Answer:
The value is [tex]n =23[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 20
The sample mean is [tex]\= x = 3..61 \ years[/tex]
The standard deviation is [tex]\sigma = 0.63 \ years[/tex]
The margin of error is [tex]E = 0.17 \ years[/tex]
From the question we are told the confidence level is 80% , hence the level of significance is
[tex]\alpha = (100 - 80 ) \%[/tex]
=> [tex]\alpha = 0.20[/tex]
Generally from the normal distribution table the critical value of is
[tex]Z_{\frac{\alpha }{2} } = 1.282[/tex]
Generally the sample size to estimate the mean number of years required to recoup an investment in a UCLA MBA to within 2 months is mathematically represented as
[tex]n = [\frac{Z_{\frac{\alpha }{2} } * \sigma }{E} ] ^2[/tex]
=> [tex]n = [\frac{1.282 * 0.63}{0.17} ] ^2[/tex]
=> [tex]n =23[/tex]
