Question

Need problem solving process and the steps

version 3 Questions 19 - 20 A medical researcher is interested in the percentage of doctors who recommend aspirin rather than other pain killers for their patients with headaches. A random sample of 100 doctors results in 10 who indicate that they recommend aspirin. Use the following approximations: 70.16 = 0.4, 0.09 = 0.3, 12011 and 145 12. Q19 Determine the 99% confidence interval for the proportion of doctors who recommend aspirin. (a) (6.16%, 13.84%) (b) (4.29%, 15.71%) (e) (2.26%, 17.74% (d) (5.33%, 14.67% (e) (3.47%, 16.53% Answer 2.26-17.74 Q20 The researcher wants to have a margin of error smaller than 7 percentage points at the confidence level of 99%. What is the minimum required sample size? (a) 123 (b) 167 (c) 218 (d) 276 (e) 340 Answer 123

Answer 1

19. ATQ n = 100 i.e total number of doctors in the sample

p=10/100 = 0.1 i.e Number of doctor recommended aspirin divided by total number of doctors in the sample.

Similarly, q=90/100 = 0.9

Z_α/2= 2.58 (from z tables)

Confidence interval = [p - z_α/2√(pq/n) , p + z_α/2√(pq/n)]

= [0.1 - 2.58√(0.1*0.3/100) , 0.1 + 2.58√(0.1*0.3/100)]

= [0.1 - 2.58*0.03 , 0.1+ 2.58*0.03]

=[0.1 - 0.0774 , 0.1 + 0.0774]

=[0.0226 , 0.1774]

=[2.26% , 17.74%]

20. Margin of error(M.E) = z_α/2√(pq/n)

ATQ, M.E $\leq$ 0.07 or 7% points

$\rightarrow$ 0.07 $\geq$ z_α/2√(pq/n)

$\rightarrow$0.07 $\geq$ 2.58√(0.1*0.9/n)

$\rightarrow$0.07 $\geq$ 2.58*0.3/√n

$\rightarrow$√n $\geq$ 0.0774/0.07

$\rightarrow$√n $\geq$ 11.057

$\rightarrow$n $\geq$ 122.26

$\rightarrow$n = 123