Recall exercise 5.2.4 where researchers WIlt et al. investigated whether surgery
ID: 3049845 • Letter: R
Question
Recall exercise 5.2.4 where researchers WIlt et al. investigated whether surgery, compared to just observation, was (more) effective in improving men's survival chances after being diagnosed with prostate cancer. The researchers identified 731 men with localized prostate cancer and randomly assigned 364 to surgery and the remaining 367 to observation. All participants were followed for about 10 years. In those 10 years, 21 surgery recipients died of prostate cancer related reasons compared to 31 observation recipients.
a. Define (in words) the parameters of interest of this study. Also, assign symbols to the parameters.
b. State the appropriate null and alternative hypotheses in words.
c. State the appropriate null and alternative hypotheses in symbols.
d. Explain why it is valid to use the theory-based approach to test the hypotheses stated above.
e. Use an appropriate applet to find a theory-based p-value to test the above hypotheses. Report the standardized statistic as well as the p-value.
f. Use an appropriate applet to find a theory-based 99% confidence interval and interpret the resulting interval in the context of the study.
g. Based on your findings, state a complete conclusion about the study. Be sure to address significance, estimation (confidence interval), causation, and generalization.
Explanation / Answer
Given that,
sample one, x1 =21, n1 =364, p1= x1/n1=0.058
sample two, x2 =31, n2 =367, p2= x2/n2=0.084
null, Ho: p1 = p2
alternate, H1: p1 != p2
level of significance, = 0.01
from standard normal table, two tailed z /2 =2.576
since our test is two-tailed
reject Ho, if zo < -2.576 OR if zo > 2.576
we use test statistic (z) = (p1-p2)/(p^q^(1/n1+1/n2))
zo =(0.058-0.084)/sqrt((0.071*0.929(1/364+1/367))
zo =-1.408
| zo | =1.408
critical value
the value of |z | at los 0.01% is 2.576
we got |zo| =1.408 & | z | =2.576
make decision
hence value of |zo | < | z | and here we do not reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != -1.4082 ) = 0.1591
hence value of p0.01 < 0.1591,here we do not reject Ho
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a. Define (in words) the parameters of interest of this study. Also, assign symbols to the parameters.
null, Ho: p1 = p2
alternate, H1: p1 != p2
b. State the appropriate null and alternative hypotheses in words.
to find the difftrence in percentage of men died when comparing two studies surgery, observation case
c. State the appropriate null and alternative hypotheses in symbols.
null, there is no significance in study between both
e. Use an appropriate applet to find a theory-based p-value to test the above hypotheses. Report the standardized statistic as well as the p-value.
test statistic: -1.408
p-value: 0.1591
f. Use an appropriate applet to find a theory-based 99% confidence interval and interpret the resulting interval in the context of the study.
given that,
sample one, x1 =21, n1 =364, p1= x1/n1=0.0577
sample two, x2 =31, n2 =367, p2= x2/n2=0.0845
CI = (p1-p2) ± sqrt( p1 * (1-p1)/n1 + p2 * (1-p2)/n2 )
where,
p1, p2 = proportion of both sample observation
n1,n2 = size of both group
a = 1 - (confidence Level/100)
Za/2 = Z-table value
CI = confidence interval
CI = [ (0.0577-0.0845) ± 2.58 * 0.019]
= [ -0.0757 , 0.0222 ]
g. Based on your findings, state a complete conclusion about the study. Be sure to address significance, estimation (confidence interval), causation, and generalization.
we have enough evidence to conclude that there is no significnace diffrence between the methods to apply
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