Answer:
a) 217
b) 1351
c) 5403
Step-by-step explanation:
Given that:
confidence interval (c) = 0.95
[tex]\alpha =1-0.95=0.05\\\frac{\alpha }{2} =\frac{0.05}{2}=0.025[/tex]
The Z score of [tex]\frac{\alpha }{2}[/tex] is from the z table is given as:
[tex]Z_{\frac{\alpha }{2} }=Z_{0.025}=1.96[/tex]
Range = $45000 - $30000 = $15000
The standard deviation (σ) is given as:
[tex]\sigma=\frac{Range}{4} =\frac{15000}{4}=3750[/tex]
Sample size (n) is given as:
[tex]n=(\frac{Z_{\frac{\alpha}{2} }\sigma}{E} )^2[/tex]
a) E = $500
[tex]n=(\frac{Z_{\frac{\alpha}{2} }\sigma}{E} )^2= (\frac{1.96*3750}{500} )^2[/tex] ≈ 217
b) [tex]n=(\frac{Z_{\frac{\alpha}{2} }\sigma}{E} )^2= (\frac{1.96*3750}{200} )^2[/tex] ≈ 1351
c) [tex]n=(\frac{Z_{\frac{\alpha}{2} }\sigma}{E} )^2= (\frac{1.96*3750}{100} )^2[/tex] ≈ 5403
Answer:
217
1341
5403
No
Step-by-step explanation:
Given:
c = 95%
E = 500,200,100
RANGE = 45000 — 30000 = 15000
The standard deviation is approximately one forth of the range:
σ=RANGE/4
=15000/4
=3750
Formula sample size:
n = ((z_[tex]\alpha[/tex]/2*σ)/E)^2
For confidence level 1—a = 0.95, determine z_[tex]\alpha[/tex]/2 = z_0.025 using table 1 (look up 0.025 in the table, the z-score is then the found z-score with opposite sign):
z_[tex]\alpha[/tex]/2 = 1.96
The sample size is then (round up!):
a.n = ((z_[tex]\alpha[/tex]/2*σ)/E)^2 =217
b. n = ((z_[tex]\alpha[/tex]/2*σ)/E)^2 =1351
c. n = ((z_[tex]\alpha[/tex]/2*σ)/E)^2 =5403
d. It is not recommendable to try to obtain the $100 margin of error, because it will cost a lot of time and money to obtain such a large random sample.
