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.

The correct t value for a 95% confidence interval with 80 degrees of freedom (n-1 = 81-1 = 80) is closer to the value provided in option B, 1.998. This is because for large samples, the t-distribution approaches the z-distribution, but with a sample size of 81, the exact value from the t-distribution should be used, which is typically found in t-tables and is slightly different from the z-value of 1.96 used for the normal distribution.