A random sample of 81 SAT scores of students applying for merit scholarships showed an average of 1400 with a standard deviation of 300. The t value needed to develop the 95% confidence interval for the population mean SAT score is
A) 1.96.
B) 1.998.
C) 1.645.
D) 1.28.

Question

Quizplus · Accepted Answer

For a 95% confidence interval with a sample size greater than 30 (in this case, 81), the t-distribution should be used. The degrees of freedom (df) are n - 1 = 80. Looking up the t-value for 80 degrees of freedom for a 95% confidence interval in a t-table or using statistical software typically yields a value very close to 1.98 or 2. However, since the exact value for 80 degrees of freedom is not provided, the closest option given is 1.998, which is a reasonable approximation for the t-value in this context.

A Random Sample of 81 SAT Scores of Students Applying