Answer: 53
Step-by-step explanation:
As per given , we have
Standard deviation : [tex]\sigma= 9000[/tex]
Significance level : [tex]\alpha:1-0.97=0.03[/tex]
Critical value for 97% confidence : [tex]z_{\alpha/2}=2.17[/tex]
[using z-value table]
Margin of error : E=2700
Formula to find the sample size :
[tex]n=(\dfrac{z_{\alpha/2}\cdot\sigma}{E})^2[/tex]
i.e . [tex]n=(\dfrac{2.17\cdot9000}{2700})^2[/tex]
Simplify ,
[tex]n=52.3211111111\approx53[/tex]
Hence, the minimum sample size needed = 53
The minimum sample size needed 53.
We have given that the standard deviation =9000
significant level can be calculated by,
α=1-0.97=0.03
and critical value for 97% is given by,
[tex]Z(\alpha /2)=2.17[/tex]
using Z value table the margin error is E=2700
[tex]n=(\frac{Z_(\alpha /2)\cdot \sigma }{E} )^{2}[/tex]
[tex]n=(\frac{(2.17\cdot 9000 }{2700} )^{2}[/tex]
[tex]n=52.3211111111\\n=53[/tex]
Therefore the minimum sample size needed 53.
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