Assume that all grade-point averages are to be standardized on a scale between 0 and 4. How many grade-point averages must be obtained so that the sample mean is within 0.011 of the populationmean? Assume that a 99% confidence level is desired. If using the range rule of thumb, σ can be estimated as range/4 = 4-0/4 = 1. (a) what is the required sample size? (b) Does the sample size seem practical? Explain why.
Accepted Solution
A:
Answer:a) The required sample size n= 55011,57025 b) The sample size is not practical, because that size is extremely large and would be very costly to collect, normally the size have to be significant but no to large to avoid cost unnecessaryStep-by-step explanation:Range [tex] σ = \frac{4-0}{4} = 1[/tex][tex]E = 0,011 \\c= 99 %\\[/tex]⇒ 0,99Sample size can be determinate using equation:[tex]n=(\frac{Z_{\alpha /2 * σ} }{E})^{2}[/tex] Using confidence level desired 99% [tex]Z_{\alpha /2}[/tex] = 2,58 Table used :Confidence [tex]Z_{\alpha/2 }[/tex] 90 % 1,60 95 % 1,96 99 % 2,58 99,9 % 3,291So replacing: [tex]n=(\frac{2,58 * 1 }{0,011})^{2}[/tex] [tex]n= 234,5454545^{2} \\n=55011,57025[/tex]