Answer:
The sample size is [tex]n =326 [/tex]
Step-by-step explanation:
From the question we are told that
The rough estimate of the standard deviation is [tex]\sigma = 0.14[/tex]
The interval width is [tex]w = 0.04[/tex]
Generally the margin of error is mathematically represented as
[tex]E = \frac{w}{2}[/tex]
=> [tex]E = \frac{0.04}{2}[/tex]
=> [tex]E = 0.02[/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 * 0.14 }{0.02} ] ^2[/tex]
=> [tex]n =326 [/tex]
