A random sample of 10 observations was selected from a normal population distribution. The sample mean and sample standard deviations were 20 and 3.2, respectively. A 95% prediction interval for a single observation selected from the same population is
A) 20 $\pm$
6)152
B) 20 $\pm$
4)244
C) 20 $\pm$
7)962
D) 20 $\pm$
7)592
E) None of the above answers are correct.

Question

Quizplus · Accepted Answer

The correct answer is D because the 95% prediction interval for a single observation selected from the same population is 20 $\pm$ 7)592. This is calculated using the formula:PI = x̄ $\pm$ t(n-1, 1-α/2) * (s/√n)where:x̄ is the sample means is the sample standard deviationn is the sample sizeα is the level of significancet(n-1, 1-α/2) is the critical value from the t-distribution with n-1 degrees of freedom and a significance level of α/2

A Random Sample of 10 Observations Was Selected from a Normal