For this problem, carry at least four digits after the decimal in your calculati
ID: 3229030 • Letter: F
Question
For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.
A random sample of 5670 physicians in Colorado showed that 3359 provided at least some charity care (i.e., treated poor people at no cost).
(a) Let p represent the proportion of all Colorado physicians who provide some charity care. Find a point estimate for p. (Round your answer to four decimal places.)
(b) Find a 99% confidence interval for p. (Round your answers to three decimal places.)
Give a brief explanation of the meaning of your answer in the context of this problem.
99% of the confidence intervals created using this method would include the true proportion of Colorado physicians providing at least some charity care.1% of the confidence intervals created using this method would include the true proportion of Colorado physicians providing at least some charity care. 1% of all confidence intervals would include the true proportion of Colorado physicians providing at least some charity care.99% of all confidence intervals would include the true proportion of Colorado physicians providing at least some charity care.
(c) Is the normal approximation to the binomial justified in this problem? Explain.
No; np < 5 and nq > 5.Yes; np < 5 and nq < 5. No; np > 5 and nq < 5.Yes; np > 5 and nq > 5.
lower limit upper limitExplanation / Answer
a.
Given that,
possibile chances (x)=3359
sample size(n)=5670
success rate ( p )= x/n = 0.5924
success probability,( po )=0.5924
failure probability,( qo) = 0.4076
null, Ho:p=0.5924
alternate, H1: p<0.5924
level of significance, = 0.05
from standard normal table,left tailed z /2 =1.64
since our test is left-tailed
reject Ho, if zo < -1.64
we use test statistic z proportion = p-po/sqrt(poqo/n)
zo=0.59242-0.5924/(sqrt(0.24146224)/5670)
zo =0.0025
| zo | =0.0025
critical value
the value of |z | at los 0.05% is 1.64
we got |zo| =0.002 & | z | =1.64
make decision
hence value of |zo | < | z | and here we do not reject Ho
p-value: left tail - Ha : ( p < 0.00249 ) = 0.50099
hence value of p0.05 < 0.50099,here we do not reject Ho
ANSWERS
---------------
null, Ho:p=0.5924
alternate, H1: p<0.5924
test statistic: 0.0025
critical value: -1.64
decision: do not reject Ho
p-value: 0.50099
b.
Confidence Interval For Proportion
CI = p ± Z a/2 Sqrt(p*(1-p)/n)))
x = Mean
n = Sample Size
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
No. of success(x)=3359
Sample Size(n)=5670
Sample proportion = x/n =0.5924
Confidence Interval = [ 0.5924 ±Z a/2 ( Sqrt ( 0.5924*0.408) /5670)]
= [ 0.5924 - 2.576* Sqrt(0) , 0.5924 + 2.58* Sqrt(0) ]
= [ 0.576,0.609]
99% of all confidence intervals would include the true proportion of Colorado physicians providing at least some charity care.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.