2 onrs oundnt 130 of them dovelopednous sydm P h y cahe brain 0 0329% for those

Question

2 onrs oundnt 130 of them dovelopednous sydm P h y cahe brain 0 0329% for those using cell phones Complete parts (a) and (b) or nervous system Prior to this study of cell phone use, the rate of such cancer was found to be a, use the sample data to construct a 90% confidence interval estmate of the percentage of cell phone users who develop cancer of the brain or nervous system Round to three decimal places as needed.) b. Do cell phone users appear to have a rate of cancer of the brain or nervous system that is different from the rate of such cancer among those not using cell phones? Why or why not? 0 A, Yes, because 00329% is icluded in the confidence interval. B. No, because 0.0329% is not included in the confidence interval. ° C. No, because 0.0329% is induded in the confidence interval D. Yes, because 00329% is not included ithe confidence interval.

Explanation / Answer

TRADITIONAL METHOD
given that,
possibile chances (x)=139
sample size(n)=420092
success rate ( p )= x/n = 0.0003309
I.
sample proportion = 0.0003309
standard error = Sqrt ( (0.0003309*0.9996691) /420092) )
= 0.0000281
II.
margin of error = Z a/2 * (stanadard error)
where,
Za/2 = Z-table value
level of significance, = 0.1
from standard normal table, two tailed z /2 =1.645
margin of error = 1.645 * 0.0000281
= 0.0000462
III.
CI = [ p ± margin of error ]
confidence interval = [0.0003309 ± 0.0000462]
= [ 0.0002847 , 0.000377]
-----------------------------------------------------------------------------------------------
DIRECT METHOD
given that,
possibile chances (x)=139
sample size(n)=420092
success rate ( p )= x/n = 0.0003309
CI = confidence interval
confidence interval = [ 0.0003309 ± 1.645 * Sqrt ( (0.0003309*0.9996691) /420092) ) ]
= [0.0003309 - 1.645 * Sqrt ( (0.0003309*0.9996691) /420092) , 0.0003309 + 1.645 * Sqrt ( (0.0003309*0.9996691) /420092) ]
= [0.0002847 , 0.000377]
-----------------------------------------------------------------------------------------------
interpretations:
1. We are 90% sure that the interval [ 0.0002847 , 0.000377] contains the true population proportion
2. If a large number of samples are collected, and a confidence interval is created
for each sample, 90% of these intervals will contains the true population proportion

C.no, beacuse 0.000329 is included in the confidence interval

Related Questions

Navigate

• Browse (All)
• Browse 2
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.