Question

Suppose the 90% confidence interval for the mean SAT scores of applicants at a business college is given by [1,693, 1,850]. This confidence interval uses the sample mean and the sample standard deviation based on 25 observations. Use Table 2.

What are the sample mean and the sample standard deviation used when computing the interval? (Round "t" value to 3 decimal places and “Sample mean” and "Sample standard deviation" to 2 decimal places.)

  

Sample mean
Sample standard deviation

Answer 1

Solution:

We have,

alpha = 1 - 0.90 = 0.10 n = 25   

so    From t-table

Now,

Width = Upper limit - Lower limit

  

Now,

   Symmetric about mean

  

  

Hence,

Sample mean = 1771.5

Sample standard deviation = 458.83