Answer:
The value is [tex]n =1508[/tex]
Step-by-step explanation:
From the question we are told that
The margin of error is [tex]E = 0.03[/tex]
Here we will assume that sample proportion of businesses that plan to buy office furniture in the next 90 days to be [tex]\^ p = 0.5[/tex]
From the question we are told the confidence level is 98% , hence the level of significance is
[tex]\alpha = (100 - 98 ) \%[/tex]
=> [tex]\alpha = 0.02[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 2.33 [/tex]
Generally the sample size is mathematically evaluated as
[tex]n =[ \frac{ Z_{\frac{\alpha }{2} } }{E}] ^2 * [\^ p (1 - \^ p )][/tex]
=> [tex]n =[ \frac{ 2.33}{0.03}] ^2 * [0.5 (1 - 0.5 )][/tex]
=> [tex]n =1508[/tex]
