Answer:
The minimum sample size is [tex]n = 2295 [/tex]
Step-by-step explanation:
From the question we are told that
The margin of error is [tex]E = 0.09[/tex]
The sample mean is [tex]\= x = 6.6[/tex]
The variance is [tex]\sigma^2 = 4.84[/tex]
Generally the standard deviation is mathematically represented as
[tex]\sigma = \sqrt{\sigma^2}[/tex]
=> [tex]\sigma = \sqrt{4.84 }[/tex]
=> [tex]\sigma = 2.2[/tex]
From the question we are told the confidence level is 95% , hence the level of significance is
[tex]\alpha = (100 - 95 ) \%[/tex]
=> [tex]\alpha = 0.05[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the sample size is mathematically represented as
[tex]n = [\frac{Z_{\frac{\alpha }{2} } * \sigma }{E} ] ^2[/tex]
=> [tex]n = [\frac{1.96 * 2.2 }{0.09} ] ^2[/tex]
=> [tex]n = 2295 [/tex]
