Question

Assume that all​ grade-point averages are to be standardized on a scale between 0 and 6. How many​ grade-point averages must be obtained so that the sample mean is within 0.01 of the population​ mean? Assume that a 98​% confidence level is desired. If using the range rule of​ thumb, sigma can be estimated as $\frac{r}{4} = \frac{6-0}{4} = 1.5$. Does the sample size seem​ practical?

Answer 1

Answer:

The sample size should be 122,150 and the sample size is not practical.

Step-by-step explanation:

Consider the provided information.

The sample mean is within 0.01 of the population​ mean.

E=0.01

σ=1.5

Confidence level is 98​%

1-α=0.98

α=1-0.98=0.02

Formula for sample size is: $n=(\frac{z_{\alpha/2}\sigma}{E})^2$

By using the normal probability table: $z_{\alpha/2}=z_{0.01}\approx2.33$

Substitute the respective values in the above formula.

$n=(\frac{2.33\times 1.5}{0.01})^2\approx122150$

Sample size doesn't seem practical as 122,150 is extremely large number.