Question

In making the decision to return to school for an MBA, prospective students desire to know the time it will take to recoup their investment (forgone wages plus tuition and other direct costs). The time it will take to recoup their investment is normally distributed. You are in charge of estimating this time for a brochure advertising an MBA program at UCLA. You randomly sample 20 past UCLA MBA students and find that the sample average is 3.61 years with a standard deviation of 0.63 years. To estimate the mean number of years required to recoup an investment in a UCLA MBA to within 2 months (0.17 years) with 80% confidence, the sample size should be approximately

Answer 1

The value is
`n =23`

Explanation:

From the question we are told that

The sample size is n = 20

The sample mean is
`\= x = 3..61 \ years`

The standard deviation is
`\sigma = 0.63 \ years`

The margin of error is
`E = 0.17 \ years`

From the question we are told the confidence level is 80% , hence the level of significance is

`\alpha = (100 - 80 ) \%`

=>
`\alpha = 0.20`

Generally from the normal distribution table the critical value of is

`Z_{(\alpha )/(2) } =  1.282`

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

`n = [\frac{Z_{(\alpha )/(2) } *  \sigma }{E} ] ^2`

=>
`n = [(1.282 *  0.63)/(0.17) ] ^2`

=>
`n =23`