Answer:
The sample size is [tex]n = 426 [/tex]
Step-by-step explanation:
From the question we are told that
The population variance is [tex]\sigma^2 = 1.44[/tex]
The mean is [tex]\= x = 6[/tex]
The margin of error is E = 0.15
Generally the standard deviation is mathematically represented as
[tex]\sigma = \sqrt{\sigma^2 }[/tex]
=> [tex]\sigma = \sqrt{1.44 }[/tex]
=> [tex]\sigma = 1.2[/tex]
From the question we are told the confidence level is 99% , hence the level of significance is
[tex]\alpha = (100 - 99 ) \%[/tex]
=> [tex]\alpha = 0.01[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 2.58[/tex]
Generally the sample size is mathematically represented as
[tex]n = [\frac{Z_{\frac{\alpha }{2} } * \sigma }{E} ] ^2[/tex]
=> [tex]n = [\frac{2.58 * 1.2 }{0.15} ] ^2[/tex]
=> [tex]n = 426 [/tex]
