Question

You measure 28 textbooks' weights, and find they have a mean weight of 76 ounces. Assume the population standard deviation is 12.3 ounces. Based on this, construct a 95% confidence interval for the true population mean textbook weight. 

Give your answers as decimals, to two places

Answer 1

SOLUTION :

Sample size is small ( less than 30) = 28 

So, t-statistic will be applicable.

Confidence level = 95% = 0.95

So, 

Alpha = ( 1 - 0.95) = 0.05  (Two tails basis)

Degree of freedom, dF = 28 - 1 = 27

From t-table, 

For alpha 0.05 (two tails) and dF of 27 , value of t = 2.052 

So, 95% confidence interval is : - 2.052 to + 2.052 

Now = t = (X - m) / (SD/sqrt(n)) = (X - 76) / (12.3/sqrt(28)) = (X - 76)/2.3245

=> X = 76  * (+/- t) * 2.3245 

=> X lower = 76 - 2.052 * 2.3245 = 71.23

=> X upper = 76 + 2.052 *2.3245 = 80.77

So, 95% confidence interval is : From 71.23 ounces to 80.77 ounces.

(ANSWER).