Statistics question: A random sample of 40 statistics students had an average test grade of 81.5

Question

A random sample of 40 statistics students had an average test grade of 81.5 and a standard deviation of 10.2. Construct the confidence interval for the population mean, μ if c = 0.90.

 

The answer is = (78.8, 84.2)  i just need help figuring out how to get this 

Answer 1

I am going to assume 'c' in your equation refers to the confidence level. 

 

The question asks you to find a 90% confidence interval for the true population mean based on a random sample of size (n) 40 with a sample mean test grade of 81.5 and sample standard deviation (sd) of 10.2. 

 

Since the sample size is greater than 30, the central limit theorem can be used to construct confidence interval for the true mean. The formula for obtaining the confidence interval is: 

 

sample mean -/+ z_0.9 * sd/(n)^0.5  ,where z_0.9 is the 90^th percentile for the standard normal distribution. z_0.9 is equal 1.644854. Plugging in the unkowns in the above formula, you get the answer you are looking for. 

 

I hope this helps. 

Kidane