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Vasectomies and Prostate Cancer. Refer to Exercise 11.106 and determine and interpret a 98% confidence interval for the difference between the prostate cancer rates of men who have had a vasectomy and those who have not.

Short Answer

Expert verified

There is 98%interval for the difference between the proportion is(-0.00334,-0.0046)

Step by step solution

01

Given Information

The given values are,

x1=69,n1=21300,x2=113,n2=22000,p~1=0.00324,p~2=0.00514

02

Explanation

The formula for zis given by,

z=p~1-p~2p~p1-p~p1m1+1m2

Calculate the value of za2with 98%confidence level is 2.33.

The98%confidence interval is.

p~1-p~2±za2p~1-p~pn1+p~1-p~pn2

=(0.00324-0.00514)±2.330.00324(1-0.00324)21300+0.00514(1-0.00514)22000

=-0.0019±0.00144

Therefore, there is 98%interval for the difference between the proportion is(-0.00334,-0.0046)

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Most popular questions from this chapter

We have given a likely range for the observed value of a sample proportion p^

0.7orless

a. Based on the given range, identify the educated guess that should be used for the observed value of p^to calculate the required sample size for a prescribed confidence level and margin of error.

b. Identify the observed values of the sample proportion that will yield a larger margin of error than the one specified if the educated guess is used for the sample-size computation.

Margin of error=0.01

Confidence level=90%

Educated guess=0.9

(a) Obtain a sample size that will ensure a margin of error of at most the one specified (provided of course that the observed value of the sample proportion is further from 0.5that of the educated guess.

(b). Compare your answer to the corresponding one and explain the reason for the difference, if any.

Indicted Governor. On Thursday, June 13, 1996, thenArizona Governor Fife Symington was indicted on 23counts of fraud and extortion. Just hours after the federal prosecutors announced the indictment, several polls were conducted of Arizonans asking whether they thought Symington should resign. A poll conducted by Research 91Ó°ÊÓ, Inc., that appeared in the Phoenix Gazette, revealed that 58%of Arizonans felt that Symington should resign; it had a margin of error of plus or minus 4.9 percentage points. Another poll, conducted by Phoenix-based Behavior Research Center and appearing in the Tempe Daily News, reported that 54% of Arizonans felt that Symington should resign; it had a margin of error of plus or minus 4.4 percentage points. Can the conclusions of both polls be correct? Explain your answer.

a. Determine the sample proportion.

b. Decide whether using the one-proportion z-test is appropriate.

c. If appropriate, use the one-proportion z-test to perform the specified hypothesis test.

x=16

n=20

H0:p=0.7

Ha:p≠0.7

a=0.05

1Neutropenia. Neutropenia is an abnormally low number o neutrophils (a type of white blood cell) in the blood. Chemotherapy often reduces the number of neutrophils to a level that makes the patient susceptible to fever and infections. G. Bucaneve et al. published a study of such cancer patients in the paper "Levofloxacin to Prevent Bacterial Infection in Patients With Cancer and Neutropenia" (New England Journal of Medicine, Vol. 353, No, 10, pp. 977-987). For the study. 375 patients were randomly assigned to receive a daily dose of levofloxacin, and 363 were given a placebo. In the group receiving levofloxacin, fever was present in 243 patients for the duration of neutropenia, whereas fever was experienced by 308 patients in the placebo group.

a. At the1% significance level, do the data provide sufficient evidence to conclude that levofloxacin is effective in reducing the occurrence of fever in such patients?

b. Find a98% confidence level for the difference in the proportions of such cancer patients who would experience fever for the duration of neutropenia

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