Probability and Statistics for Engineering and the Sciences
9th Edition
ISBN: 9781305251809
Author: Jay L. Devore
Publisher: Cengage Learning
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Chapter 15, Problem 34SE
a.
To determine
Find the smallest
b.
To determine
Find the confidence level and the confidence interval.
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(c) An epidemiologist is worried about the ever increasing trend of malaria in a certain locality and wants to estimate the proportion of people infected in the peak malaria transmission period. If he takes a random sample of 150 people in that locality during the peak transmission period and finds that 60 of them are positive for malaria, find i. 99% confidence interval for the proportion of the whole infected people in that locality during the peak malaria transmission period.
(a)A random sample of 25 college males was obtained and each was asked to report their actual height and what they wished as their ideal height. A 95% confidence interval for µd = average difference between their ideal and actual heights was 0.8" to 2.2". Based on this interval, which one of the null hypotheses below (versus a two-sided alternative) can be rejected?
all the above
c. H0: µd = 1.5
H0: µd = 0.5
b. H0: µd = 1.0
H0: µd = 2.0
(b)Which of the following is a correct form of an alternate hypothesis for paired data?
H1: μd = p
H1: μ1 ≠ μ2
H1: μd > 0
H1: μ1 = μ2
(C)Which of the following is always the null hypothesis for two sample proportions?
d. H0: p1 = 3
H0: p1 < μ2
H0: p1 ≠ p2
H0: p1 = p2
Suppose X1 ,...,X100 are i.i.d. N(μ,3).
(a) Find a 90% two sided confidence interval for μ, if ̄X (Read X bar)= 10.
(b) Can you want to test H0:μ= 11 versus H1:μ (NOT EQUAL) 11 at level.1?
(c) Does the value 11 lie in the confidence interval of part (a)?
Chapter 15 Solutions
Probability and Statistics for Engineering and the Sciences
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- An investigator has calculated a 95 percent confidence interval for a one-sample t test and found: P{97.0≤μ≤105.0}=0.95. If the investigator wants to test the hull hypothesis H0: μ=100,with α=0.05, the investigator should:arrow_forwardFind the critical value zα/2 needed to construct a(n) 98.3% confidence interval.arrow_forwardA random sample of 25 college males was obtained and each was asked to report their actual height and what they wished as their ideal height. A 95% confidence interval for _µ_d = average difference between their ideal and actual heights was 0.8" to 2.2". Based on this interval, which one of the null hypotheses below (versus a two-sided alternative) can be rejected? Select one: a. H0: µd = 2.0 b. H0: µd = 1.0 c. H0: µd = 1.5 d. H0: µd = 0.5arrow_forward
- 3. In a random sample of 300 persons eating lunch at a Lexington pizzeria, 270 ordered pizza. a) Find and interpret a 95% confidence interval for the true proportion of people who eat pizza at this Lexington pizzeria? b) If we take 270/300 = 0.90 as an estimate of the corresponding true proportion, with what confidence can we assert that our error is less than 0.04?arrow_forwardA corresponding relationship between confidence intervals and two-tailed hypothesis tests also is valid for other parameters, such as p, ?1 − ?2, or p1 − p2, which we will study in later sections.) Whenever the value of k given in the null hypothesis falls outside the c = 1 – α confidence interval for the parameter, we reject H0. For example, consider a two-tailed hypothesis test with ? = 0.01 and H0: ? = 21H1: ? ≠ 21 A random sample of size 30 has a sample mean x = 22 from a population with standard deviation ? = 3. (a) What is the value of c = 1 − ?? Using the methods of Chapter 7, construct a 1 − ? confidence interval for ? from the sample data. (Round your answers to two decimal places.) lower limit upper limitarrow_forwardFind z given a 94% confidence interval and a= 0.06. z = ?arrow_forward
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- In Exercises 9–14, construct the confidence interval for the difference μ1 − μ2 for the given level and values of , , s1, s2, n1, and n2. Level 90%: = 104.6, = 92.9, s1 = 4.8, s2 = 6.9, n1 = 26, n2 = 19 Solve using ti 84 plusarrow_forwardIn describing the findings of a 2010 Public ReligionResearch Institute poll, the researchers reported a 3%margin of error at a 95% confidence level. If instead theyhad used a 99% confidence level, their margin of errorwould have been:A) still 3%, because the same sample is used.B) more than 3%, because they reported greaterconfidence.C) less than 3%, because they reported greaterconfidence.D) more than 3%, because this sample is too small.E) less than 3%, because this sample is too small.arrow_forwardDetermine the point estimate of the population mean and margin of error for the confidence interval with lower bound of 8 and upper bound of 24. A. x=24, E=8 B. x=16, E=16 C. x=8, E=16 D. x=16, E=arrow_forward
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