance level and type of test? What standardized test statistic will be used? What is the standard test statistic? What is the Statistical Decision? What is the statistical decision in the statement form?arrow_forwardDr. Chapman conducted an experiment in which participants watched paint dry for 30 minutes twice, once being paid $1 and once being paid $30. When comparing the samples, he calculated t = 3.57. He assumed α = .01 with df = 5, so the tcv = ±4.032. Because the calculated value was: A. greater than the critical value, Dr. Chapman can reject the null hypothesis. B. greater than the critical value, Dr. Chapman failed to reject the null hypothesis. C. less than the critical value, Dr. Chapman failed to reject the null hypothesis. D. less than the critical value, Dr. Chapman can reject the null hypothesis.arrow_forwardThe test statistic of z= -1.90 is obtained when testing the claim that p<0.26. a. Using a significance level of a=0.01, find the critical value(s). b. Should we reject Upper H 0 or should we fail to reject Upper H 0?arrow_forward
- The 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_forwardM1= 37 SS1=360 n1=11 M2= 43 SS2=576 n2=10 Assume two failed test and alpha= .05 What is the critical value?arrow_forwardIn a test of H0:p=0.4 against Ha:p≠0.4, a sample of size 100 produces z=1.28 for the value of the test statistic. Thus the p-value of the test is approximately equal to?arrow_forward
- Match the p-values with the appropriate conclusion: I. 0.00001 II. 0.0189 III. 0.0611 IV. 0.4234(a) The evidence against the null hypothesis is significant, but only at the 10% level. (b) The evidence against the null and in favor of the alternative is very strong. (c) There is not enough evidence to reject the null hypothesis, even at the 10% level. (d) The result is significant at a 5% level but not at a 1% level.arrow_forward- Let I = 1.135013 be the sample mean of an iid sample r1,..., x50 from a gamma population Gamma(1, 3). Here B > 0 is the unknown parameter of interest. Construct an approximate 95%-CI for B.arrow_forwardSee the attached image for the introduction. In terms of variables xi and parameters βi, write the null and alternative hypotheses for testing whether, after including Price/Square Feet(x2) in the model already, the further incorporation of the other 2 explanatory variables (x1, x3) adds any useful information for explaining pricey. Also, give the value of the F statistic and its degrees of freedom (df).arrow_forward
- If 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_forwardAre seatbelts effective at saving lives? We wish to examine whether or not the use of seatbelts reduces fatalities at the alpha = 0.05 level of significance. Let p N represent the proportion of non-seatbelt wearing passengers who were involved in a crash and died and represent the proportion of seatbelt wearing passengers who were involved in a crash and died. 1. Which would be correct hypotheses for this test? H 0 :p N =p Y ,H 1 :p N <p Y O H 0 :p N =p Y ,H 1 :p N ne p Y H 0 :p N =p Y ,H 1 :p N > mathfrak P Y O H 0 :p N ne p Y , H 1 :p N >p Y In a random sample of 335 non-seatbelt wearing passengers involved in a car crash, 34 were killed. In a random sample of 398 seatbelt wearing passengers involved in a car crash , 18 were killed. 2. Find the test statistic (2 decimal places) 3. Give the P-value (4 decimal places) please only answer 2 and 3!arrow_forwardThe test statistics of z = 3.15 is obtained when testing the claim that p > 0.27. Use the significance level of α=0.01 to find the critical value(s).arrow_forward
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