Question

A student wanted to construct a 95% confidence interval for the mean age of students in her statistics class. She randomly selected nine students. Their mean age was 19.1 years, with a sample standard deviation of 1.5 years. What is the 95% confidence interval for the population mean?

Answer 1

Answer:

95% confidence interval for the population mean is 20.255 and 17.945

Step-by-step explanation:

given data

mean = 19.1

standard deviation = 1.5

n = 9

to find out

95% confidence interval for the population mean

solution

we know 95% confidence interval formula i.e.

mean +/- t * standard deviation/$\sqrt{n}$   .............1

here t for 9 students 2.31 ( from t table)

so put all value n t standard deviation and mean in equation 1

= mean +/- t * standard deviation/$\sqrt{n}$

= 19.1 +/- 2.31 * 1.5/$\sqrt{9}$

= 19.1 +/- 2.31 * 1.5/$\sqrt{9}$  

= 20.255 and 17.945

95% confidence interval for the population mean is 20.255 and 17.945